Reduction scheme for coupled Dirac systems

TL;DR

This paper presents a reduction scheme for coupled Dirac systems, simplifying their analysis by relating them to lower-dimensional systems, with applications to graphene and bilayer graphene under various interactions.

Contribution

It introduces a novel algebraic reduction method for coupled Dirac systems, enabling easier analysis of complex quantum interactions in two-dimensional materials.

Findings

Reduction scheme simplifies coupled Dirac systems analysis.

Applicable to graphene and bilayer graphene with distortions or spin-orbit interactions.

Explicit examples demonstrate non-uniform interactions in space and time.

Abstract

We analyze a class of coupled quantum systems whose dynamics can be understood via two uncoupled, lower-dimensional quantum settings with auxiliary interactions. The general reduction scheme, based on algebraic properties of the potential term, is discussed in detail for two-dimensional Dirac Hamiltonian. We discuss its possible application in description of Dirac fermions in graphene or bilayer graphene in presence of distortion scattering or spin-orbit interaction. We illustrate the general results on the explicit examples where the involved interactions are non-uniform in space and time.