Time-dependent massless Dirac fermions in graphene

TL;DR

This paper derives explicit analytical solutions for time-dependent massless Dirac fermions in graphene using the Lewis-Riesenfeld invariant method, addressing a Hamiltonian with explicit time dependence and a time-varying magnetic field.

Contribution

It introduces a novel application of the Lewis-Riesenfeld method to solve the time-dependent Dirac equation in graphene, including supersymmetric invariant decoupling.

Findings

Explicit solutions for time-dependent Dirac fermions in graphene

Decoupling of spinor components into supersymmetric invariants

Framework for analyzing graphene under time-varying magnetic fields

Abstract

Using the Lewis-Riesenfeld method of invariants we construct explicit analytical solutions for the massless Dirac equation in 2+1 dimensions describing quasi-particles in graphene. The Hamiltonian of the system considered contains some explicit time-dependence in addition to one resulting from being minimally coupled to a time-dependent magnetic field. The eigenvalue equations for the two spinor components of the Lewis-Riesenfeld invariant are found to decouple into a pair of supersymmetric invariants in a similar fashion as the known decoupling for the time-independent Dirac Hamiltonians.