Invariant expansion for the trigonal band structure of graphene

TL;DR

This paper uses symmetry and group theory to derive an invariant Hamiltonian expansion for graphene's trigonal band structure, capturing effects of external fields, strain, and spin-orbit coupling.

Contribution

It provides a systematic, symmetry-based derivation of the Hamiltonian for graphene near the K points, including new terms beyond previous tight-binding results.

Findings

Derived an invariant Hamiltonian expansion for graphene

Identified new contributions from external fields and spin-orbit coupling

Reproduced and extended previous tight-binding results

Abstract

We present a symmetry analysis of the trigonal band structure in graphene, elucidating the transformational properties of the underlying basis functions and the crucial role of time-reversal invariance. Group theory is used to derive an invariant expansion of the Hamiltonian for electron states near the K points of the graphene Brillouin zone. Besides yielding the characteristic k-linear dispersion and higher-order corrections to it, this approach enables the systematic incorporation of all terms arising from external electric and magnetic fields, strain, and spin-orbit coupling up to any desired order. Several new contributions are found, in addition to reproducing results obtained previously within tight-binding calculations. Physical ramifications of these new terms are discussed.