Efficient numerical method for evaluating normal and anomalous time-domain equilibrium Green's functions in inhomogeneous systems

Löthman, Tomas; Triola, Christopher Lawrence Charles; Cayao, Jorge; Black-Schaffer, Annica M.

doi:10.1103/physrevb.104.125405

Title: Efficient numerical method for evaluating normal and anomalous time-domain equilibrium Green's functions in inhomogeneous systems

Journal Article · 02 September 2021 · Physical Review. B

DOI: https://doi.org/10.1103/physrevb.104.125405 · OSTI ID:1825439

Löthman, Tomas ^[1];

^[2]; Cayao, Jorge ^[1]; Black-Schaffer, Annica M. ^[1]

Uppsala Univ. (Sweden)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

In this work we develop EPOCH (equilibrium propagator by orthogonal polynomial chain), a computationally efficient method to calculate the time-dependent equilibrium Green's functions, including the anomalous Green's functions of superconductors, to capture the time evolution in large inhomogeneous systems. The EPOCH method generalizes the Chebyshev wave-packet propagation method from quantum chemistry and efficiently incorporates the Fermi-Dirac statistics that is needed for equilibrium quantum condensed matter systems. The computational cost of EPOCH scales only linearly in the system degrees of freedom, generating an extremely efficient algorithm also for very large systems. We demonstrate the power of the EPOCH method by calculating the time evolution of an excitation near a superconductor–normal metal interface in two and three dimensions, capturing transmission as well as normal and Andreev reflections.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: Swedish Research Council (SRC); European Union (EU); Knut and Alice Wallenberg Foundation

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1825439

Report Number(s):: LA-UR--20-23078

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 12 Vol. 104; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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