Carrier concentrations and optical conductivity of a band-inverted semimetal in two and three dimensions

Here we study the single-particle, electronic transport and optical properties of a gapped system described by a simple two-band Hamiltonian with inverted valence bands. We analyze its properties in the three-dimensional (3D) and the two-dimensional (2D) case. The insulating phase changes into a metallic phase when the band gap is set to zero. The metallic phase in the 3D case is characterized by a nodal surface. This nodal surface is equivalent to a nodal ring in two dimensions. Within a simple theoretical framework, we calculate the density of state, the total and effective charge carrier concentration, the Hall concentration and the Hall coefficient, for both 2D and 3D cases. The main result is that the three concentrations always differ from one another in the present model. These concentrations can then be used to resolve the nature of the electronic ground state. Similarly, the optical conductivity is calculated and discussed for the insulating phase. We show that there are no optical excitations in the metallic phase. Finally, we compare the calculated optical conductivity with the rule-of-thumb derivation using the joint density of states.