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

Abstract

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.

Signatures of merging Dirac points in optics and transport

“…3 are for comparison with our merging Dirac points model and are for the semi-Dirac limit. 37 In this model, the dependence on Ω goes as 35,37 . The dashed black horizontal lines apply to the pure Dirac limit discussed in the text and agree perfectly with the solid lines at small Ω/2∆.…”

“…For the semi-Dirac limit, we get 2.66 for xx and 1. 35 for yy, again shown as purple dashed curves aroundT = 5. This holds for anyT in semi-Dirac.…”

“…The thermal conductivity κ(T ) as a function of temperature T or more precisely κ xx (T )/T and κ yy (T )/T follows from Eqs. (35) and (36) with an additional factor of (ω/T ) 2 included in the integration overω and the factor of electric charge squared is dropped. The Lorenz number L(T ) is related in the usual way to σ dc (T ) and κ(T )/T and is given by…”

“…For the numerical evaluation of Eqs. (35) to (37), it is convenient to introduce new functions G xx 1 (T ) and G xx 2 (T ) and equivalent quantities for the yy direction with…”

“…In one direction, the band structure is "relativistic" (energy is linear in momentum), while in the other it is "nonrelativistic" (energy is quadratic in momentum). Ziegler et al 35 have considered the optical conductivity within a tight-binding model which includes a high energy van Hove singularity. They also discuss the diffusion regime.…”