Lattice symmetries, spectral topology and opto-electronic properties of graphene-like materials

The topology of the band structure, which is determined by the lattice symmetries, has a strong influence on the transport properties. Here we consider an anisotropic honeycomb lattice and study the effect of a continuously deformed band structure on the optical conductivity and on diffusion due to quantum fluctuations. In contrast to the behavior at an isotropic node we find super- and subdiffusion for the anisotropic node. The spectral saddle points create van Hove singularities in the optical conductivity, which could be used to characterize the spectral properties experimentally.