Gauge fields and curvature in graphene

TL;DR

This paper explores how curvature affects the electronic properties of graphene by coupling the Dirac equation to curved space, revealing new terms in the effective Hamiltonian and their physical implications.

Contribution

It introduces a covariant formalism for describing curved graphene and proposes models for singular and regular curvature effects on electronic behavior.

Findings

Effective Hamiltonian includes additional curvature-related terms

Some terms correspond to standard models, others are novel

Curvature models predict distinct physical phenomena in graphene

Abstract

The low energy excitations of graphene can be described by a massless Dirac equation in two spacial dimensions. Curved graphene is proposed to be described by coupling the Dirac equation to the corresponding curved space. This covariant formalism gives rise to an effective hamiltonian with various extra terms. Some of them can be put in direct correspondence with more standard tight binding or elasticity models while others are more difficult to grasp in standard condensed matter approaches. We discuss this issue, propose models for singular and regular curvature and describe the physical consequences of the various proposals.