Pushing the limit of quantum transport simulations

Abstract

Simulations of quantum transport in coherent conductors have evolved into mature techniques that are used in fields of physics ranging from electrical engineering to quantum nanoelectronics and material science. The most efficient general-purpose algorithms have a computational cost that scales as $L^{6\dots 7}$ in 3D, which on the one hand is a substantial improvement over older algorithms, but on the other hand still severely restricts the size of the simulation domain, limiting the usefulness of simulations through strong finite-size effects. Here, we present a novel class of algorithms that, for certain systems, allows to directly access the thermodynamic limit. Our approach, based on the Green's function formalism for discrete models, targets systems which are mostly invariant by translation, i.e. invariant by translation up to a finite number of orbitals and/or quasi-1D electrodes and/or the presence of edges or surfaces. Our approach is based on an automatic calculation of the poles and residues of series expansions of the Green's function in momentum space. This expansion allows to integrate analytically in one momentum variable. We illustrate our algorithms with several applications: devices with graphene electrodes that consist of half an infinite sheet; Friedel oscillation calculations of infinite 2D systems in presence of an impurity; quantum spin Hall physics in presence of an edge; the surface of a Weyl semi-metal in presence of impurities and electrodes connected to the surface. In this last example, we study the conduction through the Fermi arcs of the topological material and its resilience to the presence of disorder. Our approach provides a practical route for simulating 3D bulk systems or surfaces as well as other setups that have so far remained elusive.

20 pages, 13 figures

References in corpus (8)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• The Kernel Polynomial Method
• A knitting algorithm for calculating Green functions in quantum systems
• Linear Scaling Quantum Transport Methodologies
• Diffusion and criticality in undoped graphene with resonant scatterers
• Low Temperature Lanczos Method
• Quantum Transport in Weyl Semimetal Thin Films in the Presence of Spin-Orbit Coupled Impurities
• Color-dependent conductance of graphene with adatoms

Cited by in corpus (6)

• Giant Anomalous Hall Effect due to Double-Degenerate Quasi Flat Bands
• Boundary Green's function approach for spinful single-channel and multichannel Majorana nanowires
• Gigantic tunneling magnetoresistance in magnetic Weyl semimetal tunnel junctions
• 2D topological matter from a boundary Green's functions perspective: Faddeev-LeVerrier algorithm implementation
• Chebyshev Polynomial Method to Landauer-Büttiker Formula of Quantum Transport in Nanostructures
• Current-induced torques in magnetic Weyl semimetal tunnel junctions