# sisl.physics.RecursiveSI

class sisl.physics.RecursiveSI(spgeom, infinite, eta=0.0001)

Bases: SemiInfinite

Self-energy object using the Lopez-Sancho Lopez-Sancho algorithm

Methods

 green(E[, k, dtype, eps]) Return a dense matrix with the bulk Green function at energy E and k-point k (default Gamma). scattering_matrix(*args, **kwargs) Calculate the scattering matrix by first calculating the self-energy Calculate the scattering matrix from the self-energy self_energy(E[, k, dtype, eps, bulk]) Return a dense matrix with the self-energy at energy E and k-point k (default Gamma). self_energy_lr(E[, k, dtype, eps, bulk]) Return two dense matrices with the left/right self-energy at energy E and k-point k (default Gamma).
__init__(spgeom, infinite, eta=0.0001)

Create a SelfEnergy object from any SparseGeometry

green(E, k=(0, 0, 0), dtype=None, eps=1e-14, **kwargs)[source]

Return a dense matrix with the bulk Green function at energy E and k-point k (default Gamma).

Parameters
• E (float/complex) – energy at which the calculation will take place

• k (array_like, optional) – k-point at which the Green function should be evaluated. the k-point should be in units of the reciprocal lattice vectors.

• dtype (numpy.dtype) – the resulting data type

• eps (float, optional) – convergence criteria for the recursion

• **kwargs (dict, optional) – arguments passed directly to the self.parent.Pk method (not self.parent.Sk), for instance spin

Returns

the self-energy corresponding to the semi-infinite direction

Return type

numpy.ndarray

scattering_matrix(*args, **kwargs)

Calculate the scattering matrix by first calculating the self-energy

Any arguments that is passed to this method is directly passed to self_energy.

See self_energy for details.

This corresponds to:

$\boldsymbol\Gamma = i(\boldsymbol\Sigma - \boldsymbol \Sigma ^\dagger)$

Examples

Calculating both the self-energy and the scattering matrix.

>>> SE = SelfEnergy(...)
>>> self_energy = SE.self_energy(0.1)
>>> gamma = SE.scattering_matrix(0.1)


For a huge performance boost, please do:

>>> SE = SelfEnergy(...)
>>> self_energy = SE.self_energy(0.1)
>>> gamma = SE.se2scat(self_energy)


Notes

When using both the self-energy and the scattering matrix please use se2scat after having calculated the self-energy, this will be much, MUCH faster!

se2scat

converting the self-energy to the scattering matrix

self_energy

the used routine to calculate the self-energy before calculating the scattering matrix

static se2scat(SE)

Calculate the scattering matrix from the self-energy

$\boldsymbol\Gamma = i(\boldsymbol\Sigma - \boldsymbol \Sigma ^\dagger)$
Parameters

SE (matrix) – self-energy matrix

self_energy(E, k=(0, 0, 0), dtype=None, eps=1e-14, bulk=False, **kwargs)[source]

Return a dense matrix with the self-energy at energy E and k-point k (default Gamma).

Parameters
• E (float/complex) – energy at which the calculation will take place

• k (array_like, optional) – k-point at which the self-energy should be evaluated. the k-point should be in units of the reciprocal lattice vectors.

• dtype (numpy.dtype) – the resulting data type

• eps (float, optional) – convergence criteria for the recursion

• bulk (bool, optional) – if true, $$E\cdot \mathbf S - \mathbf H -\boldsymbol\Sigma$$ is returned, else $$\boldsymbol\Sigma$$ is returned (default).

• **kwargs (dict, optional) – arguments passed directly to the self.parent.Pk method (not self.parent.Sk), for instance spin

Returns

the self-energy corresponding to the semi-infinite direction

Return type

numpy.ndarray

self_energy_lr(E, k=(0, 0, 0), dtype=None, eps=1e-14, bulk=False, **kwargs)[source]

Return two dense matrices with the left/right self-energy at energy E and k-point k (default Gamma).

Note calculating the LR self-energies simultaneously requires that their chemical potentials are the same. I.e. only when the reference energy is equivalent in the left/right schemes does this make sense.

Parameters
• E (float/complex) – energy at which the calculation will take place, if complex, the hosting eta won’t be used.

• k (array_like, optional) – k-point at which the self-energy should be evaluated. the k-point should be in units of the reciprocal lattice vectors.

• dtype (numpy.dtype, optional) – the resulting data type, default to np.complex128

• eps (float, optional) – convergence criteria for the recursion

• bulk (bool, optional) – if true, $$E\cdot \mathbf S - \mathbf H -\boldsymbol\Sigma$$ is returned, else $$\boldsymbol\Sigma$$ is returned (default).

• **kwargs (dict, optional) – arguments passed directly to the self.parent.Pk method (not self.parent.Sk), for instance spin

Returns

• left (numpy.ndarray) – the left self-energy

• right (numpy.ndarray) – the right self-energy