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

Abstract

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.

17 pages, 5 figures. Published version

References in corpus (7)

• The Kernel Polynomial Method
• An On-Demand Coherent Single Electron Source
• Prospects for Spin-Based Quantum Computing
• Chebyshev-BdG: an efficient numerical approach to inhomogeneous superconductivity
• Tkwant: a software package for time-dependent quantum transport
• Disorder-robust $p$-wave pairing with odd frequency dependence in normal metal-conventional superconductor junctions
• Efficient Linear Scaling Approach for Computing the Kubo Hall Conductivity

Cited by in corpus (7)

• Superconducting phenomena in systems with unconventional magnets
• Disorder-robust $p$-wave pairing with odd frequency dependence in normal metal-conventional superconductor junctions
• Fast Fourier-Chebyshev approach to real-space simulations of the Kubo formula
• High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin-orbit effects and p-wave superconductivity
• SuperConga: an open-source framework for mesoscopic superconductivity
• Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models
• Emergence of Imaginary Time Crystals in the non-Hermitian Su-Schrieffer-Heeger model