phtavncSilePHtrans¶

class sisl.io.tbtrans.phtavncSilePHtrans(filename, mode='r', lvl=0, access=1, *args, **kwargs)[source]¶

PHtrans file object

Attributes

`E`	Sampled energy-points in file
`a_buf`	Atomic indices (0-based) of device atoms
`a_dev`	Atomic indices (0-based) of device atoms
`base_file`	File of the current Sile
`cell`	Unit cell in file
`chemical_potential`
`current`
`current_parameter`
`elecs`	List of electrodes
`electron_temperature`
`fano`
`file`	File of the current Sile
`geom`	The associated geometry from this file
`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
`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

Methods

`ADOS`(self[, elec, E, kavg, atom, orbital, …])	Spectral density of states (DOS) (1/eV).
`Adensity_matrix`(self, elec, E[, kavg, isc, …])	Spectral function density matrix at energy `E` (1/eV)
`BDOS`(self[, elec, E, kavg, sum, norm])	Bulk density of states (DOS) (1/eV).
`DOS`(self[, E, kavg, atom, orbital, sum, norm])	Green function density of states (DOS) (1/eV).
`Eindex`(self, E)	Return the closest energy index corresponding to the energy `E`
`__init__`(self, filename[, mode, lvl, access])	Initialize self.
`a2p`(self, atom)	Return the pivoting orbital indices (0-based) for the atoms
`atom_ACOHP`(self, elec, E[, kavg, isc, uc])	Atomic COHP curve of the spectral function
`atom_ACOOP`(self, elec, E[, kavg, isc, uc])	Atomic COOP curve of the spectral function
`atom_COHP`(self, E[, kavg, isc, uc])	Atomic COHP curve of the Green function
`atom_COHP_from_orbital`(self, COHP[, uc])	Calculate the atomic COHP curve from the orbital COHP
`atom_COOP`(self, E[, kavg, isc, uc])	Atomic COOP curve of the Green function
`atom_COOP_from_orbital`(self, COOP[, uc])	Calculate the atomic COOP curve from the orbital COOP
`atom_current`(self, elec, E[, kavg, activity])	Atomic current of atoms
`atom_current_from_orbital`(self, Jij[, activity])	Atomic current of atoms by passing the orbital current
`bond_current`(self, elec, E[, kavg, isc, …])	Bond-current between atoms (sum of orbital currents)
`bond_current_from_orbital`(self, Jij[, only, uc])	Bond-current between atoms (sum of orbital currents) from an external orbital current
`btd`(self[, elec])	Block-sizes for the BTD method
`close`(self)
`density_matrix`(self, E[, kavg, isc, geometry])	Density matrix from the Green function at energy `E` (1/eV)
`dir_file`(self[, filename])	File of the current Sile
`eta`(self[, elec])	The imaginary part used when calculating the self-energies in eV (or for the device
`exist`(self)	Query whether the file exists
`info`(self[, elec])	Information about the calculated quantities available for extracting in this file
`iter`(self[, group, dimension, variable, …])	Iterator on all groups, variables and dimensions.
`kT`(self, elec)	Electron bath temperature [eV]
`kindex`(self, k)	Return the index of the k-point that is closests to the queried k-point (in reduced coordinates)
`mu`(self, elec)	Return the chemical potential associated with the electrode elec
`n_btd`(self[, elec])	Number of blocks in the BTD partioning
`norm`(self[, atom, orbital, norm])	Normalization factor depending on the input
`o2p`(self, orbital)	Return the pivoting indices (0-based) for the orbitals
`orbital_ACOHP`(self, elec, E[, kavg, isc])	Orbital resolved COHP analysis of the spectral function
`orbital_ACOOP`(self, elec, E[, kavg, isc])	Orbital COOP analysis of the spectral function
`orbital_COHP`(self, E[, kavg, isc])	Orbital resolved COHP analysis of the Green function
`orbital_COOP`(self, E[, kavg, isc])	Orbital COOP analysis of the Green function
`orbital_current`(self, elec, E[, kavg, isc, only])	Orbital current originating from elec as a sparse matrix
`pivot`(self[, in_device, sort])	Pivoting orbitals for the full system
`read`(self, \args, \\*kwargs)	Generic read method which should be overloaded in child-classes
`read_data`(self, \args, \\*kwargs)	Read specific type of data.
`read_geometry`(self, \args, \\*kwargs)	Returns Geometry object from this file
`read_supercell`(self)	Returns SuperCell object from this file
`reflection`(self[, elec, kavg, from_single])	Reflection into electrode elec
`transmission`(self[, elec_from, elec_to, kavg])	Transmission from elec_from to elec_to.
`transmission_bulk`(self[, elec, kavg])	Bulk transmission for the elec electrode
`transmission_eig`(self[, elec_from, elec_to, …])	Transmission eigenvalues from elec_from to elec_to.
`vector_current`(self, elec, E[, kavg, only])	Vector for each atom describing the mean path for the current travelling through the atom
`vector_current_from_bond`(self, Jab)	Vector for each atom being the sum of bond-current times the normalized bond between the atoms
`write`(self, \args, \\*kwargs)	Generic write method which should be overloaded in child-classes
`write_geometry`(self, \args, \\*kwargs)	This is not meant to be used
`write_tbtav`(self, \args, \\*kwargs)	Wrapper for writing the k-averaged TBT.AV.nc file.

