Generalized Kubo Formulas for the Transport Properties of Incommensurate 2D Atomic Heterostructures

TL;DR

This paper develops an exact mathematical framework for calculating transport properties in incommensurate 2D atomic heterostructures, extending C* algebra methods to these complex systems.

Contribution

It introduces a novel formulation for transport coefficients in incommensurate 2D systems using C* algebra, with numerical methods demonstrated on a 1D model.

Findings

Exact formulation for transport coefficients in incommensurate systems

Numerical methods validated on a 1D bilayer model

Framework applicable to aperiodic and disordered materials

Abstract

We give an exact formulation for the transport coefficients of incommensurate two-dimensional atomic multilayer systems in the tight-binding approximation. This formulation is based upon the C* algebra framework introduced by Bellissard and collaborators to study aperiodic solids (disordered crystals, quasicrystals, and amorphous materials), notably in the presence of magnetic fields (quantum Hall effect). We also present numerical approximations and test our methods on a one-dimensional incommensurate bilayer system.