sisl.io.tbtrans.tbtavncSileTBtrans

class sisl.io.tbtrans.tbtavncSileTBtrans(filename, mode='r', lvl=0, access=1, *args, **kwargs)

Bases: tbtncSileTBtrans

TBtrans average file object

This Sile implements the writing of the TBtrans output *.TBT.AV.nc sile which contains the k-averaged quantities related to the NEGF code TBtrans.

See tbtncSileTBtrans for details as this object is essentially a copy of it.

Methods

`ADOS`([elec, E, kavg, atoms, orbitals, sum, norm])	Spectral density of states (DOS) (1/eV).
`Adensity_matrix`(elec, E[, kavg, isc, ...])	Spectral function density matrix at energy `E` (1/eV)
`BDOS`([elec, E, kavg, sum, norm])	Bulk density of states (DOS) (1/eV).
`DOS`([E, kavg, atoms, orbitals, sum, norm])	Green function density of states (DOS) (1/eV).
`Eindex`(E)	Return the closest energy index corresponding to the energy `E`
`a2p`(atoms)	Return the pivoting orbital indices (0-based) for the atoms, possibly on an electrode
`a_down`(elec[, bulk])	Down-folding atomic indices for a given electrode
`a_elec`(elec)	Electrode atomic indices for the full geometry (sorted)
`atom_ACOHP`(E[, elec, kavg, isc, orbitals, uc])	Atomic COHP curve of the spectral function
`atom_ACOOP`(E[, elec, kavg, isc, orbitals, uc])	Atomic COOP curve of the spectral function
`atom_COHP`(E[, kavg, isc, orbitals, uc])	Atomic COHP curve of the Green function
`atom_COOP`(E[, kavg, isc, orbitals, uc])	Atomic COOP curve of the Green function
`atom_current`([elec, elec_other, activity, ...])	Atomic current of atoms, a scalar quantity quantifying how much currents flows through an atom
`atom_transmission`(E[, elec, activity, kavg, ...])	Atomic transmission at energy `E` of atoms, a scalar quantity quantifying how much transmission flows through an atom
`base_directory`([relative_to])	Retrieve the base directory of the file, relative to the path relative_to
`bloch`(elec)	Bloch-expansion coefficients for an electrode
`bond_current`([elec, elec_other, kavg, isc, ...])	Bond current between atoms (sum of orbital currents)
`bond_transmission`(E[, elec, kavg, isc, ...])	Bond transmission between atoms at a specific energy
`btd`([elec])	Block-sizes for the BTD method in the device/electrode region
`chemical_potential`(elec)	Return the chemical potential associated with the electrode elec
`close`()
`current`([elec_from, elec_to, kavg])	Current from from to to using the k-weights and energy spacings in the file.
`current_parameter`(elec_from, mu_from, ...[, ...])	Current from from to to using the k-weights and energy spacings in the file.
`density_matrix`(E[, kavg, isc, orbitals, ...])	Density matrix from the Green function at energy `E` (1/eV)
`dir_file`([filename, filename_base])	File of the current Sile
`electron_temperature`(elec)	Electron bath temperature [Kelvin]
`eta`([elec])	The imaginary part used when calculating the self-energies in eV (or for the device
`info`([elec])	Information about the calculated quantities available for extracting in this file
`iter`([group, dimension, variable, levels, root])	Iterator on all groups, variables and dimensions.
`kT`(elec)	Electron bath temperature [eV]
`kindex`(k)	Return the index of the k-point that is closests to the queried k-point (in reduced coordinates)
`mu`(elec)	Return the chemical potential associated with the electrode elec
`n_btd`([elec])	Number of blocks in the BTD partioning
`na_down`(elec)	Number of atoms in the downfolding region (without device downfolded region)
`no_down`(elec)	Number of orbitals in the downfolding region (plus device downfolded region)
`no_e`(elec)	Number of orbitals in the downfolded region of the electrode in the device
`norm`([atoms, orbitals, norm])	Normalization factor depending on the input
`o2p`(orbitals[, elec])	Return the pivoting indices (0-based) for the orbitals, possibly on an electrode
`orbital_ACOHP`(E[, elec, kavg, isc, orbitals])	Orbital resolved COHP analysis of the spectral function
`orbital_ACOOP`(E[, elec, kavg, isc, orbitals])	Orbital COOP analysis of the spectral function
`orbital_COHP`(E[, kavg, isc, orbitals])	Orbital resolved COHP analysis of the Green function
`orbital_COOP`(E[, kavg, isc, orbitals])	Orbital COOP analysis of the Green function
`orbital_current`([elec, elec_other, kavg, ...])	Orbital current originating from elec as a sparse matrix
`orbital_transmission`(E[, elec, kavg, isc, ...])	Transmission at energy `E` between orbitals originating from elec
`pivot`([elec, in_device, sort])	Return the pivoting indices for a specific electrode (in the device region) or the device
`pivot_down`(elec)	Pivoting orbitals for the downfolding region of a given electrode
`read`(args, *kwargs)	Generic read method which should be overloaded in child-classes
`read_data`(args, *kwargs)	Read specific type of data.
`read_geometry`(args, *kwargs)	Returns Geometry object from this file
`read_lattice`()	Returns Lattice object from this file
`reflection`([elec, kavg, from_single])	Reflection into electrode elec
`sparse_atom_to_vector`(Dab)	Reduce an atomic sparse matrix to a vector contribution of each atom
`sparse_orbital_to_atom`(Dij[, uc, sum_dup])	Reduce a sparse matrix in orbital sparse to a sparse matrix in atomic indices
`sparse_orbital_to_scalar`(Dij[, activity])	Atomic scalar contribution of atoms for a sparse orbital matrix
`sparse_orbital_to_vector`(Dij[, uc, sum_dup])	Reduce an orbital sparse matrix to a vector contribution of each atom
`transmission`([elec_from, elec_to, kavg])	Transmission from elec_from to elec_to.
`transmission_bulk`([elec, kavg])	Bulk transmission for the elec electrode
`transmission_eig`([elec_from, elec_to, kavg])	Transmission eigenvalues from elec_from to elec_to.
`vector_current`([elec, elec_other, kavg, ...])	Vector for each atom being the sum of bond currents times the normalized bond vector between the atoms
`vector_transmission`(E[, elec, kavg, isc, ...])	Vector for each atom being the sum of bond transmissions times the normalized bond vector between the atoms
`write`(args, *kwargs)	Generic write method which should be overloaded in child-classes
`write_tbtav`(args, *kwargs)	Wrapper for writing the k-averaged TBT.AV.nc file.
`E`	Sampled energy-points in file
`a_buf`	Atomic indices (0-based) of device atoms
`a_dev`	Atomic indices (0-based) of device atoms (sorted)
`base_file`	File of the current Sile
`cell`	Unit cell in file
`elecs`	List of electrodes
`fano`
`file`	File of the current Sile
`geom`	Same as `geometry`, but deprecated
`geometry`	The associated geometry from this file
`k`	Sampled k-points in file
`kpt`	Sampled k-points in file
`lasto`	Last orbital of corresponding atom
`nE`	Number of energy-points in file
`na`	Returns number of atoms in the cell
`na_b`	Number of atoms in the buffer region
`na_buffer`	Number of atoms in the buffer region
`na_d`	Number of atoms in the device region
`na_dev`	Number of atoms in the device region
`na_u`	Returns number of atoms in the cell
`ne`	Number of energy-points in file
`nk`	Number of k-points in file
`nkpt`	Always return 1, this is to signal other routines
`no`	Returns number of orbitals in the cell
`no_d`	Number of orbitals in the device region
`no_u`	Returns number of orbitals in the cell
`noise_power`
`o_dev`	Orbital indices (0-based) of device orbitals (sorted)
`plot`	Handles all plotting possibilities for a class
`shot_noise`
`wk`	Weights of k-points in file
`wkpt`	Always return [1.], this is to signal other routines
`xa`	Atomic coordinates in file
`xyz`	Atomic coordinates in file

ADOS(elec=0, E=None, kavg=True, atoms=None, orbitals=None, sum=True, norm='none') → ndarray

Spectral density of states (DOS) (1/eV).

Extract the spectral DOS from electrode elec on a selected subset of atoms/orbitals in the device region

\[\mathrm{ADOS}_\mathfrak{el}(E) = \frac{1}{2\pi N} \sum_{i\in\{I\}} [\mathbf{G}(E)\Gamma_\mathfrak{el}\mathbf{G}^\dagger]_{ii}(E)\]

The normalization constant (\(N\)) is defined in the routine norm and depends on the arguments.

