Excitonic BCS-BEC crossover at finite temperature: Effects of repulsion and electron-hole mass difference

Abstract

The BCS to Bose-Einstein condensation (BEC) crossover of electron-hole $(e\text{\ensuremath{-}}h)$ pairs in optically excited semiconductors is studied using the two-band Hubbard model with both repulsive and attractive interactions. Applying the self-consistent $t$-matrix approximation combined with a local approximation, we examine the properties of a normal phase and an excitonic instability. The transition temperature from the normal phase to an $e\text{\ensuremath{-}}h$ pair condensed one is studied to clarify the crossover from an $e\text{\ensuremath{-}}h$ BCS-like state to an excitonic Bose-Einstein condensation, which takes place on increasing the $e\text{\ensuremath{-}}h$ attraction strength. To investigate effects of the repulsive interaction and the $e\text{\ensuremath{-}}h$ mass difference, we calculate the transition temperature for various parameters of the interaction strengths, the $e\text{\ensuremath{-}}h$ particle density, and the mass difference. While the transition temperature in the $e\text{\ensuremath{-}}h$ BCS regime is sufficiently suppressed by the repulsive interaction, that of the excitonic BEC is largely insensitive to it. We also show quantitatively that in the whole regime the mass difference leads to large suppression of the transition temperature.