ADOS(self, elec=0, E=None, kavg=True, atom=None, orbital=None, sum=True, norm='none')¶

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

\[\mathrm{ADOS}_\mathfrak{el}(E) = \frac{1}{2\pi N} \sum_{\nu\in \mathrm{atom}/\mathrm{orbital}} [\mathbf{G}(E)\Gamma_\mathfrak{el}\mathbf{G}^\dagger]_{\nu\nu}(E)\]

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

Parameters

elec: str, int, optional: electrode originating spectral function
Efloat 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
atomarray_like of int or bool, optional: only return for a given set of atoms (default to all). NOT allowed with orbital keyword
orbitalarray_like of int or bool, optional: only return for a given set of orbitals (default to all) NOT allowed with atom keyword
sumbool, 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).

See also

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

Adensity_matrix(self, elec, E, kavg=True, isc=None, geometry=None)¶

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

\[\rho_{\mathbf A_{\mathfrak{el}}}(E, \mathbf r) = \frac{1}{2\pi}\sum_{\nu\mu}\phi_\nu(\mathbf r)\phi_\mu(\mathbf r) \Re[\mathbf A_{\mathfrak{el}, \nu\mu}(E)]\]

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
Efloat 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].
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.

Returns

DensityMatrix: object containing the Geometry and the density matrix elements

See also

density_matrix: Green function density matrix

BDOS(self, elec=0, E=None, kavg=True, sum=True, norm='none')¶

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

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

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

Parameters

elec: str, int, optional: electrode where the bulk DOS is returned
Efloat 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
sumbool, 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 or normed by total number of orbitals. Currently one cannot extract DOS per atom/orbital.

See also

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

DOS(self, E=None, kavg=True, atom=None, orbital=None, sum=True, norm='none')¶

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

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

\[\mathrm{DOS}(E) = -\frac{1}{\pi N} \sum_{\nu\in \mathrm{atom}/\mathrm{orbital}} \Im \mathbf{G}_{\nu\nu}(E)\]

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

Parameters

Efloat 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
atomarray_like of int or bool, optional: only return for a given set of atoms (default to all). NOT allowed with orbital keyword
orbitalarray_like of int or bool, optional: only return for a given set of orbitals (default to all) NOT allowed with atom keyword
sumbool, 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)

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(self, E)¶

Return the closest energy index corresponding to the energy E

Parameters

Efloat or int: if int, return it-self, else return the energy index which is closests to the energy.

a2p(self, atom)¶

Return the pivoting orbital indices (0-based) for the atoms

This is equivalent to:

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

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

Parameters

atomarray_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

atom_ACOHP(self, elec, E, kavg=True, isc=None, uc=False)¶

Atomic COHP curve of the spectral function

Parameters

elec: str or int: the electrode of the spectral function
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].
ucbool, 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.