Parameters:

elec (str, int, optional) – electrode originating spectral function
E (float or int, optional) – optionally only return the DOS of atoms at a given energy point
kavg (bool, int, optional) – whether the returned DOS is k-averaged, or an explicit (unweighed) k-point is returned
atoms (array_like of int or bool, optional) – only return for a given set of atoms (default to all). NOT allowed with orbitals keyword. If True it will use all atoms in the device. False is equivalent to None.
orbitals (array_like of int or bool, optional) – only return for a given set of orbitals (default to all) NOT allowed with atoms keyword. If True it will use all orbitals in the device. False is equivalent to None.
sum (bool, optional) – whether the returned quantities are summed or returned as is, i.e. resolved per atom/orbital.
norm ({'none', 'atom', 'orbital', 'all'}) – how the normalization of the summed DOS is performed (see norm routine).

Return type:

ndarray

See also

DOS: the total density of states (including bound states)
BDOS: the bulk density of states in an electrode

Adensity_matrix(elec, E, kavg=True, isc=None, orbitals=None, geometry=None) → csr_matrix

Spectral function density matrix at energy E (1/eV)

The density matrix can be used to calculate the LDOS in real-space.

The \(\mathrm{LDOS}(E, \mathbf r)\) may be calculated using the density routine. Basically the LDOS in real-space may be calculated as

\[\boldsymbol\rho_{\mathbf A_{\mathfrak{el}}}(E, \mathbf r) = \frac{1}{2\pi}\sum_{ij}\phi_i(\mathbf r)\phi_j(\mathbf r) \Re[\mathbf A_{\mathfrak{el}, ij}(E)]\]

where \(\phi\) are the orbitals. Note that the broadening used in the TBtrans calculations ensures the broadening of the density, i.e. it should not be necessary to perform energy averages over the density matrices.

Parameters:

elec (str or int) – the electrode of originating electrons
E (float or int) – the energy or the energy index of density matrix. If an integer is passed it is the index, otherwise the index corresponding to Eindex(E) is used.
kavg (bool, int, optional) – whether the returned density matrix is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned density matrix from unit-cell ([None, None, None]) to the given supercell, the default is all density matrix elements for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].
orbitals (array-like or dict, optional) – only retain density matrix elements for a subset of orbitals, all other are set to 0.
geometry (Geometry, optional) – geometry that will be associated with the density matrix. By default the geometry contained in this file will be used. However, then the atomic species are probably incorrect, nor will the orbitals contain the basis-set information required to generate the required density in real-space.

Return type:

csr_matrix

See also

density_matrix: Green function density matrix

Returns:: object containing the Geometry and the density matrix elements
Return type:: DensityMatrix

BDOS(elec=0, E=None, kavg=True, sum=True, norm='none') → ndarray

Bulk density of states (DOS) (1/eV).

Extract the bulk DOS from electrode elec.

\[\mathrm{BDOS}_\mathfrak{el}(E) = -\frac{1}{\pi} \Im\mathbf{G}(E)\]

This returns the density of states for the full (Bloch-expanded) electrode. When norm is ‘none’, the DOS is the full DOS for all electrode atoms (fully expanded), if you want to get the DOS for the minimal (un-expanded) electrode unit-cell, then divide by np.prod(tbt.bloch(elec)). When norm is anything else, it will be normalised to the number of atoms/orbitals in the electrode.

Parameters:

elec (str, int, optional) – electrode where the bulk DOS is returned
E (float or int, optional) – optionally only return the DOS of atoms at a given energy point
kavg (bool, int, optional) – whether the returned DOS is k-averaged, or an explicit (unweighed) k-point is returned
sum (bool, optional) – whether the returned quantities are summed or returned as is, i.e. resolved per atom/orbital.
norm ({'none', 'atom', 'orbital', 'all'}) – whether the returned quantities are summed over all orbitals or normed by number of orbitals in the electrode. Currently one cannot extract DOS per atom/orbital.

Return type:

ndarray

See also

DOS: the total density of states (including bound states)
ADOS: the spectral density of states from an electrode

DOS(E=None, kavg=True, atoms=None, orbitals=None, sum=True, norm='none') → ndarray

Green function density of states (DOS) (1/eV).

Extract the DOS on a selected subset of atoms/orbitals in the device region

\[\mathrm{DOS}(E) = -\frac{1}{\pi N} \sum_{i\in \{I\}} \Im \mathbf{G}_{ii}(E)\]

The normalization constant (\(N\)) is defined in the routine norm and depends on the arguments.

Parameters:

E (float or int, optional) – optionally only return the DOS of atoms at a given energy point
kavg (bool, int, optional) – whether the returned DOS is k-averaged, or an explicit (unweighed) k-point is returned
atoms (array_like of int or bool, optional) – only return for a given set of atoms (default to all). NOT allowed with orbitals keyword. If True it will use all atoms in the device. False is equivalent to None.
orbitals (array_like of int or bool, optional) – only return for a given set of orbitals (default to all) NOT allowed with atoms keyword. If True it will use all orbitals in the device. False is equivalent to None.
sum (bool, optional) – whether the returned quantities are summed or returned as is, i.e. resolved per atom/orbital.
norm ({'none', 'atom', 'orbital', 'all'}) – how the normalization of the summed DOS is performed (see norm routine)

Return type:

ndarray

See also

ADOS: the spectral density of states from an electrode
BDOS: the bulk density of states in an electrode

property E: Sampled energy-points in file

Eindex(E)

Return the closest energy index corresponding to the energy E

Parameters:: E (float or int or str) – if int, return it-self, else return the energy index which is closests to the energy. For a str it will be parsed to a float and treated as such.

__init__(filename, mode='r', lvl=0, access=1, *args, **kwargs): Just to pass away the args and kwargs

a2p(atoms)

Return the pivoting orbital indices (0-based) for the atoms, possibly on an electrode

This is equivalent to:

>>> p = self.o2p(self.geometry.a2o(atom, True))

Will warn if an atom requested is not in the device list of atoms.

Parameters:: atoms (array_like or int) – atomic indices (0-based)

property a_buf: Atomic indices (0-based) of device atoms

property a_dev: Atomic indices (0-based) of device atoms (sorted)

a_down(elec, bulk=False)

Down-folding atomic indices for a given electrode

Parameters:

elec (str or int) – electrode to retrieve indices for
bulk (bool, optional) – whether the returned indices are only in the pristine electrode, or the down-folding region (electrode + downfolding region, not in device)

a_elec(elec)

Electrode atomic indices for the full geometry (sorted)

Parameters:: elec (str or int) – electrode to retrieve indices for

atom_ACOHP(E, elec=0, kavg=True, isc=None, orbitals=None, uc=False) → csr_matrix

Atomic COHP curve of the spectral function

Parameters:

E (float or int) – the energy or the energy index of COHP. If an integer is passed it is the index, otherwise the index corresponding to Eindex(E) is used.
elec (str or int, optional) – the electrode of the spectral function
kavg (bool, int, optional) – whether the returned COHP is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned COHP from unit-cell ([None, None, None]) to the given supercell, the default is all COHP for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].
orbitals (array-like or dict, optional) – only retain COHP matrix elements for a subset of orbitals, all other are set to 0.
uc (bool, optional) – whether the returned COHP are only in the unit-cell. If True this will return a sparse matrix of shape = (self.na, self.na), else, it will return a sparse matrix of shape = (self.na, self.na * self.n_s). One may figure out the connections via sc_index.

Return type:

csr_matrix

See also

orbital_COOP: orbital resolved COOP analysis of the Green function
atom_COOP: atomic COOP analysis of the Green function
orbital_ACOOP: orbital resolved COOP analysis of the spectral function
atom_ACOOP: atomic COOP analysis of the spectral function
orbital_COHP: orbital resolved COHP analysis of the Green function
atom_COHP: atomic COHP analysis of the Green function
orbital_ACOHP: orbital resolved COHP analysis of the spectral function

atom_ACOOP(E, elec=0, kavg=True, isc=None, orbitals=None, uc=False) → csr_matrix

Atomic COOP curve of the spectral function

The atomic COOP are a sum over all orbital COOP:

\[\mathrm{COOP}_{IJ} = \sum_{i\in I}\sum_{j\in J} \mathrm{COOP}_{ij}\]

This is a shorthand for calling orbital_ACOOP and sparse_orbital_to_atom in order.

