  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.
