Graphene: from point defects to tunable twins

I will begin with a brief account of the computational methodology used in calculations. We divide
calculations into three main steps: a first harmonic step aimed at building a pattern of defects into the
lattice followed by a fully-nonlinear relaxation, and as a final step we investigate charge-carrier
transmission across the structures that spontaneously arise in the graphene layer. Then, I will evaluate a
number of point defect configurations in monolayer graphene and document different accommodation
mechanisms. Finally, I will show 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.