Parameters:

E (float or int) – the energy or the energy index of COOP. If an integer is passed it is the index, otherwise the index corresponding to Eindex(E) is used.
elec (str or int, optional) – the electrode of the spectral function
kavg (bool, int, optional) – whether the returned COOP is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned COOP from unit-cell ([None, None, None]) to the given supercell, the default is all COOP for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].
orbitals (array-like or dict, optional) – only retain COOP matrix elements for a subset of orbitals, all other are set to 0.
uc (bool, optional) – whether the returned COOP are only in the unit-cell. If True this will return a sparse matrix of shape = (self.na, self.na), else, it will return a sparse matrix of shape = (self.na, self.na * self.n_s). One may figure out the connections via sc_index.

Return type:

csr_matrix

See also

orbital_COOP: orbital resolved COOP analysis of the Green function
atom_COOP: atomic COOP analysis of the Green function
orbital_ACOOP: orbital resolved COOP analysis of the spectral function
orbital_COHP: orbital resolved COHP analysis of the Green function
atom_COHP: atomic COHP analysis of the Green function
orbital_ACOHP: orbital resolved COHP analysis of the spectral function
atom_ACOHP: atomic COHP analysis of the spectral function

atom_COHP(E, kavg=True, isc=None, orbitals=None, uc=False) → csr_matrix

Atomic COHP curve of the Green function

The atomic COHP are a sum over all orbital COHP:

\[\mathrm{COHP}_{IJ} = \sum_{i\in I}\sum_{j\in J} \mathrm{COHP}_{ij}\]

Parameters:

E (float or int) – the energy or the energy index of COHP. If an integer is passed it is the index, otherwise the index corresponding to Eindex(E) is used.
kavg (bool, int, optional) – whether the returned COHP is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned COHP from unit-cell ([None, None, None]) to the given supercell, the default is all COHP for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].
orbitals (array-like or dict, optional) – only retain COHP matrix elements for a subset of orbitals, all other are set to 0.
uc (bool, optional) – whether the returned COHP are only in the unit-cell. If True this will return a sparse matrix of shape = (self.na, self.na), else, it will return a sparse matrix of shape = (self.na, self.na * self.n_s). One may figure out the connections via sc_index.

Return type:

csr_matrix

See also

orbital_COOP: orbital resolved COOP analysis of the Green function
atom_COOP: atomic COOP analysis of the Green function
orbital_ACOOP: orbital resolved COOP analysis of the spectral function
atom_ACOOP: atomic COOP analysis of the spectral function
orbital_COHP: orbital resolved COHP analysis of the Green function
orbital_ACOHP: orbital resolved COHP analysis of the spectral function
atom_ACOHP: atomic COHP analysis of the spectral function

atom_COOP(E, kavg=True, isc=None, orbitals=None, uc=False) → csr_matrix

Atomic COOP curve of the Green function

The atomic COOP are a sum over all orbital COOP:

\[\mathrm{COOP}_{IJ} = \sum_{i\in I}\sum_{j\in J} \mathrm{COOP}_{ij}\]

Parameters:

E (float or int) – the energy or the energy index of COOP. If an integer is passed it is the index, otherwise the index corresponding to Eindex(E) is used.
kavg (bool, int, optional) – whether the returned COOP is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned COOP from unit-cell ([None, None, None]) to the given supercell, the default is all COOP for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].
orbitals (array-like or dict, optional) – only retain COOP matrix elements for a subset of orbitals, all other are set to 0.
uc (bool, optional) – whether the returned COOP are only in the unit-cell. If True this will return a sparse matrix of shape = (self.na, self.na), else, it will return a sparse matrix of shape = (self.na, self.na * self.n_s). One may figure out the connections via sc_index.

Return type:

csr_matrix

See also

orbital_COOP: orbital resolved COOP analysis of the Green function
orbital_ACOOP: orbital resolved COOP analysis of the spectral function
atom_ACOOP: atomic COOP analysis of the spectral function
orbital_COHP: orbital resolved COHP analysis of the Green function
atom_COHP: atomic COHP analysis of the Green function
orbital_ACOHP: orbital resolved COHP analysis of the spectral function
atom_ACOHP: atomic COHP analysis of the spectral function

atom_current(elec=0, elec_other=1, activity=True, kavg=True, isc=None, orbitals=None) → ndarray

Atomic current of atoms, a scalar quantity quantifying how much currents flows through an atom

The atomic current is a single number specifying a figure of the magnitude current flowing through each atom. It is thus not a quantity that can be related to the physical current flowing in/out of atoms but is merely a number that provides an idea of how much current this atom is redistributing.

The atomic current may have two meanings based on these two equations

\[\begin{split}\mathbf j_I^{|a|} &=\frac 12 \sum_{\{J\}} \Big| \sum_{i\in I}\sum_{j\in J} \mathbf J_{ij} \Big| \\ \mathbf j_I^{|o|} &=\frac 12 \sum_{i\in I}\sum_{j\in\{J\}} \big| J_{ij} \big|\end{split}\]

\[\]

If the activity is requested (activity=True) \(\mathbf j_I^{\mathcal A} = \sqrt{\mathbf j_I^{|a|} \mathbf j_I^{|o|} }\) is returned.

If activity=False \(\mathbf j_I^{|a|}\) is returned.

For geometries with all atoms only having 1-orbital, they are equivalent.

Generally the activity current is a more rigorous figure of merit for the current flowing through an atom. More so than than the summed absolute atomic current due to the following reasoning. The activity current is a geometric mean of the absolute bond current and the absolute orbital current. This means that if there is an atom with a large orbital current it will have a larger activity current.

Parameters:

elec (str, int, optional) – the originating electrode
elec_other (str, int, optional) – this electrode determines the other chemical potential. As such the orbital currents does not reflect the current going from elec to elec_other!
activity (bool, optional) – True to return the activity current, see explanation above
kavg (bool, int, optional) – whether the returned orbital current is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned bond currents from the unit-cell ([None, None, None]) to the given supercell, the default is all orbital currents for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].
orbitals (array-like or dict, optional) – only retain orbital currents for a subset of orbitals.

Return type:

ndarray

Examples

>>> Jij = tbt.orbital_current(0, 1, what="all") # orbital current originating from electrode ``0``
>>> Ja = tbt.sparse_orbital_to_scalar(Jij)

Notes

Calculating the current between two electrodes with the same chemical potential will return a matrix filled with 0’s since there is no bias window.

The currents does not reflect the current going from elec_from to elec_other!

See also

orbital_transmission: energy resolved transmission between orbitals
orbital_current: bias window integrated transmissions
bond_transmission: energy resolved transmissions between atoms
bond_current: bias window integrated transmissions (orbital current summed over orbitals)
vector_transmission: an atomic field transmission for each atom (Cartesian representation of bond-transmissions)
vector_current: an atomic field current for each atom (Cartesian representation of bond-currents)
atom_transmission: energy resolved atomic transmission for each atom (scalar representation of bond-transmissions)

atom_transmission(E, elec=0, activity=True, kavg=True, isc=None, orbitals=None) → ndarray

Atomic transmission at energy E of atoms, a scalar quantity quantifying how much transmission flows through an atom

The atomic transmission is a single number specifying a figure of the magnitude transmission flowing through each atom. It is thus not a quantity that can be related to the physical transmission flowing in/out of atoms but is merely a number that provides an idea of how much this atom is redistributing.

The atomic transmission may have two meanings based on these two equations

\[\begin{split}T_I^{|a|} &=\frac 12 \sum_{\{J\}} \Big| \sum_{i\in I}\sum_{j\in J} \mathbf T_{ij} \Big| \\ T_I^{|o|} &=\frac 12 \sum_{i\in I}\sum_{j\in\{J\}} \big| T_{ij} \big|\end{split}\]

\[\]

If the activity is requested (activity=True) \(T_I^{\mathcal A} = \sqrt{T_I^{|a|} T_I^{|o|} }\) is returned. If the activity current is requested (activity=True)

If activity=False \(T_I^{|a|}\) is returned.

For geometries with all atoms only having 1-orbital, they are equivalent.

Generally the activity is a more rigorous figure of merit for the transmission flowing through an atom. More so than than the summed absolute atomic transmission due to the following reasoning. The activity transmission is a geometric mean of the absolute bond transmission and the absolute orbital transmission. This means that if there is an atom with a large orbital transmission it will have a larger activity.

