sisl.physics.RecursiveSI

class sisl.physics.RecursiveSI

Bases: SemiInfinite

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

Methods

broadening_matrix(*args, **kwargs)	Calculate the broadening matrix by first calculating the self-energy
green(E[, k, dtype, atol])	Return a dense matrix with the bulk Green function at energy E and k-point k (default Gamma).
se2broadening(SE)	Calculate the broadening matrix from the self-energy
self_energy(E[, k, dtype, atol, bulk])	Return a dense matrix with the self-energy at energy E and k-point k (default Gamma).
self_energy_lr(E[, k, dtype, atol, bulk])	Return two dense matrices with the left/right self-energy at energy E and k-point k (default Gamma).

broadening_matrix(*args, **kwargs)

Calculate the broadening 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:

$$\mathbf{\Gamma }=i(\mathbf{\Sigma }-{\mathbf{\Sigma }}^{†})$$

Examples

Calculating both the self-energy and the broadening matrix.

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

For a huge performance boost, please do:

>>> SE = SelfEnergy(...)
>>> self_energy = SE.self_energy(0.1)
>>> gamma = SE.se2broadening(self_energy)

Notes

When using both the self-energy and the broadening matrix please use se2broadening after having calculated the self-energy, this will be much, MUCH faster!

See also

se2broadening

converting the self-energy to the broadening matrix

self_energy

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

green(E, k=(0, 0, 0), dtype=None, atol=1e-14, **kwargs)

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

Parameters:

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

• k (Sequence[float]) – 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

• atol (float) – 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

static se2broadening(SE)

Calculate the broadening matrix from the self-energy

$$\mathbf{\Gamma }=i(\mathbf{\Sigma }-{\mathbf{\Sigma }}^{†})$$

Parameters:

SE (matrix) – self-energy matrix

self_energy(E, k=(0, 0, 0), dtype=None, atol=1e-14, bulk=False, **kwargs)

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

Parameters:

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

• k (Sequence[float]) – 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

• atol (float) – convergence criteria for the recursion

• bulk (bool) – if true, $E\cdot \mathbf{S}-\mathbf{H}-\mathbf{\Sigma }$ is returned, else $\mathbf{\Sigma }$ 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, atol=1e-14, bulk=False, **kwargs)

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

• k (Sequence[float]) – 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

• atol (float) – convergence criteria for the recursion

• bulk (bool) – if true, $E\cdot \mathbf{S}-\mathbf{H}-\mathbf{\Sigma }$ is returned, else $\mathbf{\Sigma }$ 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