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qttools.obc.spectral#

source module qttools.obc.spectral

Classes

  • Spectral — Spectral open-boundary condition solver.

source class Spectral(nevp: NEVP, block_sections: int = 1, min_decay: float = 0.001, max_decay: float | None = None, num_ref_iterations: int = 2, x_ii_formula: str = 'self-energy', two_sided: bool = False, treat_pairwise: bool = True, pairing_threshold: float = 0.25, min_propagation: float = 0.01, residual_tolerance: float = 0.001, residual_normalization: str | None = 'eigenvalue', warning_threshold: float = 0.1)

Bases : OBCSolver

Spectral open-boundary condition solver.

This technique of obtaining the surface Green's function is based on the solution of a non-linear eigenvalue problem (NEVP), defined via the system-matrix blocks in the semi-infinite contacts.

Those eigenvalues corresponding to reflected modes are filtered out, so that only the ones that correspond to modes that propagate into the leads or those that decay away from the system are retained.

The surface Green's function is then calculated from these filtered eigenvalues and eigenvectors.

Initializes the spectral OBC solver.

Parameters

  • nevp : NEVP — The non-linear eigenvalue problem solver to use.

  • block_sections : int, optional — The number of sections to split the periodic matrix layer into.

  • min_decay : float, optional — The decay threshold after which modes are considered to be evanescent.

  • max_decay : float, optional — The maximum decay to consider for evanescent modes. If not provided, the maximum decay is set to the logarithm of the outer radius of the contour annulus if applicable. Otherwise, it is set to log(10).

  • num_ref_iterations : int, optional — The number of refinement iterations to perform on the surface Green's function.

  • x_ii_formula : str, optional — The formula to use for the calculation of the surface Green's function. The default is via the boundary "self-energy". The other option is "direct". The "self-energy" formula corresponds to Equation (13.1) in the paper 1 and the "direct" formula corresponds to Equation (15).

  • two_sided : bool, optional — Whether to solve the NEVP for both left and right eigenvectors, and construct the surface Green's function from both.

  • treat_pairwise : bool, optional — Whether to match complex conjugate modes and treat them in pairs during the determining of reflected modes.

  • pairing_threshold : float, optional — The threshold for which two modes are considered to be a mode pair.

  • min_propagation : float, optional — The minimum ratio between the real and imaginary part of the group velocity of a mode. This ratio is used to determine how clearly a mode propagates.

  • residual_tolerance : float, optional — The tolerance for the residual of the NEVP.

  • residual_normalization : str | None, optional — The formula to use for the normalization of the residual. The default is the "operator" formula. The other options are "eigenvalue" and None. The "operator" formula corresponds to normalization by the Frobenius norm of the operator, the "eigenvalue" formula corresponds to normalization by the absolute of the eigenvalues, and None results in no normalization.

  1. S. Brück, et al., Efficient algorithms for large-scale quantum transport calculations, The Journal of Chemical Physics, 2017. ↩