Parameters:

E (float or int) – the energy or the energy index of the transmission. If an integer is passed it is the index, otherwise the index corresponding to Eindex(E) is used. Be careful about passing 0 as that will be interpreted as an index.
elec (str, int, optional) – the originating electrode
activity (bool, optional) – True to return the activity, see explanation above
kavg (bool, int, optional) – whether the returned atomic transmissions are k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned transmissions from the unit-cell ([None, None, None]) to the given supercell, the default is all orbital transmissions are used for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].
orbitals (array-like or dict, optional) – only retain orbital currents for a subset of orbitals.

Return type:

ndarray

Examples

>>> Jij = tbt.orbital_transmission(-1., what"all") # transmission @ E=-1 eV from electrode ``0``
>>> Ja = tbt.sparse_orbital_to_scalar(Jij)

See also

orbital_transmission: energy resolved transmission between orbitals
orbital_current: bias window integrated transmissions
bond_transmission: energy resolved transmissions between atoms
bond_current: bias window integrated transmissions (orbital current summed over orbitals)
vector_transmission: an atomic field transmission for each atom (Cartesian representation of bond-transmissions)
vector_current: an atomic field current for each atom (Cartesian representation of bond-currents)
atom_current: the atomic current for each atom (scalar representation of bond-currents)

base_directory(relative_to='.'): Retrieve the base directory of the file, relative to the path relative_to

property base_file: File of the current Sile

bloch(elec)

Bloch-expansion coefficients for an electrode

Parameters:: elec (str or int) – bloch expansions of electrode

bond_current(elec=0, elec_other=1, kavg=True, isc=None, what: str = 'all', orbitals=None, uc=False) → csr_matrix

Bond current between atoms (sum of orbital currents)

Short hand function for calling orbital_current and sparse_orbital_to_atom.

The bond currents are a sum over all orbital currents:

\[J_{IJ} = \sum_{i\in I}\sum_{j\in J} J_{ij}\]

Parameters:

elec (str, int) – the electrode of originating electrons
elec_other (str, int, optional) – this electrode determines the other chemical potential. As such the orbital currents does not reflect the current going from elec to elec_other!
kavg (bool, int, optional) – whether the returned bond current is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned bond currents from the unit-cell ([None, None, None]) (default) to the given supercell. If [None, None, None] is passed all bond currents are returned.
what ({"all"/"both"/"+-"/"inout", "+"/"out", "-"/"in"}) – If +/out is supplied only the positive currents are used (going out) for -/in, only the negative currents are used (going in), else return both. Please see discussion in orbital_current.
orbitals (array-like or dict, optional) – only retain currents for a subset of orbitals before calculating bond current Passed directly to orbital_current.
uc (bool, optional) – whether the returned currents are only in the unit-cell (supercell currents will be folded to their unit-cell equivalents). If True this will return a sparse matrix of shape = (self.na, self.na), else, it will return a sparse matrix of shape = (self.na, self.na * self.n_s). One may figure out the connections via sc_index.

Return type:

csr_matrix

Examples

>>> Jij = tbt.orbital_current(0, 1, what="out") # orbital current originating from electrode ``0``
>>> Jab1 = tbt.sparse_orbital_to_atom(Jij)
>>> Jab2 = tbt.bond_current(0, 1, what="out")
>>> Jab1 == Jab2
True

Notes

Calculating the current between two electrodes with the same chemical potential will return a matrix filled with 0’s since there is no bias window.

The currents does not reflect the current going from elec_from to elec_other!

See also

orbital_transmission: energy resolved transmission between orbitals
orbital_current: bias window integrated transmissions
bond_transmission: energy resolved transmissions between atoms
vector_transmission: an atomic field transmission for each atom (Cartesian representation of bond-transmissions)
vector_current: an atomic field current for each atom (Cartesian representation of bond-currents)
atom_transmission: energy resolved atomic transmission for each atom (scalar representation of bond-transmissions)
atom_current: the atomic current for each atom (scalar representation of bond-currents)

bond_transmission(E, elec=0, kavg=True, isc=None, what: str = 'all', orbitals=None, uc=False) → csr_matrix

Bond transmission between atoms at a specific energy

Short hand function for calling orbital_transmission and sparse_orbital_to_atom.

The bond transmissions are a sum over all orbital transmissions

\[T_{IJ}(E) = \sum_{i\in I}\sum_{j\in J} T_{ij}(E)\]

Parameters:

E (float or int) – the energy or the energy index of the transmission. If an integer is passed it is the index, otherwise the index corresponding to Eindex(E) is used. Be careful about passing 0 as that will be interpreted as an index.
elec (str, int, optional) – the electrode of originating electrons
kavg (bool, int, optional) – whether the returned bond transmissions is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned transmissions from the unit-cell ([None, None, None]) (default) to the given supercell. If [None, None, None] is passed all transmissions are returned.
what ({"all"/"both"/"+-"/"inout", "+"/"out", "-"/"in"}) – If +/out is supplied only the positive transmissions are used (going out) for -/in, only the negative transmissions are used (going in), else return both. Please see discussion in orbital_transmission.
orbitals (array-like or dict, optional) – only retain transmissions for a subset of orbitals before calculating bond transmissions Passed directly to orbital_transmission.
uc (bool, optional) – whether the returned transmissions are only in the unit-cell (supercell bonds will be folded to their unit-cell equivalents). If True this will return a sparse matrix of shape = (self.na, self.na), else, it will return a sparse matrix of shape = (self.na, self.na * self.n_s). One may figure out the connections via sc_index.

Return type:

csr_matrix

Examples

>>> Jij = tbt.orbital_transmission(-1.0, what="out") # orbital transmission @ E = -1 eV originating from electrode ``0``
>>> Jab1 = tbt.sparse_orbital_to_atom(Jij)[
>>> Jab2 = tbt.bond_transmission(-1.0, what="out")
>>> Jab1 == Jab2
True

See also

orbital_transmission: energy resolved transmission between orbitals
orbital_current: bias window integrated transmissions
bond_current: bias window integrated transmissions (orbital current summed over orbitals)
vector_transmission: an atomic field transmission for each atom (Cartesian representation of bond-transmissions)
vector_current: an atomic field current for each atom (Cartesian representation of bond-currents)
atom_transmission: energy resolved atomic transmission for each atom (scalar representation of bond-transmissions)
atom_current: the atomic current for each atom (scalar representation of bond-currents)

btd(elec=None)

Block-sizes for the BTD method in the device/electrode region

Parameters:: elec (str or int, optional) – the BTD block sizes for the device (if none), otherwise the downfolding BTD block sizes for the electrode

property cell: Unit cell in file

chemical_potential(elec): Return the chemical potential associated with the electrode elec

close()

current(elec_from=0, elec_to=1, kavg=True) → float

Current from from to to using the k-weights and energy spacings in the file.

Calculates the current as:

\[I(\mu_t - \mu_f) = \frac{e}{h}\int\!\mathrm{d}E\, T(E) [n_F(\mu_t, k_B T_t) - n_F(\mu_f, k_B T_f)]\]

The chemical potential and the temperature are taken from this object.

Parameters:

elec_from (str, int, optional) – the originating electrode
elec_to (str, int, optional) – the absorbing electrode (different from elec_from)
kavg (bool, int, optional) – whether the returned current is k-averaged, or an explicit (unweighed) k-point is returned

Return type:

float

See also

current_parameter: to explicitly set the electronic temperature and chemical potentials
chemical_potential: routine that defines the chemical potential of the queried electrodes
kT: routine that defines the electronic temperature of the queried electrodes

current_parameter(elec_from, mu_from, kt_from, elec_to, mu_to, kt_to, kavg=True) → float

Current from from to to using the k-weights and energy spacings in the file.

Calculates the current as:

\[I(\mu_t - \mu_f) = \frac{e}{h}\int\!\mathrm{d}E\, T(E) [n_F(\mu_t, k_B T_t) - n_F(\mu_f, k_B T_f)]\]

The chemical potential and the temperature are passed as arguments to this routine.

Parameters:

elec_from (str, int) – the originating electrode
mu_from (float) – the chemical potential of the electrode (in eV)
kt_from (float) – the electronic temperature of the electrode (in eV)
elec_to (str, int) – the absorbing electrode (different from elec_from)
mu_to (float) – the chemical potential of the electrode (in eV)
kt_to (float) – the electronic temperature of the electrode (in eV)
kavg (bool, int, optional) – whether the returned current is k-averaged, or an explicit (unweighed) k-point is returned

Return type:

float

See also

current: which calculates the current with the chemical potentials and temperatures set in the TBtrans calculation

density_matrix(E, kavg=True, isc=None, orbitals=None, geometry=None) → csr_matrix

Density matrix from the Green function at energy E (1/eV)

The density matrix can be used to calculate the LDOS in real-space.

