Optical conductivity of graphene with second-nearest neighbors coupling

Optical transparency experiments show that optical conductivity depends on the fine structure constant, as it can be fully explained within the effective theory of two-dimensional relativistic Dirac fermions. In this work, we investigate how this property is affected by second-nearest-neighbors coupling t’. Within a field theoretical representation in the continuum approximation arising from an underlying tight- binding atomistic model, we obtain the dependence of the optical conductivity on frequency, temperature and finite chemical potential. We investigated the model in the Keldysh contour representation at zero temperature[1], as well as in Matsubara space for finite temperature and chemical potential[2]. Our results reproduce the universal and experimentally verified value at zero frequency and, more importantly, they reveal that a small but still measurable shift in the conductance minimum at finite temperatures arises as a function of the second-nearest neighbors hopping t’, thus providing the possibility to directly measure this parameter in transport experiments.

References:

[1] H. Falomir, M. Loewe, E. Muñoz, and A. Raya, PHYS.L REV. B 98, 195430 (2018)
[2] H. Falomir, E. Muñoz, M. Loewe, and R. Zamora, Submitted (2019).