See also

orbital_COHP: orbital resolved COHP analysis of the Green function
atom_COHP_from_orbital: transfer an orbital COHP to atomic COHP
atom_COHP: atomic COHP analysis of the Green function
atom_ACOOP: atomic COOP analysis of the spectral function

atom_ACOOP(self, elec, E, kavg=True, isc=None, uc=False)¶

Atomic COOP curve of the spectral function

Parameters

elec: str or int: the electrode of the spectral function
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].
ucbool, 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.

See also

orbital_COOP: orbital resolved COOP analysis of the Green function
atom_COOP_from_orbital: transfer an orbital COOP to atomic COOP
atom_COOP: atomic COOP analysis of the Green function
atom_ACOHP: atomic COHP analysis of the spectral function

atom_COHP(self, E, kavg=True, isc=None, uc=False)¶

Atomic COHP curve of the Green 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.
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].
ucbool, 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.

See also

orbital_COHP: orbital resolved COHP analysis of the Green function
atom_COHP_from_orbital: transfer an orbital COHP to atomic COHP
atom_ACOHP: atomic COHP analysis of the spectral function
atom_COOP: atomic COOP analysis of the Green function

atom_COHP_from_orbital(self, COHP, uc=False)¶

Calculate the atomic COHP curve from the orbital COHP

The atomic COHP are a sum over all orbital COHP:

\[\mathrm{COHP}_{\alpha\beta} = \sum_{\nu\in\alpha}\sum_{\mu\in\beta} \mathrm{COHP}_{\nu\mu}\]

Parameters

COHPscipy.sparse.csr_matrix: the orbital COHP as retrieved from orbital_COHP or orbital_ACOHP
ucbool, 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.

See also

orbital_COHP: orbital resolved COHP analysis of the Green function
orbital_ACOHP: orbital resolved COHP analysis of the spectral function
atom_COHP: atomic COHP analysis of the Green function

atom_COOP(self, E, kavg=True, isc=None, uc=False)¶

Atomic COOP curve of the Green function

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].
ucbool, 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.

See also

orbital_COOP: orbital resolved COOP analysis of the Green function
atom_COOP_from_orbital: transfer an orbital COOP to atomic COOP
atom_ACOOP: atomic COOP analysis of the spectral function
atom_COHP: atomic COHP analysis of the Green function

atom_COOP_from_orbital(self, COOP, uc=False)¶

Calculate the atomic COOP curve from the orbital COOP

The atomic COOP are a sum over all orbital COOP:

\[\mathrm{COOP}_{\alpha\beta} = \sum_{\nu\in\alpha}\sum_{\mu\in\beta} \mathrm{COOP}_{\nu\mu}\]

Parameters

COOPscipy.sparse.csr_matrix: the orbital COOP as retrieved from orbital_COOP or orbital_ACOOP
ucbool, 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.

See also

orbital_COOP: orbital resolved COOP analysis of the Green function
orbital_ACOOP: orbital resolved COOP analysis of the spectral function
atom_COOP: atomic COOP analysis of the Green function

atom_current(self, elec, E, kavg=True, activity=True)¶

Atomic current of atoms

Short hand function for calling orbital_current and atom_current_from_orbital.

Parameters

elec: str, int: the electrode of originating electrons
E: float or int: the energy or energy index of the atom current.
kavg: bool, int, optional: whether the returned atomic current is k-averaged, or an explicit (unweighed) k-point is returned
activity: bool, optional: whether the activity current is returned, see atom_current_from_orbital for details.

See also

orbital_current: the orbital current between individual orbitals
bond_current_from_orbital: transfer the orbital current to bond current
bond_current: the bond current (orbital current summed over orbitals)
vector_current: an atomic field current for each atom (Cartesian representation of bond-currents)

atom_current_from_orbital(self, Jij, activity=True)¶

Atomic current of atoms by passing the orbital current

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

\[\begin{split}J_\alpha^{|a|} &=\frac{1}{2} \sum_\beta \Big| \sum_{\nu\in \alpha}\sum_{\mu\in \beta} J_{\nu\mu} \Big| \\ J_\alpha^{|o|} &=\frac{1}{2} \sum_\beta \sum_{\nu\in \alpha}\sum_{\mu\in \beta} \big| J_{\nu\mu} \big|\end{split}\]

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

If activity=False \(J_\alpha^{|a|}\) 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

Jij: scipy.sparse.csr_matrix: the orbital currents as retrieved from orbital_current
activity: bool, optional: True to return the activity current, see explanation above

Examples

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

property base_file¶: File of the current Sile

bond_current(self, elec, E, kavg=True, isc=None, only='+', uc=False)¶

Bond-current between atoms (sum of orbital currents)

Short hand function for calling orbital_current and bond_current_from_orbital.