The \(\mathrm{LDOS}(E, \mathbf r)\) may be calculated using the density routine. Basically the LDOS in real-space may be calculated as

\[\boldsymbol\rho_{\mathbf G}(E, \mathbf r) = -\frac{1}{\pi}\sum_{ij}\phi_i(\mathbf r)\phi_j(\mathbf r) \Im[\mathbf G_{ij}(E)]\]

where \(\phi\) are the orbitals. Note that the broadening used in the TBtrans calculations ensures the broadening of the density, i.e. it should not be necessary to perform energy averages over the density matrices.

Parameters:

E (float or int) – the energy or the energy index of density matrix. If an integer is passed it is the index, otherwise the index corresponding to Eindex(E) is used.
kavg (bool, int, optional) – whether the returned density matrix is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned density matrix from unit-cell ([None, None, None]) to the given supercell, the default is all density matrix elements for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].
orbitals (array-like or dict, optional) – only retain density matrix elements for a subset of orbitals, all other are set to 0.
geometry (Geometry, optional) – geometry that will be associated with the density matrix. By default the geometry contained in this file will be used. However, then the atomic species are probably incorrect, nor will the orbitals contain the basis-set information required to generate the required density in real-space.

Return type:

csr_matrix

See also

Adensity_matrix: spectral function density matrix

Returns:: object containing the Geometry and the density matrix elements
Return type:: DensityMatrix

dir_file(filename=None, filename_base=''): File of the current Sile

property elecs: List of electrodes

electron_temperature(elec)

Electron bath temperature [Kelvin]

Parameters:: elec (str or int) – electrode to extract the temperature from

See also

kT: bath temperature in [eV]

eta(elec=None)

The imaginary part used when calculating the self-energies in eV (or for the device

Parameters:: elec (str, int, optional) – electrode to extract the eta value from. If not specified (or None) the device region eta will be returned.

fano = None

property file: File of the current Sile

property geom: Same as geometry, but deprecated

property geometry: The associated geometry from this file

info(elec=None)

Information about the calculated quantities available for extracting in this file

Parameters:: elec (str or int) – the electrode to request information from

iter(group=True, dimension=True, variable=True, levels=-1, root=None)

Iterator on all groups, variables and dimensions.

This iterator iterates through all groups, variables and dimensions in the Dataset

The generator sequence will _always_ be:

Group

Dimensions in group

Variables in group

As the dimensions are generated before the variables it is possible to copy groups, dimensions, and then variables such that one always ensures correct dependencies in the generation of a new SileCDF.

Parameters:

group (bool (True)) – whether the iterator yields Group instances
dimension (bool (True)) – whether the iterator yields Dimension instances
variable (bool (True)) – whether the iterator yields Variable instances
levels (int (-1)) – number of levels to traverse, with respect to root variable, i.e. number of sub-groups this iterator will return.
root (str (None)) – the base root to start iterating from.

Examples

Script for looping and checking each instance.

>>> for gv in self.iter():
...     if self.isGroup(gv):
...         # is group
...     elif self.isDimension(gv):
...         # is dimension
...     elif self.isVariable(gv):
...         # is variable

property k: Sampled k-points in file

kT(elec)

Electron bath temperature [eV]

Parameters:: elec (str or int) – electrode to extract the temperature from

See also

electron_temperature: bath temperature in [K]

kindex(k)

Return the index of the k-point that is closests to the queried k-point (in reduced coordinates)

Parameters:: k (array_like of float or int) – the queried k-point in reduced coordinates \(]-0.5;0.5]\). If int return it-self.

property kpt: Sampled k-points in file

property lasto: Last orbital of corresponding atom

mu(elec): Return the chemical potential associated with the electrode elec

property nE: Number of energy-points in file

n_btd(elec=None)

Number of blocks in the BTD partioning

Parameters:: elec (str or int, optional) – if None the number of blocks in the device region BTD matrix. Else the number of BTD blocks in the electrode down-folding.

property na: Returns number of atoms in the cell

property na_b: Number of atoms in the buffer region

property na_buffer: Number of atoms in the buffer region

property na_d: Number of atoms in the device region

property na_dev: Number of atoms in the device region

na_down(elec)

Number of atoms in the downfolding region (without device downfolded region)

Parameters:: elec (str or int) – Number of downfolding atoms for electrode elec

property na_u: Returns number of atoms in the cell

property ne: Number of energy-points in file

property nk: Number of k-points in file

property nkpt: Always return 1, this is to signal other routines

property no: Returns number of orbitals in the cell

property no_d: Number of orbitals in the device region

no_down(elec)

Number of orbitals in the downfolding region (plus device downfolded region)

Parameters:: elec (str or int) – Number of downfolding orbitals for electrode elec

no_e(elec)

Number of orbitals in the downfolded region of the electrode in the device

Parameters:: elec (str or int) – Specify the electrode to query number of downfolded orbitals

property no_u: Returns number of orbitals in the cell

noise_power = None

norm(atoms=None, orbitals=None, norm='none') → int

Normalization factor depending on the input

The normalization can be performed in one of the below methods. In the following \(N\) refers to the normalization constant that is to be used (i.e. the divisor):

'none': \(N=1\)
'all': \(N\) equals the number of orbitals in the total device region.
'atom': \(N\) equals the total number of orbitals in the selected atoms. If orbitals is an argument a conversion of orbitals to the equivalent unique atoms is performed, and subsequently the total number of orbitals on the atoms is used. This makes it possible to compare the fraction of orbital DOS easier.
'orbital': \(N\) is the sum of selected orbitals, if atoms is specified, this is equivalent to the ‘atom’ option.

Parameters:

atoms (array_like of int or bool, optional) – only return for a given set of atoms (default to all). NOT allowed with orbitals keyword
orbitals (array_like of int or bool, optional) – only return for a given set of orbitals (default to all) NOT allowed with atoms keyword
norm ({'none', 'atom', 'orbital', 'all'}) – how the normalization of the summed DOS is performed (see norm routine)

Return type:

int

o2p(orbitals, elec=None)

Return the pivoting indices (0-based) for the orbitals, possibly on an electrode

Will warn if an orbital requested is not in the device list of orbitals.

Parameters:

orbitals (array_like or int) – orbital indices (0-based)
elec (str or int or None, optional) – electrode to return pivoting indices of (if None it is the device pivoting indices).

property o_dev

Orbital indices (0-based) of device orbitals (sorted)

See also

pivot: retrieve the device orbitals, non-sorted

orbital_ACOHP(E, elec=0, kavg=True, isc=None, orbitals=None) → csr_matrix

Orbital resolved COHP analysis of the spectral function

This will return a sparse matrix, see scipy.sparse.csr_matrix for details. Each matrix element of the sparse matrix corresponds to the COHP of the underlying geometry.

The COHP analysis can be written as:

\[\mathrm{COHP}^{\mathbf A}_{ij} = \frac{1}{2\pi} \Re\big[\mathbf A_{ij} \mathbf H_{ij} \big]\]

Parameters:

E (float or int) – the energy or the energy index of COHP. If an integer is passed it is the index, otherwise the index corresponding to Eindex(E) is used.
elec (str or int, optional) – the electrode of the spectral function
kavg (bool, int, optional) – whether the returned COHP is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned COHP from unit-cell ([None, None, None]) to the given supercell, the default is all COHP for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].
orbitals (array-like or dict, optional) – only retain COHP matrix elements for a subset of orbitals, all other are set to 0.

Return type:

csr_matrix

See also

orbital_COOP: orbital resolved COOP analysis of the Green function
atom_COOP: atomic COOP analysis of the Green function
orbital_ACOOP: orbital resolved COOP analysis of the spectral function
atom_ACOOP: atomic COOP analysis of the spectral function
orbital_COHP: orbital resolved COHP analysis of the Green function
atom_COHP: atomic COHP analysis of the Green function
atom_ACOHP: atomic COHP analysis of the spectral function

orbital_ACOOP(E, elec=0, kavg=True, isc=None, orbitals=None) → csr_matrix

Orbital COOP analysis of the spectral function

This will return a sparse matrix, see csr_matrix for details. Each matrix element of the sparse matrix corresponds to the COOP of the underlying geometry.

