Effective Hamiltonian for electron waves in artificial graphene: A first principles derivation

TL;DR

This paper develops a first principles effective medium theory to describe electron wave propagation in semiconductor heterostructures with honeycomb symmetry, revealing similarities and differences with graphene's Dirac physics.

Contribution

It introduces a novel first principles formalism for effective Hamiltonians in zero-gap semiconductor heterostructures, clarifying their relation to graphene physics.

Findings

Near the K-point, electron dynamics are described by a Dirac-like equation.

The effective Hamiltonian for honeycomb-structured heterostructures matches graphene's pseudospinor formalism.

Other zero-gap superlattices can have different effective Hamiltonians, often with single-component wavefunctions.

Abstract

We propose a first principles effective medium formalism to study the propagation of electron waves in semiconductor heterostructures with a zero-band gap. Our theory confirms that near the K-point the dynamics of a two-dimensional electron gas modulated by an external electrostatic potential with honeycomb symmetry is described by the same pseudospinor formalism and Dirac massless equation as a graphene monolayer. Furthermore, we highlight that even though other superlattices based on semiconductors with a zincblende-type structure can have a zero band-gap and a linear energy-momentum dispersion, the corresponding effective medium Hamiltonian is rather different from that of graphene, and can be based on a single-component wavefunction.