Strain-displacement relations and strain engineering in 2d materials

TL;DR

This paper develops a systematic approach to calculate strain-displacement relations in 2D materials, revealing corrections for non-Bravais lattices and their impact on electronic properties like pseudo-magnetic fields.

Contribution

It introduces a general method for strain-displacement calculations in 2D materials, with applications to graphene, highlighting corrections to existing theories and their effects on electromechanical coupling.

Findings

Corrected strain-displacement relations for non-Bravais lattices.

Good agreement between models and Dirac equation predictions.

Strain-induced pseudo-magnetic field renormalization.

Abstract

We investigate the electromechanical coupling in 2d materials. For non-Bravais lattices, we find important corrections to the standard macroscopic strain - microscopic atomic-displacement theory. We put forward a general and systematic approach to calculate strain-displacement relations for several classes of 2d materials. We apply our findings to graphene as a study case, by combining a tight binding and a valence force-field model to calculate electronic and mechanical properties of graphene nanoribbons under strain. The results show good agreement with the predictions of the Dirac equation coupled to continuum mechanics. For this long wave-limit effective theory, we find that the strain-displacement relations lead to a renormalization correction to the strain-induced pseudo-magnetic fields. Implications for nanomechanical properties and electromechanical coupling in 2d materials are discussed.