The COOP analysis can be written as:

\[\mathrm{COOP}^{\mathbf A}_{ij} = \frac{1}{2\pi} \Re\big[\mathbf A_{ij} \mathbf S_{ji} \big]\]

The sum of the COOP DOS is equal to the DOS:

\[\mathrm{ADOS}_{i} = \sum_j \mathrm{COOP}^{\mathbf A}_{ij}\]

One can calculate the (diagonal) balanced COOP analysis, see JPCM 15 (2003), 7751-7761 for details. The DBCOOP is given by:

\[\begin{split}D &= \sum_i \mathrm{COOP}^{\mathbf A}_{ii} \\ \mathrm{DBCOOP}^{\mathbf A}_{ij} &= \mathrm{COOP}^{\mathbf A}_{ij} / D\end{split}\]

The BCOOP can be looked up in the reference above.

Parameters:

E (float or int) – the energy or the energy index of COOP. If an integer is passed it is the index, otherwise the index corresponding to Eindex(E) is used.
elec (str or int, optional) – the electrode of the spectral function
kavg (bool, int, optional) – whether the returned COOP is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned COOP from unit-cell ([None, None, None]) to the given supercell, the default is all COOP for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].
orbitals (array-like or dict, optional) – only retain COOP matrix elements for a subset of orbitals, all other are set to 0.

Return type:

csr_matrix

Examples

>>> ACOOP = tbt.orbital_ACOOP(-1.0) # COOP @ E = -1 eV from ``0`` spectral function
>>> ACOOP[10, 11] # COOP value between the 11th and 12th orbital
>>> ACOOP.sum(1).A[tbt.o_dev, 0] == tbt.ADOS(0, sum=False)[tbt.Eindex(-1.0)]
>>> D = ACOOP.diagonal().sum()
>>> ADBCOOP = ACOOP / D

See also

orbital_COOP: orbital resolved COOP analysis of the Green function
atom_COOP: atomic COOP analysis of the Green function
atom_ACOOP: atomic COOP analysis of the spectral function
orbital_COHP: orbital resolved COHP analysis of the Green function
atom_COHP: atomic COHP analysis of the Green function
orbital_ACOHP: orbital resolved COHP analysis of the spectral function
atom_ACOHP: atomic COHP analysis of the spectral function

orbital_COHP(E, kavg=True, isc=None, orbitals=None) → csr_matrix

Orbital resolved COHP analysis of the Green function

This will return a sparse matrix, see scipy.sparse.csr_matrix for details. Each matrix element of the sparse matrix corresponds to the COHP of the underlying geometry.

The COHP analysis can be written as:

\[\mathrm{COHP}^{\mathbf G}_{ij} = \frac{-1}{2\pi} \Im\big[(\mathbf G - \mathbf G^\dagger)_{ij} \mathbf H_{ji} \big]\]

Parameters:

E (float or int) – the energy or the energy index of COHP. If an integer is passed it is the index, otherwise the index corresponding to Eindex(E) is used.
kavg (bool, int, optional) – whether the returned COHP is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned COHP from unit-cell ([None, None, None]) to the given supercell, the default is all COHP for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].
orbitals (array-like or dict, optional) – only retain COHP matrix elements for a subset of orbitals, all other are set to 0.

Return type:

csr_matrix

Examples

>>> COHP = tbt.orbital_COHP(-1.0) # COHP @ E = -1 eV
>>> COHP[10, 11] # COHP value between the 11th and 12th orbital

See also

orbital_COOP: orbital resolved COOP analysis of the Green function
atom_COOP: atomic COOP analysis of the Green function
orbital_ACOOP: orbital resolved COOP analysis of the spectral function
atom_ACOOP: atomic COOP analysis of the spectral function
atom_COHP: atomic COHP analysis of the Green function
orbital_ACOHP: orbital resolved COHP analysis of the spectral function
atom_ACOHP: atomic COHP analysis of the spectral function

orbital_COOP(E, kavg=True, isc=None, orbitals=None) → csr_matrix

Orbital COOP analysis of the Green function

This will return a sparse matrix, see scipy.sparse.csr_matrix for details. Each matrix element of the sparse matrix corresponds to the COOP of the underlying geometry.

The COOP analysis can be written as:

\[\mathrm{COOP}^{\mathbf G}_{ij} = \frac{-1}{2\pi} \Im\big[(\mathbf G - \mathbf G^\dagger)_{ij} \mathbf S_{ji} \big]\]

The sum of the COOP DOS is equal to the DOS:

\[\mathrm{DOS}_{i} = \sum_j \mathrm{COOP}^{\mathbf G}_{ij}\]

One can calculate the (diagonal) balanced COOP analysis, see JPCM 15 (2003), 7751-7761 for details. The DBCOOP is given by:

\[\begin{split}D &= \sum_i \mathrm{COOP}^{\mathbf G}_{ii} \\ \mathrm{DBCOOP}^{\mathbf G}_{ij} &= \mathrm{COOP}^{\mathbf G}_{ij} / D\end{split}\]

The BCOOP can be looked up in the reference above.

Parameters:

E (float or int) – the energy or the energy index of COOP. If an integer is passed it is the index, otherwise the index corresponding to Eindex(E) is used.
kavg (bool, int, optional) – whether the returned COOP is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned COOP from unit-cell ([None, None, None]) to the given supercell, the default is all COOP for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].
orbitals (array-like or dict, optional) – only retain COOP matrix elements for a subset of orbitals, all other are set to 0.

Return type:

csr_matrix

Examples

>>> COOP = tbt.orbital_COOP(-1.0) # COOP @ E = -1 eV
>>> COOP[10, 11] # COOP value between the 11th and 12th orbital
>>> COOP.sum(1).A[tbt.o_dev, 0] == tbt.DOS(sum=False)[tbt.Eindex(-1.0)]
>>> D = COOP.diagonal().sum()
>>> DBCOOP = COOP / D

See also

atom_COOP: atomic COOP analysis of the Green function
orbital_ACOOP: orbital resolved COOP analysis of the spectral function
atom_ACOOP: atomic COOP analysis of the spectral function
orbital_COHP: orbital resolved COHP analysis of the Green function
atom_COHP: atomic COHP analysis of the Green function
orbital_ACOHP: orbital resolved COHP analysis of the spectral function
atom_ACOHP: atomic COHP analysis of the spectral function

orbital_current(elec=0, elec_other=1, kavg=True, isc=None, what: str = 'all', orbitals=None) → csr_matrix

Orbital current originating from elec as a sparse matrix

This is the bias window integrated quantity of orbital_transmission. As such it represents how the current is flowing at an applied bias from a given electrode.

\[J_{ij} = \frac eh\int_{\mu_1}^{\mu_2} \!\mathrm dE\, T_{ij} [n_F(\mu_2, k_B T_2) - n_F(\mu_1, k_B T_1)]\]

with \(T_{\langle\rangle}\) being the electronic temperature of the respective reservoir.

Parameters:

elec (str, int, optional) – the originating electrode
elec_other (str, int, optional) – this electrode determines the other chemical potential. As such the orbital currents does not reflect the current going from elec to elec_other!
kavg (bool, int, optional) – whether the returned orbital current is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned bond currents from the unit-cell ([None, None, None]) to the given supercell, the default is all orbital currents for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].
what ({"all"/"both"/"+-"/"inout", "+"/"out", "-"/"in"}) – which orbital currents to return, all, positive (outgoing) or negative (incoming). Default to "all" because it can then be used in the subsequent default arguments for sparse_orbital_to_atom and sparse_orbital_to_scalar.
orbitals (array-like or dict, optional) – only retain orbital currents for a subset of orbitals.

Return type:

csr_matrix

Notes

Calculating the current between two electrodes with the same chemical potential will return a matrix filled with 0’s since there is no bias window.

The currents does not reflect the current going from elec_from to elec_other!

See also

orbital_transmission: energy resolved transmission between orbitals
bond_transmission: energy resolved transmissions between atoms
bond_current: bias window integrated transmissions (orbital current summed over orbitals)
vector_transmission: an atomic field transmission for each atom (Cartesian representation of bond-transmissions)
vector_current: an atomic field current for each atom (Cartesian representation of bond-currents)
atom_transmission: energy resolved atomic transmission for each atom (scalar representation of bond-transmissions)
atom_current: the atomic current for each atom (scalar representation of bond-currents)

orbital_transmission(E, elec=0, kavg=True, isc=None, what: str = 'all', orbitals=None) → csr_matrix

Transmission at energy E between orbitals originating from elec

Each matrix element of the sparse matrix corresponds to the orbital indices of the underlying geometry (including buffer and electrode atoms).

