Curved-space Dirac description of elastically deformed monolayer graphene is generally incorrect

TL;DR

The paper demonstrates that the common assumption of a Dirac description in curved space for elastically deformed graphene is generally incorrect, showing that large magnetic fields from strain disrupt this approximation.

Contribution

It provides a rigorous real space gradient expansion analysis revealing the limitations of the curved-space Dirac model for strained graphene.

Findings

Large magnetic fields from generic strain invalidate Dirac truncation.

Only flat-space Dirac with gauge fields is consistent in perturbation.

Fine tuning magnetic fields can allow Dirac description in curved space.

Abstract

Undistorted monolayer graphene has energy bands which cross at protected Dirac points. It elastically deforms and much research has assumed the Dirac description persists, now in a curved space and coupled to a gauge field related to lattice strain. We show this is incorrect by using a real space gradient expansion to study how the Dirac equation derives from the tight binding model. Generic spatially varying hopping functions give rise to large magnetic fields which spoil the truncation in derivatives. In the perturbative regime, the only consistent truncation to Dirac is one with nontrivial gauge field but in flat space. One can instead fine tune the magnetic field to be small, and we derive the resulting differential condition that the hopping functions must satisfy to yield a consistent truncation to Dirac in curved space. We consider whether mechanical effects might impose this fine tuning, but find this is not the case for a simple elastic membrane model.