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-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-h pair condensed one is studied to clarify the crossover from an e-h BCS-like state to an excitonic Bose-Einstein condensation, which takes place on increasing the e-h attraction strength. To investigate effects of the repulsive interaction and the e-h mass difference, we calculate the transition temperature for various parameters of the interaction strengths, the e-h particle density, and the mass difference. While the transition temperature in the e-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.

Exciton Mott transition and quantum condensation in electron‐hole systems

“…Electrons and holes in solids involve not only the e-h attractive Coulomb interaction U but also the repulsive n=0.25 Figure 5 The condensation temperature T c as a function of U for U = 0, 1, and 2 at n = 0.25 and γ ≡ t h /t e = 1 [12]. The dotted line denotes the result from the BCS theory.…”

Two-Band Model for Coherent Excitonic Condensates

“…(15) indicates that the phase stiffness in the system of excitonic pairs is characterized by an energy scale proportional to ∆t e t h /(t e + t h ) for all the values of the Coulomb interaction parameter U and it is related to the motion of the center of mass of e-h composed quasiparticle, because t e t h /(t e + t h ) ≈ (m e + m h ) −1 [9] implying that the exchange coupling parameter becomes proportional to the excitonic BEC critical temperature [9,19]. The numerical evaluations of J for the case T = 0 are shown in Fig.…”

“…[9], where it is shown that the excitonic insulator state is an excitonium state, where the incoherent e-h bound pairs are formed, and furthermore, at lower temperatures, the BEC of excitons appears in consequence of reconfiguration and coherent condensation of the preformed excitonic pairs. In the whole BCS-BEC transition region the e-h mass difference leads to a large suppression of the BEC transition temperature, which is proved to be not the same as the excitonic pair formation temperature [9].…”

“…The low density system of excitons behaves like the usual Bose gas, while the high density system of bound e-h pairs behaves like the system of weakly coupled Cooper pairs. Thus the resulting BCS-BEC crossover [9][10][11][12][13][14] represents an interesting theoretical problem typical for the excitonic systems.…”

Superfluidity and density order in a bilayer extended Hubbard model

“…[13]. The inclusion of an interlayer or interband interaction opens the possibility of exciton formation and condensation, which has been studied using determinantal Monte Carlo simulations [14], exact diagonalization [15], DMFT [16,17], and various other theoretical approaches [18,19].…”