Nonlocal Optical Response in Topological Phase Transitions in the Graphene Family*

We investigate the electromagnetic response of staggered two-dimensional materials of the graphene family, including graphene, silicene, germanene, and stanene, as they are driven through various topological phase transitions using external fields. Utilizing Kubo formalism, we compute their optical conductivity tensor taking into account the frequency and wave vector of the electromagnetic excitations, and study its behavior over the full electronic phase diagram of the materials. We compute the Plasmon dispersion relation for different phases.