Two-Band Model for Coherent Excitonic Condensates

We consider the excitonic correlations in the two-band solid state system composed of the valence band and conduction band electrons. We treat the phase coherence mechanism in the system by presenting the electron operator as a fermion attached to the U(1) phase-flux tube. The emergent bosonic gauge field, related to the phase variables appears to be crucial for the coherent Bose-Einstein condensation of excitons. We calculate the normal excitonic Green functions, and the single-particle density of states functions being a convolution between bosonic and fermionic counterparts. We obtain the total density of states as a sum of two independent parts. For the coherent normal fermionic density of states, there is no hybridization-gap found in the system due to strong coherence effects and phase stiffness.