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AIP conference proceedings

Exciton Mott Transition and Pair Condensation in Electron-Hole Systems: Dynamical Mean-Field Theory

Yuh Tomio, Tetsuo Ogawa

Published Jan 1, 2006• 3 citations
Publisher

Abstract

The exciton Mott transition and electron‐hole (e‐h) pair condensation are studied using a two‐band Hubbard model with both repulsion and attraction. With the use of the dynamical mean‐field theory, we clarify the phase diagram for the phase transitions at zero and finite temperatures. Away from half‐filling we find an exciton insulating phase, which is followed by the formation of incoherent e‐h pairs, and the first‐order transition between a metallic phase and the exciton insulating phase. We also examine the transition temperature to an e‐h pair condensed phase where BEC‐BCS crossover takes place, and discuss characteristic features of the finite‐temperature phase diagram.

DOI
10.1063/1.2355190

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The exciton Mott transition and electron‐hole (e‐h) pair condensation are studied using a two‐band Hubbard model with both repulsion and attraction. With the use of the dynamical mean‐field theory, we clarify the phase diagram for the phase transitions at zero and finite temperatures. Away from half‐filling we find an exciton insulating phase, which is followed by the formation of incoherent e‐h pairs, and the first‐order transition between a metallic phase and the exciton insulating phase. We also examine the transition temperature to an e‐h pair condensed phase where BEC‐BCS crossover takes place, and discuss characteristic features of the finite‐temperature phase diagram.
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 ttt-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.
We study the optical properties of an electron–hole two-band Hubbard model with interactions of electron–electron (hole–hole) repulsion U and electron–hole attraction U '. In the case of two types of correlated insulators at half filling, viz. , the Mott–Hubbard type and the biexciton type, interband linear absorption/gain spectra including excitonic effects are calculated analytically using two-site dynamical mean-field theory and ladder approximation. We show that an exciton-like peak structure emerges because of an “exciton” in the sea of correlated fermions when U ' is larger than a certain critical value. The binding energy of the photoinduced excitonic bound state and the spectral intensity are evaluated as a function of U '. The emergence and absence of the exciton-like peak suggests that there are two different insulating mechanisms in the Mott–Hubbard insulating state of the electron–hole system: one is attributable to only U and the other is attributable to both U and U '; the latter is called the excitonic Mott–Hubbard insulating state. The intrinsic difference of the mechanisms cannot be captured from only single-particle properties such as the density of states, but it appears clearly in optical properties reflecting two-particle correlations.
The ground-state phase diagram of the half-filled repulsive Hubbard model in a bilayer is investigated using cluster dynamical mean-field theory. For weak to intermediate values of Coulomb repulsion UUU, the system undergoes a transition from a Mott-insulating phase to a metallic phase and then onto a band-insulating phase as the interlayer hopping is increased. In the strong-coupling case, the model exhibits a direct crossover from a Mott-insulating phase to a band-insulating phase. These results are robust with respect to the presence or absence of magnetic order.
A dynamical mean-field theory analysis of the attractive Hubbard model in the normal phase is carried out upon restricting to solutions where superconducting order is not allowed. A clear first-order pairing transition as a function of the coupling takes place at all the electron densities out of half filling between a Fermi liquid, stable for U<U(c), and an insulating bound pairs phase for U>U(c), and it is accompanied by phase separation. The spectral function in the metallic phase is constituted by a low-energy structure around the Fermi level, which disappears discontinuously at U = U(c), and two high-energy features (Hubbard bands), which persist in the insulating phase.
Using the dynamical mean-field approximation we investigate the formation of excitonic condensate in the two-band Hubbard model in the vicinity of the spin-state transition. With temperature and band filling as the control parameters we realize all symmetry allowed spin-triplet excitonic phases, some exhibiting a ferromagnetic polarization. While the transitions are first order at low temperatures, at elevated temperatures continuous transitions are found that give rise to a multicritical point. Rapid but continuous transition between ferromagnetic and nonmagnetic excitonic phases allows switching of uniform magnetization by small changes of chemical potential.
We study the electron-hole pair (or excitonic) condensation in the extended Falicov-Kimball model at finite temperatures based on the cluster mean-field-theory approach, where we make the grand canonical exact-diagonalization analysis of small clusters using the sine-square deformation function. We thus calculate the ground-state and finite-temperature phase diagrams of the model, as well as its optical conductivity and single-particle spectra, thereby clarifying how the preformed pair states appear in the strong-coupling regime of excitonic insulators. We compare our results with experiment on Ta2_22​NiSe5_55​.