Optical Properties of the $\alpha$-$T_3$ Model

The $\alpha$-$T_3$ model, recently introduced by Raoux et. al [1], provides a continuous evolution between the honeycomb lattice of graphene and the $T_3$ or dice lattice. It is characterized by a variable Berry phase that changes continuously from $\pi$ to $0$. We present our calculations of optical properties of the $\alpha$-$T_3$ model, including the Hall quantization and optical conductivity, with an emphasis on the effect of the variable Berry’s phase of the model. In particular, we describe the continuous evolution of the Hall quantization from a relativistic to a non-relativistic regime. \newline [1] A. Raoux, M. Morigi, J.-N. Fuchs, F. Piechon, and G. Montambaux, Phys. Rev. Lett. 112, 026402 (2014)