Reduction scheme for coupled Dirac systems

Abstract

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.