Thermal properties of Dirac fermions in Xenes: Model studies

The thermal properties and the electrical conductance are studied for 2D electron gases in doped Xenes -- graphene, silicene, germanene, stanene, and plumbene -- applying a four-band model to describe the low-energy Dirac-fermion-like electronic excitations. Spin-orbit interactions to discriminate the five Xenes and the influence of an electric field in the normal direction, are taken into account. The density of states and the spectral behavior of the current-current correlation function allow the calculation of the Onsager coefficients. They give analytical formulas for the electronic contributions to the heat capacity and thermal conductance. Also, the electrical conductance can be described within the same framework, if the scattering properties of the electron gases are simulated by constant broadening parameters. For all these thermal and transport properties, only a weak variation with the Xene is found, because of their small spin-orbit-induced gaps, with the exception of plumbene. The heat capacity of Xenes does not show a Schottky anomaly. The thermal conductance increases linearly or quadratically with temperature depending on the temperature range. A similar behavior characterizes the electrical conductance. The dominance of Dirac fermions, i.e., linear bands, determines the ratio of electron thermal conductance and electric conductance, which depends on doping level and temperature. It violates the Wiedemann-Franz law known for 3D electron gases with parabolic energy-momentum dispersion. The Lorenz number is generally much larger for 2D electron gases with almost Dirac character of the dispersion relation.