Strain-tuning of transport gaps and semiconductor-to-conductor phase transition in twinned graphene

Abstract

We show, through the use of the Landauer-Büttiker (LB) formalism and a tight-binding (TB) model, that the transport gap of twinned graphene can be tuned through the application of a uniaxial strain in the direction normal to the twin band. Remarkably, we find that the transport gap Egap bears a square-root dependence on the control parameter ϵx−ϵc, where ϵx is the applied uniaxial strain and ϵc∼19% is a critical strain. We interpret this dependence as evidence of criticality underlying a continuous phase transition, with ϵx−ϵc playing the role of control parameter and the transport gap Egap playing the role of order parameter. For ϵx<ϵc, the transport gap is non-zero and the material is semiconductor, whereas for ϵx>ϵc the transport gap closes to zero and the material becomes conductor, which evinces a semiconductor-to-conductor phase transition. The computed critical exponent of 1/2 places the transition in the meanfield universality class, which enables far-reaching analogies with other systems in the same class.