On the possibility of an excitonic insulator at the semiconductor-semimetal transition

TL;DR

This paper investigates the conditions under which an excitonic insulator can form at the pressure-induced semiconductor-semimetal transition, providing a theoretical framework for critical temperature and exciton condensation.

Contribution

It develops a model linking pressure-controlled energy gaps to excitonic insulator formation, including effects of mass asymmetry and BEC-BCS crossover behavior.

Findings

Critical temperature depends on pressure and energy gap.

Mass asymmetry suppresses BCS pairing.

Strong coupling regime aligns with BEC transition temperatures.

Abstract

We calculate the critical temperature below which an excitonic insulator exists at the pressure-induced semiconductor-semimetal transition. Our approach is based on an effective-mass model for valence and conduction band electrons interacting via a statically screened Coulomb potential. Assuming pressure to control the energy gap, we derive, in the spirit of a BEC-BCS crossover scenario, a set of equations which determines, as a function of the energy gap (pressure), the chemical potentials for the two bands, the screening wave number, and the critical temperature. We (i) show that in leading order the chemical potentials are not affected by the exciton states, (ii) verify that on the strong coupling (semiconductor) side the critical temperatures obtained from the linearized gap equation coincide with the transition temperatures for BEC of non-interacting bosons, (iii) demonstrate that mass asymmetry strongly suppresses BCS-type pairing, and (iv) discuss in the context of our theory recent experimental claims for exciton condensation in ${\rm TmSe_{0.45}Te_{0.55}}$.