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

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 $\mathrm{TmS}{\mathrm{e}}_{0.45}\mathrm{T}{\mathrm{e}}_{0.55}$.

16 pages, 8 figures, revised version, including a short discussion of electron-hole liquids vs. excitonic phases

References in corpus (3)

• BCS-BEC crossover at finite temperature in the broken-symmetry phase
• Models of coherent exciton condensation
• Coherent transport in homojunction between excitonic insulator and semimetal

Cited by in corpus (6)

• Evidence for an excitonic insulator phase in 1T-TiSe${}_2$
• Spontaneous exciton condensation in 1T-TiSe2: a BCS-like approach
• Critical Temperature Curve in the BEC-BCS Crossover
• Bound state formation and nature of the excitonic insulator phase in the extended Falicov-Kimball model
• Correlation effects in partially ionized mass asymmetric electron-hole plasmas
• Generalizing Planck's Law: Nonequilibrium Emission of Excited Media