Parameters

elecstr, int: the electrode of originating electrons
Efloat or int: A float for energy in eV, int for explicit energy index Unlike orbital_current this may not be None as the down-scaling of the orbital currents may not be equivalent for all energy points.
kavgbool, int, optional: whether the returned bond current is k-averaged, or an explicit (unweighed) k-point is returned
iscarray_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.
only{‘+’, ‘-‘, ‘all’}: If “+” is supplied only the positive orbital currents are used, for “-“, only the negative orbital currents are used, else return the sum of both. Please see discussion in orbital_current.
ucbool, optional: whether the returned bond-currents 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.

See also

orbital_current: the orbital current between individual orbitals
bond_current_from_orbital: transfer the orbital current to bond current
atom_current: the atomic current for each atom (scalar representation of bond-currents)
vector_current: an atomic field current for each atom (Cartesian representation of bond-currents)

Examples

>>> Jij = tbt.orbital_current(0, -1.0, only='+') # orbital current @ E = -1 eV originating from electrode ``0``
>>> Jab1 = tbt.bond_current_from_orbital(Jij)
>>> Jab2 = tbt.bond_current(0, -1.0)
>>> Jab1 == Jab2
True

bond_current_from_orbital(self, Jij, only='+', uc=False)¶

Bond-current between atoms (sum of orbital currents) from an external orbital current

Conversion routine from orbital currents into bond currents.

The bond currents are a sum over all orbital currents:

\[J_{\alpha\beta} = \sum_{\nu\in\alpha}\sum_{\mu\in\beta} J_{\nu\mu}\]

where if

only='+': only \(J_{\nu\mu} > 0\) are summed onto the corresponding atom,
only='-': only \(J_{\nu\mu} < 0\) are summed onto the corresponding atom,
only='all': all \(J_{\nu\mu}\) are summed onto the corresponding atom.

Parameters

Jijscipy.sparse.csr_matrix: the orbital currents as retrieved from orbital_current
only{‘+’, ‘-‘, ‘all’}: If “+” is supplied only the positive orbital currents are used, for “-“, only the negative orbital currents are used, else return both.
ucbool, optional: whether the returned bond-currents 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.

See also

orbital_current: the orbital current between individual orbitals
bond_current: the bond current (orbital current summed over orbitals)
atom_current: the atomic current for each atom (scalar representation of bond-currents)
vector_current: an atomic field current for each atom (Cartesian representation of bond-currents)

Examples

>>> Jij = tbt.orbital_current(0, -1.0) # orbital current @ E = -1 eV originating from electrode ``0``
>>> Jab = tbt.bond_current_from_orbital(Jij)
>>> Jab[2,3] # bond current between atom 3 and 4

btd(self, elec=None)¶

Block-sizes for the BTD method

Parameters

elecstr 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 cell¶: Unit cell in file

chemical_potential = None¶

close(self)¶

current = None¶

current_parameter = None¶

density_matrix(self, E, kavg=True, isc=None, geometry=None)¶

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

\[\rho_{\mathbf G}(E, \mathbf r) = -\frac{1}{\pi}\sum_{\nu\mu}\phi_\nu(\mathbf r)\phi_\mu(\mathbf r) \Im[\mathbf G_{\nu\mu}(E)]\]

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

Efloat 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].
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.

