Krylov subspace method for evaluating the self-energy matrices in electron transport calculations

We present a Krylov subspace method for evaluating the self-energy matrices used in the Green's function formulation of electron transport in nanoscale devices. A procedure based on the Arnoldi method is employed to obtain solutions of the quadratic eigenvalue problem associated with the infinite layered systems of the electrodes. One complex and two real shift-and-invert transformations are adopted to select interior eigenpairs with complex eigenvalues on or in the vicinity of the unit circle that correspond to the propagating and evanescent modes of most influence in electron transport calculations. Numerical tests within a density functional theory framework are provided to validate the accuracy and robustness of the proposed method, which in most cases is an order of magnitude faster than conventional methods.