Semi-metal insulator phase transitions in graphene - the role of anisotropy

Abstract

Graphene is an interesting system for condensed matter physicists because of many potential technological applications. It is interesting to theorists as an abelian strongly coupled system that has some of the interesting properties of QCD. We are particularly interested in studying the effects of anisotropic strain of the graphene lattice on the critical coupling, which determines the transition point for graphene from a conductor to an insulator. We use a low energy effective theory and a Schwinger-Dyson approach. The full set of coupled equations is numerically very difficult to solve, and so previous calculations have made many simplifying assumptions in order to make the procedure tractable. These simplifications have led to disagreement about the effect anisotropy has on the critical coupling constant. We have studied the effect of some common approximations including polarization tensor approximations and vertex ansaetze. In this talk we discuss the motivation for several of these approximations, and show that in some cases their effect on the critical coupling is significant. We discuss more accurate ways to solve the non-perturbative low energy effective theory, and its ability to predict the critical coupling of the phase transition.