Returns

DensityMatrix: object containing the Geometry and the density matrix elements

See also

Adensity_matrix: spectral function density matrix

dir_file(self, filename=None)¶: File of the current Sile

property elecs¶: List of electrodes

electron_temperature = None¶

eta(self, elec=None)¶

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

Parameters

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

exist(self)¶: Query whether the file exists

fano = None¶

property file¶: File of the current Sile

property geom¶: The associated geometry from this file

property geometry¶: The associated geometry from this file

info(self, elec=None)¶

Information about the calculated quantities available for extracting in this file

Parameters

elecstr or int: the electrode to request information from

iter(self, 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

groupbool (True): whether the iterator yields Group instances
dimensionbool (True): whether the iterator yields Dimension instances
variablebool (True): whether the iterator yields Variable instances
levelsint (-1): number of levels to traverse, with respect to root variable, i.e. number of sub-groups this iterator will return.
rootstr (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(self, elec)¶: Electron bath temperature [eV]

kindex(self, k)¶

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

Parameters

karray_like of float: the queried k-point in reduced coordinates \(]-0.5;0.5]\).

property kpt¶: Sampled k-points in file

property lasto¶: Last orbital of corresponding atom

mu(self, elec)¶: Return the chemical potential associated with the electrode elec

property nE¶: Number of energy-points in file

n_btd(self, elec=None)¶

Number of blocks in the BTD partioning

Parameters

elecstr 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

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

property no_u¶: Returns number of orbitals in the cell

noise_power = None¶

norm(self, atom=None, orbital=None, norm='none')¶

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 orbital is an argument a conversion of orbital 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 atom is specified, this is equivalent to the ‘atom’ option.

Parameters

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

o2p(self, orbital)¶

Return the pivoting indices (0-based) for the orbitals

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

Parameters

orbitalarray_like or int: orbital indices (0-based)

property o_dev¶: Orbital indices (0-based) of device orbitals

orbital_ACOHP(self, elec, E, kavg=True, isc=None)¶

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:

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

Parameters

elec: str or int: the electrode of the spectral function
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].

See also

orbital_COHP: orbital resolved COHP analysis of the Green function
atom_COHP_from_orbital: atomic COHP analysis from an orbital COHP
atom_COHP: atomic COHP analysis of the Green function
atom_ACOHP: atomic COHP analysis of the spectral function
orbital_COOP: orbital resolved COOP analysis of the Green function
atom_COOP_from_orbital: transfer an orbital COOP to atomic COOP
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_ACOOP(self, elec, E, kavg=True, isc=None)¶

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:

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

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

\[\mathrm{ADOS}_{\nu} = \sum_\mu \mathrm{COOP}^{\mathbf A}_{\nu\mu}\]

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

\[\begin{split}D &= \sum_\nu \mathrm{COOP}^{\mathbf A}_{\nu\nu} \\ \mathrm{DBCOOP}^{\mathbf A}_{\nu\mu} &= \mathrm{COOP}^{\mathbf A}_{\nu\mu} / D\end{split}\]

The BCOOP can be looked up in the reference above.

Parameters

elec: str or int: the electrode of the spectral function
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].

See also

orbital_COOP: orbital resolved COOP analysis of the Green function
atom_COOP_from_orbital: transfer an orbital COOP to atomic COOP
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_from_orbital: atomic COHP analysis from an orbital COHP
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

Examples

>>> ACOOP = tbt.orbital_ACOOP(0, -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

orbital_COHP(self, E, kavg=True, isc=None)¶

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:

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

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].

See also

atom_COHP_from_orbital: atomic COHP analysis from an orbital COHP
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: orbital resolved COOP analysis of the Green function
atom_COOP_from_orbital: transfer an orbital COOP to atomic COOP
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

Examples

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

orbital_COOP(self, E, kavg=True, isc=None)¶

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:

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

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

\[\mathrm{DOS}_{\nu} = \sum_\mu \mathrm{COOP}^{\mathbf G}_{\nu\mu}\]

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

\[\begin{split}D &= \sum_\nu \mathrm{COOP}^{\mathbf G}_{\nu\nu} \\ \mathrm{DBCOOP}^{\mathbf G}_{\nu\mu} &= \mathrm{COOP}^{\mathbf G}_{\nu\mu} / D\end{split}\]

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].

