Graphene on hexagonal lattice substrate: Stress and Pseudo-magnetic field

TL;DR

This paper predicts moiré patterns in strain and pseudo-magnetic fields in graphene on a hexagonal substrate, showing how misorientation and adhesion control these effects and can induce an energy gap consistent with experiments.

Contribution

It introduces a theoretical model linking substrate-induced deformations to tunable pseudo-magnetic fields and energy gaps in graphene.

Findings

Moiré patterns in strain and pseudo-magnetic fields are predicted.

Pseudo-magnetic field periodicity can be tuned by misorientation angle.

A significant energy gap (~23 meV) is induced by out-of-plane deformation.

Abstract

Moir'e patterns in the pseudo-magnetic field and in the strain profile of graphene (GE) when put on top of a hexagonal lattice substrate are predicted from elasticity theory. %which are confirmed by atomistic simulations. The van der Waals (vdW) interaction between GE and the substrate induces out-of-plane deformations in graphene which results in a strain field, and consequently in a pseudo-magnetic field. When the misorientation angle is about 0.5 deg. a three-fold symmetric strain field is realized that results in a pseudo-magnetic field very similar to the one proposed by F. Guinea, M. I. Katsnelson, and A. K. Geim [Nat. Phys. 6, 30 (2010)]. Our results show that the periodicity and length of the pseudo-magnetic field can be tuned in GE by changing the misorientation angle and substrate adhesion parameters and a considerable energy gap (23 meV) can be obtained due to out-of-plane deformation of graphene which is in the range of recent experimental measurements (20-30 meV).