Dirac Spectrum in Piecewise Constant One-Dimensional Potentials

TL;DR

This paper investigates the electronic states in graphene under piecewise constant potentials using the Dirac equation and transfer matrix method, revealing Dirac points, confined states, and quantum interference effects.

Contribution

It introduces a comprehensive analysis of Dirac spectra in piecewise potentials, including superlattices, trenches, and p-n junctions, with new insights into Dirac point patterns and confined states.

Findings

Dirac points appear throughout superlattice band structures.

Confined states are supported in trenches and p-n junctions.

Quantum interference effects reveal the presence of confined states.

Abstract

We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies, and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac points which are present throughout the band structure, and verify for the special case of a particle-hole symmetric potential their presence at zero energy. We also consider the cases of a single trench and a p-n junction embedded in neutral graphene, which are shown to support confined states. An analysis of conductance across these structures demonstrates that these confined states create quantum interference effects which evidence their presence.