We study dilute two-dimensional systems of interacting excitons with a moat dispersion, whose ground-state manifold consists of a set of discrete or continuously degenerate energy minima. At low densities and in the presence of contact interactions, it is known that the bosons can undergo statistical transmutation and give rise to a chiral spin liquid. Here, we show that long-range interactions such as those expected in excitonic systems introduce a rich competition between the chiral spin liquid and different kinds of Bose-Einstein condensates. The moat dispersion can favor Bose-Einstein condensation into states occupying multiple momenta, leading to inhomogeneous and supersolid phases with a highly anisotropic superfluid response. We demonstrate that a proper $T$ -matrix renormalization of the exciton-exciton interaction is essential for describing these phases and show that they can arise even from purely repulsive interactions. This formalism is employed to obtain the phase diagram of competing homogeneous and stripe condensates with the chiral spin liquid in an electron-hole bilayer model. In addition, we show how the $T$ matrix enters the familiar Gross-Pitaevskii framework and map out extended phase diagrams within a pseudopotential approximation. We place our findings in the context of real excitonic systems by discussing the roles of finite lifetimes, disorder, band-structure warping, and nonzero temperatures. We conclude that moat bands can drive Bose-Einstein condensation and supersolidity already at weak coupling, in contrast to the case of a standard parabolic dispersion.We study dilute two-dimensional systems of interacting excitons with a moat dispersion, whose ground-state manifold consists of a set of discrete or continuously degenerate energy minima. At low densities and in the presence of contact interactions, it is known that the bosons can undergo statistical transmutation and give rise to a chiral spin liquid. Here, we show that long-range interactions such as those expected in excitonic systems introduce a rich competition between the chiral spin liquid and different kinds of Bose-Einstein condensates. The moat dispersion can favor Bose-Einstein condensation into states occupying multiple momenta, leading to inhomogeneous and supersolid phases with a highly anisotropic superfluid response. We demonstrate that a proper $T$-matrix renormalization of the exciton-exciton interaction is essential for describing these phases and show that they can arise even from purely repulsive interactions. This formalism is employed to obtain the phase diagram of competing homogeneous and stripe condensates with the chiral spin liquid in an electron-hole bilayer model. In addition, we show how the $T$ matrix enters the familiar Gross-Pitaevskii framework and map out extended phase diagrams within a pseudopotential approximation. We place our findings in the context of real excitonic systems by discussing the roles of finite lifetimes, disorder, band-structure warping, and nonzero temperatures. We conclude that moat bands can drive Bose-Einstein condensation and supersolidity already at weak coupling, in contrast to the case of a standard parabolic dispersion.

cond-mat.quant-gasCross-listedarXiv:2602.18194Feb 23, 2026

Bose-Einstein Condensation of Excitons

Claude Benoit à la Guillaume, Erio Tosatti

Europhysics newsJan 1, 19740 citations

Bose-Einstein Condensation of Excitons and Biexcitons

S. A. Moskalenko, David W. Snoke

Feb 1, 2000114 citations

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

Yuh Tomio, Kotaro Honda, Tetsuo Ogawa

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.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.

arXiv:cond-mat/0606100Physical Review BJun 12, 200628 citations

Bose-Einstein condensation of excitons

Paul H. M. van Loosdrecht, D. van der Marel, K. Karpińska

Jan 1, 20030 citations

T

-matrix renormalization of the exciton-exciton interaction is essential for describing these phases and show that they can arise even from purely repulsive interactions. This formalism is employed to obtain the phase diagram of competing homogeneous and stripe condensates with the chiral spin liquid in an electron-hole bilayer model. In addition, we show how the

T

matrix enters the familiar Gross-Pitaevskii framework and map out extended phase diagrams within a pseudopotential approximation. We place our findings in the context of real excitonic systems by discussing the roles of finite lifetimes, disorder, band-structure warping, and nonzero temperatures. We conclude that moat bands can drive Bose-Einstein condensation and supersolidity already at weak coupling, in contrast to the case of a standard parabolic dispersion.

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.