See also

atom_COOP_from_orbital: transfer an orbital COOP to atomic COOP
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_from_orbital: atomic COHP analysis from an orbital COHP
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

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

orbital_current(self, elec, E, kavg=True, isc=None, only='all')¶

Orbital current originating from elec as a sparse matrix

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

When requesting orbital-currents it is vital to consider how the data needs to be analysed before extracting the data. For instance, if only local currents are interesting one should use only='+'. While if one is interested in the transmission between subset of orbitals, only='all' is the correct method.

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

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

Parameters

elec: str, int: the electrode of originating electrons
E: float or int: the energy or the energy index of the orbital current. 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 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].
only{‘all’, ‘+’, ‘-‘}: which orbital currents to return, all, positive or negative values only. Default to 'all' because it can then be used in the subsequent default arguments for bond_current_from_orbital and atom_current_from_orbital.

See also

bond_current_from_orbital: transfer the orbital current to bond current
bond_current: the bond current (orbital current summed over orbitals)
atom_current_from_orbital: transfer the orbital current to atomic current
atom_current: the atomic current for each atom (scalar representation of bond-currents)
vector_current: an atomic field current for each atom (Cartesian representation of bond-currents)

Examples

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

pivot(self, in_device=False, sort=False)¶

Pivoting orbitals for the full system

Parameters

in_devicebool, optional: whether the pivoting elements are with respect to the device region
sortbool, optional: whether the pivoting elements are sorted

read(self, *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(self, *args, **kwargs)¶

Read specific type of data.

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

Parameters

geom: bool, optional: return the geometry
atom_current: bool, optional: return the atomic current flowing through an atom (the activity current)
vector_current: bool, optional: return the orbital currents as vectors

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

read_supercell(self)¶: Returns SuperCell object from this file

reflection(self, elec=0, kavg=True, from_single=False)¶

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).

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¶

transmission(self, elec_from=0, elec_to=1, kavg=True)¶

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

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(self, elec=0, kavg=True)¶

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

See also

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

transmission_eig(self, elec_from=0, elec_to=1, kavg=True)¶

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

See also

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

vector_current(self, elec, E, kavg=True, only='+')¶

Vector for each atom describing the mean path for the current travelling through the atom

See vector_current_from_bond for details.

Parameters

elec: str or int: the electrode of originating electrons
E: float or int: the energy or energy index of the vector current. Unlike orbital_current this may not be None as the down-scaling of the orbital currents may not be equivalent for all energy points.
kavg: bool, int, optional: whether the returned vector current is k-averaged, or an explicit (unweighed) k-point is returned
only{‘+’, ‘-‘, ‘all’}: By default only sum outgoing vector currents ('+'). The incoming vector currents may be retrieved by '-', while the average incoming and outgoing direction can be obtained with 'all'. In the last case the vector currents are divided by 2 to ensure the length of the vector is compatibile with the other options given a pristine system.

Returns

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

See also

orbital_current: the orbital current between individual orbitals
bond_current_from_orbital: transfer the orbital current to bond current
bond_current: the bond current (orbital current summed over orbitals)
atom_current: the atomic current for each atom (scalar representation of bond-currents)

vector_current_from_bond(self, Jab)¶

Vector for each atom being the sum of bond-current times the normalized bond between the atoms

The vector current is defined as:

\[\mathbf J_\alpha = \sum_\beta \frac{r_\beta - r_\alpha}{|r_\beta - r_\alpha|} \cdot J_{\alpha\beta}\]

Where \(J_{\alpha\beta}\) is the bond current between atom \(\alpha\) and \(\beta\) and \(r_\alpha\) are the atomic coordinates.

Parameters

Jab: scipy.sparse.csr_matrix: the bond currents as retrieved from bond_current

Returns

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

See also

orbital_current: the orbital current between individual orbitals
bond_current_from_orbital: transfer the orbital current to bond current
bond_current: the bond current (orbital current summed over orbitals)
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(self, *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_geometry(self, *args, **kwargs)¶: This is not meant to be used

write_tbtav(self, *args, **kwargs)¶

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

fromtbtncSileTBtrans: the TBT.nc file object that has the k-sampled quantities.

property xa¶: Atomic coordinates in file

property xyz¶: Atomic coordinates in file