Theory for strained graphene beyond the Cauchy-Born rule

TL;DR

This paper develops a new theoretical framework for strained graphene that accounts for sublattice relative displacements, leading to different predictions for electronic properties compared to traditional models.

Contribution

It introduces a generalized transformation rule for bond vectors under strain, extending beyond the Cauchy-Born rule, and derives a new effective Dirac Hamiltonian for strained graphene.

Findings

Different Fermi velocity predictions due to relative displacement

Altered local density of states and optical conductivity

Implications for scanning tunneling spectroscopy and optical experiments

Abstract

The low-energy electronic properties of strained graphene are usually obtained by transforming the bond vectors according to the Cauchy-Born rule. In this work, we derive a new effective Dirac Hamiltonian by assuming a more general transformation rule for the bond vectors under uniform strain, which takes into account the strain-induced relative displacement between the two sublattices of graphene. Our analytical results show that the consideration of such relative displacement yields a qualitatively different Fermi velocity with respect to previous reports. Furthermore, from the derived Hamiltonian, we analyze effects of this relative displacement on the local density of states and the optical conductivity, as well as the implications on the scanning tunneling spectroscopy, including external magnetic field, and optical transmittance experiments of strained graphene.