When requesting orbital-transmissions it is vital to consider how the data needs to be analysed before extracting the data. For instance, if only local transmission pathways are interesting one should use what="+" to retain the positive orbital transmissions. While if one is interested in the transmission between subset of orbitals, what="all" is the correct method to account for loop transmissions.

The orbital transmissions are calculated as described in the TBtrans manual:

\[T_{ij}(E) = i [ (\mathbf H_{ji} - E\mathbf S_{ji}) \mathbf A_{ij}(E) - (\mathbf H_{ij} - E\mathbf S_{ij}) \mathbf A_{ji}(E)],\]

It is easy to show that the above matrix obeys \(T_{ij}=-T_{ji}\).

For inexperienced users it is adviced to try out all three values of what to ensure the correct physics is obtained.

This becomes even more important when the orbital transmissions are calculated with magnetic fields. With \(\mathbf B\) fields local transmission loops may form and the pathways does not necessarily flow along the transport direction.

For correct interpretation of the orbital transmissions it is vital that one integrates the full Brillouin zone without any symmetry operations, see Section 5.4 in [7].

Parameters:

E (float or int) – the energy or the energy index of the orbital transmission. If an integer is passed it is the index, otherwise the index corresponding to Eindex(E) is used. Be careful about passing 0 as that will be interpreted as an index.
elec (str, int, optional) – the electrode of originating electrons
kavg (bool, int, optional) – whether the returned orbital transmission is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned transmissions from the unit-cell ([None, None, None]) to the given supercell, the default is all transmissions for the supercell. To only get unit cell transmissions, pass [0, 0, 0].
what ({"all"/"both"/"+-"/"inout", "+"/"out", "-"/"in"}) – which transmissions to return, all, positive (outgoing) or negative (incoming).
orbitals (array-like or dict, optional) – only retain transmissions for a subset of orbitals (including their supercell equivalents)

Returns:

A scipy.sparse.csr_matrix containing the supercell transmission pathways, or
orbital transmissions.

Return type:

csr_matrix

Examples

>>> Jij = tbt.orbital_transmission(-1.0) # orbital current @ E = -1 eV originating from electrode ``0``
>>> Jij[10, 11] # orbital transmission from the 11th to the 12th orbital

>>> Jij = tbt.orbital_transmission(-1.0,
...     orbitals={tbt.geometry.atoms[0]: [0, 1]})

only retain transmissions from 1st and 2nd orbitals on first atom type (all atoms of that type in the entire structure.

See also

orbital_current: bias window integrated transmissions
bond_transmission: energy resolved transmissions between atoms
bond_current: bias window integrated transmissions (orbital current summed over orbitals)
vector_transmission: an atomic field transmission for each atom (Cartesian representation of bond-transmissions)
vector_current: an atomic field current for each atom (Cartesian representation of bond-currents)
atom_transmission: energy resolved atomic transmission for each atom (scalar representation of bond-transmissions)
atom_current: the atomic current for each atom (scalar representation of bond-currents)

pivot(elec=None, in_device=False, sort=False)

Return the pivoting indices for a specific electrode (in the device region) or the device

Parameters:

elec (str or int) – the corresponding electrode to return the pivoting indices from
in_device (bool, optional) – If True the pivoting table will be translated to the device region orbitals. If sort is also true, this would correspond to the orbitals directly translated to the geometry self.geometry.sub(self.a_dev).
sort (bool, optional) – Whether the returned indices are sorted. Mostly useful if you want to handle the device in a non-pivoted order.

Examples

>>> se = tbtncSileTBtrans(...)
>>> se.pivot()
[3, 4, 6, 5, 2]
>>> se.pivot(sort=True)
[2, 3, 4, 5, 6]
>>> se.pivot(0)
[2, 3]
>>> se.pivot(0, in_device=True)
[4, 0]
>>> se.pivot(0, in_device=True, sort=True)
[0, 1]
>>> se.pivot(0, sort=True)
[2, 3]

See also

pivot_down: for the pivot table for electrodes down-folding regions

pivot_down(elec)

Pivoting orbitals for the downfolding region of a given electrode

Parameters:: elec (str or int) – the corresponding electrode to get the pivoting indices for

plot: Handles all plotting possibilities for a class

read(*args, **kwargs)

Generic read method which should be overloaded in child-classes

Parameters:: kwargs – keyword arguments will try and search for the attribute read_<> and call it with the remaining **kwargs as arguments.

read_data(*args, **kwargs)

Read specific type of data.

This is a generic routine for reading different parts of the data-file.

Parameters:

geometry (bool, optional) – return the geometry
vector_transmission (bool, optional) – return the bond transmissions as vectors
vector_current (bool, optional) – return the bond currents as vectors
atom_transmission (bool, optional) – return the atomic transmission flowing through an atom (the activity current)
atom_current (bool, optional) – return the atomic current flowing through an atom (the activity current)

read_geometry(*args, **kwargs): Returns Geometry object from this file

read_lattice(): Returns Lattice object from this file

reflection(elec=0, kavg=True, from_single=False) → ndarray

Reflection into electrode elec

The reflection into electrode elec is calculated as:

\[R(E) = T_{\mathrm{bulk}}(E) - \sum_{\mathrm{to}} T_{\mathrm{elec}\to\mathrm{to}}(E)\]

Another way of calculating the reflection is via:

\[R(E) = T_{\mathrm{bulk}}(E) - \big\{i \mathrm{Tr}[(\mathbf G-\mathbf G^\dagger)\boldsymbol\Gamma_{\mathrm{elec}}] - \mathrm{Tr}[\mathbf G\boldsymbol\Gamma_{\mathrm{elec}}\mathbf G^\dagger\boldsymbol\Gamma_{\mathrm{elec}}]\big\}\]

Both are identical, however, numerically they may be different. Particularly when the bulk transmission is very large compared to the transmission to the other electrodes one should prefer the first equation.

Parameters:

elec (str, int, optional) – the backscattered electrode
kavg (bool, int, optional) – whether the returned reflection is k-averaged, or an explicit (unweighed) k-point is returned
from_single (bool, optional) – whether the reflection is calculated using the Green function and a single scattering matrix Eq. (2) above (true), otherwise Eq. (1) will be used (false).

Return type:

ndarray

See also

transmission: the total transmission
transmission_eig: the transmission decomposed in eigenchannels
transmission_bulk: the total transmission in a periodic lead

shot_noise = None

sparse_atom_to_vector(Dab) → ndarray

Reduce an atomic sparse matrix to a vector contribution of each atom

Notes

This routine may be moved to a sisl.utility at some point since it would be a generic routine usable for other parts of sisl.

Parameters:: Dab (csr_matrix) – the input sparse matrix in atomic indices
Return type:: ndarray

sparse_orbital_to_atom(Dij, uc=False, sum_dup=True) → csr_matrix

Reduce a sparse matrix in orbital sparse to a sparse matrix in atomic indices

This algorithm may keep the same non-zero entries, but will return a new csr_matrix with duplicate indices.

Notes

This routine may be moved to a sisl.utility at some point since it would be a generic routine usable for other parts of sisl.

Parameters:

Dij (csr_matrix) – the input sparse matrix in orbital format
uc (bool, optional) – whether the returned data are only in the unit-cell. If True this will return a sparse matrix of shape = (self.na, self.na), else, it will return a sparse matrix of shape = (self.na, self.na * self.n_s). One may figure out the connections via sc_index.
sum_dup (bool, optional) – duplicates will be summed if this is true, in this case, no duplicates are present in the returned sparse matrix. If false, duplicates may exist for multi-orbital systems.

Return type:

csr_matrix

sparse_orbital_to_scalar(Dij, activity=True) → ndarray

Atomic scalar contribution of atoms for a sparse orbital matrix

The atomic contribution is a single number specifying a figure of the magnitude of sparse matrix elements for each atom. It is thus not a quantity that can be related to any physical quantity that the sparse matrix may represent but is merely a number that provides an idea of how much this atom is governing the data in the matrix.

The atomic contribution may have two meanings based on these two equations

\[\begin{split}\mathbf a_I^{|a|} &=\frac 12 \sum_{\{J\}} \Big| \sum_{i\in I}\sum_{j\in J} \mathbf A_{ij} \Big| \\ \mathbf a_I^{|o|} &=\frac 12 \sum_{i\in I}\sum_{j\in\{J\}} \big| A_{ij} \big|\end{split}\]

If the activity is requested (activity=True) \(\mathbf a_I^{\mathcal A} = \sqrt{\mathbf a_I^{|a|} \mathbf a_I^{|o|} }\) is returned.

If activity=False \(\mathbf a_I^{|a|}\) is returned.

