Lie symmetries and 2D Material Physics

Abstract

Inspired from Lie symmetry classification, we establish a correspondence between rank two Lie symmetries and 2D material physics. The material unit cell is accordingly interpreted as the geometry of a root system. The hexagonal cells, appearing in graphene like models, are analyzed in some details and are found to be associated with A_2 and G_2 Lie symmetries. This approach can be applied to Lie supersymmetries associated with fermionic degrees of freedom. It has been suggested that these extended symmetries can offer a new way to deal with doping material geometries. Motivated by Lie symmetry applications in high energy physics, we speculate on a possible connection with (p,q) brane networks used in the string theory compactification on singular Calabi-Yau manifolds.