Transition to an excitonic insulator from a two-dimensional conventional insulator

In this paper, first, we present a general formulation to investigate the ground-state and elementary excitations of an excitonic insulator (EI) in real materials. In addition, we discuss the out-of-equilibrium state induced (albeit transiently) by high-intensity light illumination of a conventional two-dimensional (2D) insulator. We then, present various band-structure models which allow us to study the transition from a conventional insulator to an EI in 2D materials as a function of the dielectric constant, the conventional insulator gap (and chemical potential), the bandwidths of the conduction and valence bands and the Bravais lattice unit-cell size. One of the goals of this investigation is to determine which range of these experimentally determined parameters to consider in order to find the best candidate materials to realize the excitonic insulator. The numerical solution to the EI gap equation for various band-structures shows a significant and interesting momentum-dependence of the EI gap function $\Delta(\vec k)$ and of the zero-temperature electron and hole momentum-distribution across the Brillouin zone. Last, we discuss that these features can be detected by tunneling microscopy