For geometries with all atoms only having 1-orbital, they are equivalent.

Parameters:

Dij (csr_matrix) – the orbital sparse matrix.
activity (bool, optional) – True to return the atomic activity, see explanation above

Return type:

ndarray

Notes

This routine may be moved to a sisl.utility at some point since it would be a generic routine usable for other parts of sisl.

Examples

>>> Jij = tbt.orbital_current(0, -1.03, what="both") # orbital current @ E = -1 eV originating from electrode ``0``
>>> Ja = tbt.sparse_orbital_to_scalar(Jij)

sparse_orbital_to_vector(Dij, uc=False, sum_dup=True) → ndarray

Reduce an orbital sparse matrix to a vector contribution of each atom

Equivalent to calling sparse_orbital_to_atom and sparse_atom_to_vector.

Notes

This routine may be moved to a sisl.utility at some point since it would be a generic routine usable for other parts of sisl.

Parameters:

Dij (csr_matrix) – the input sparse matrix
uc (bool, optional) – whether the returned data are only in the unit-cell. If True this will return a sparse matrix of shape = (self.na, self.na), else, it will return a sparse matrix of shape = (self.na, self.na * self.n_s). One may figure out the connections via sc_index.
sum_dup (bool, optional) – duplicates will be summed if this is true, in this case, no duplicates are present in the returned sparse matrix. If false, duplicates may exist for multi-orbital systems.

Return type:

ndarray

transmission(elec_from=0, elec_to=1, kavg=True) → ndarray

Transmission from elec_from to elec_to.

The transmission between two electrodes may be retrieved from the Sile.

The transmission is calculated as:

\[T(E) = \mathrm{Tr}[\mathbf{G}\boldsymbol\Gamma_{\mathrm{from}}\mathbf{G}^\dagger\boldsymbol\Gamma_{\mathrm{to}}]\]

where all quantities are energy dependent.

Parameters:

elec_from (str, int, optional) – the originating electrode
elec_to (str, int, optional) – the absorbing electrode (different from elec_from)
kavg (bool, int, optional) – whether the returned transmission is k-averaged, or an explicit (unweighed) k-point is returned

Return type:

ndarray

See also

transmission_eig: the transmission decomposed in eigenchannels
transmission_bulk: the total transmission in a periodic lead
reflection: total reflection back into the electrode

transmission_bulk(elec=0, kavg=True) → ndarray

Bulk transmission for the elec electrode

The bulk transmission is equivalent to creating a 2 terminal device with electrode elec tiled 3 times.

Parameters:

elec (str, int, optional) – the bulk electrode
kavg (bool, int, optional) – whether the returned transmission are k-averaged, or an explicit (unweighed) k-point is returned

Return type:

ndarray

See also

transmission: the total transmission
transmission_eig: the transmission decomposed in eigenchannels
reflection: total reflection back into the electrode

transmission_eig(elec_from=0, elec_to=1, kavg=True) → ndarray

Transmission eigenvalues from elec_from to elec_to.

Parameters:

elec_from (str, int, optional) – the originating electrode
elec_to (str, int, optional) – the absorbing electrode (different from elec_from)
kavg (bool, int, optional) – whether the returned transmission eigenvalues are k-averaged, or an explicit (unweighed) k-point is returned

Return type:

ndarray

See also

transmission: the total transmission
transmission_bulk: the total transmission in a periodic lead

vector_current(elec=0, elec_other=1, kavg=True, isc=None, what: str = 'all', orbitals=None) → ndarray

Vector for each atom being the sum of bond currents times the normalized bond vector between the atoms

The vector current is defined as:

\[\mathbf J_I = \sum_J \frac{\mathbf r^{(J)} - \mathbf r^{(I)}}{|\mathbf r^{(J)} - \mathbf r^{(I)}|} \cdot J_{IJ}\]

Where \(J_{IJ}\) is the bond current between atom \(I\) and \(J\) and \(\mathbf r^{(\langle\rangle)}\) are the atomic coordinates.

Parameters:

elec (str or int) – the electrode of originating electrons
elec_other (str, int, optional) – this electrode determines the other chemical potential. As such the vector currents does not reflect the current going from elec to elec_other!
kavg (bool, int, optional) – whether the returned vector current is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned currents from the unit-cell ([None, None, None]) to the given supercell, the default is all currents for the supercell. To only get unit cell orbital currents, pass [0, 0, 0].
what ({"all"/"both"/"+-"/"inout", "+"/"out", "-"/"in"}) – The outgoing currents may be retrieved by "out". The incoming currents may be retrieved by "in", while the average incoming and outgoing direction can be obtained with "both". In the last case the vector currents are divided by 2 to ensure the length of the vector is compatible with the other options given a pristine system.
orbitals (array-like or dict, optional) – only retain currents for a subset of orbitals before calculating currents Passed directly to orbital_current.

Return type:

ndarray

Notes

Calculating the current between two electrodes with the same chemical potential will return a matrix filled with 0’s since there is no bias window.

The currents does not reflect the current going from elec_from to elec_other!

Returns:: array of vectors per atom in the Geometry (only non-zero for device atoms)
Return type:: ndarray
Parameters:: what (str)

See also

orbital_transmission: energy resolved transmission between orbitals
orbital_current: bias window integrated transmissions
bond_transmission: energy resolved transmissions between atoms
bond_current: bias window integrated transmissions (orbital current summed over orbitals)
vector_transmission: an atomic field transmission for each atom (Cartesian representation of bond-transmissions)
atom_transmission: energy resolved atomic transmission for each atom (scalar representation of bond-transmissions)
atom_current: the atomic current for each atom (scalar representation of bond-currents)

vector_transmission(E, elec=0, kavg=True, isc=None, what='all', orbitals=None) → ndarray

Vector for each atom being the sum of bond transmissions times the normalized bond vector between the atoms

The vector transmission is defined as:

\[\mathbf T_I = \sum_J \frac{\mathbf r^{(J)} - \mathbf r^{(I)}}{|\mathbf r^{(J)} - \mathbf r^{(I)}|} \cdot T_{IJ}\]

Where \(T_{IJ}\) is the bond transmission between atom \(I\) and \(J\) and \(\mathbf r^{(\langle\rangle)}\) are the atomic coordinates.

Parameters:

E (float or int) – the energy or the energy index of the transmission. If an integer is passed it is the index, otherwise the index corresponding to Eindex(E) is used. Be careful about passing 0 as that will be interpreted as an index.
elec (str or int, optional) – the electrode of originating electrons
kavg (bool, int, optional) – whether the returned vector transmission is k-averaged, or an explicit (unweighed) k-point is returned
isc (array_like, optional) – the returned vectors from the unit-cell ([None, None, None]) to the given supercell, the default is all vectors for the supercell. To only get unit cell vectors, pass [0, 0, 0].
what ({"all"/"both"/"+-"/"inout", "+"/"out", "-"/"in"}) – The outgoing vectors may be retrieved by "out". The incoming vectors may be retrieved by "in", while the average incoming and outgoing direction can be obtained with "both". In the last case the vector transmissions are divided by 2 to ensure the length of the vector is compatible with the other options; given a pristine system.
orbitals (array-like or dict, optional) – only retain transmissions for a subset of orbitals before calculating bond transmissions Passed directly to orbital_transmission.

Returns:

array of vectors per atom in the Geometry (only non-zero for device atoms)

Return type:

ndarray

See also

orbital_transmission: energy resolved transmission between orbitals
orbital_current: bias window integrated transmissions
bond_transmission: energy resolved transmissions between atoms
bond_current: bias window integrated transmissions (orbital current summed over orbitals)
vector_current: an atomic field current for each atom (Cartesian representation of bond-currents)
atom_transmission: energy resolved atomic transmission for each atom (scalar representation of bond-transmissions)
atom_current: the atomic current for each atom (scalar representation of bond-currents)

property wk: Weights of k-points in file

property wkpt: Always return [1.], this is to signal other routines

write(*args, **kwargs)

Generic write method which should be overloaded in child-classes

Parameters:: **kwargs – keyword arguments will try and search for the attribute write_ and call it with the remaining **kwargs as arguments.

write_tbtav(*args, **kwargs)[source]

Wrapper for writing the k-averaged TBT.AV.nc file.

This write requires the TBT.nc Sile object passed as the first argument, or as the keyword from=tbt argument.

Parameters:: from (tbtncSileTBtrans) – the TBT.nc file object that has the k-sampled quantities.

property xa: Atomic coordinates in file

property xyz: Atomic coordinates in file