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International Journal of Modern Physics B

FIRST-ORDER PAIRING TRANSITION AND PHASE SEPARATION IN THE ATTRACTIVE HUBBARD MODEL

Massimo Capone, Claudio Castellani, M. Grilli

Published Mar 10, 2003• 0 citations
Publisher

Abstract

The normal state properties of the Hubbard model are studied by means of the Dynamical Mean-Field Theory. Even in the gauge-symmetric subspace, a first-order transition occurs between a Fermi-liquid phase and a strong-coupling bound-pairs phase, which can be thought as a "disordered" superconductor. The transition is of first order for all densities different from n = 1, and it is accompanied by a region of phase separation between the two phases at different densities.

DOI
10.1142/s0217979203016285

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The normal state properties of the Hubbard model are studied by means of the Dynamical Mean-Field Theory. Even in the gauge-symmetric subspace, a first-order transition occurs between a Fermi-liquid phase and a strong-coupling bound-pairs phase, which can be thought as a "disordered" superconductor. The transition is of first order for all densities different from n = 1, and it is accompanied by a region of phase separation between the two phases at different densities.
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.
The finite-temperature phase diagram of the attractive Hubbard model is studied by means of the dynamical mean-field theory. We first consider the normal phase of the model by explicitly frustrating the superconducting ordering. In this case, we obtain a first-order pairing transition between a metallic phase and a paired phase formed by strongly coupled incoherent pairs. The transition line ends in a finite temperature critical point, but a crossover between two qualitatively different solutions still occurs at higher temperature. Comparing the superconducting- and the normal-phase solutions, we find that the superconducting instability always occurs before the pairing transition in the normal phase, i.e. T c > T pairing . Nevertheless, the high-temperature phase diagram at T > T c is still characterized by a crossover from a metallic phase to a preformed pair phase. We characterize this crossover by computing different observables that can be used to identify the pseudogap region, like the spin susceptibility, the specific heat and the single-particle spectral function.
We study the normal (non-superconducting) phase of attractive Hubbard model within dynamical mean field theory (DMFT) using numerical renormalization group (NRG) as impurity solver. Wide range of attractive potentials UUU is considered, from the weak-coupling limit, where superconducting instability is well described by BCS approximation, up to the strong-coupling region, where superconducting transition is described by Bose-condensation of compact Cooper pairs, which are formed at temperatures much exceeding superconducting transition temperature. We calculate density of states, spectral density and optical conductivity in the normal phase for this wide range of UUU, including the disorder effects. Also we present the results on superconducting instability of the normal state dependence on the attraction strength UUU and the degree of disorder. Disorder influence on the critical temperature TcT_cTc​ is rather weak, suggesting in fact the validity of Anderson theorem, with the account of the general widening of the conduction band due to disorder.
We study the normal (nonsuperconducting) phase of the attractive Hubbard model within the dynamical mean field theory (DMFT) using the numerical renormalization group (NRG) as an impurity solver. A wide range of attractive potentials U is considered, from the weak-coupling limit, where superconducting instability is well described by the BCS approximation, to the strong-coupling region, where the superconducting transition is described by Bose condensation of compact Cooper pairs, which are formed at temperatures much exceeding the superconducting transition temperature. We calculate the density of states, the spectral density, and the optical conductivity in the normal phase for this wide range of U, including the disorder effects. We also present the results on superconducting instability of the normal state dependence on the attraction strength U and the degree of disorder. The disorder influence on the critical temperature T c is rather weak, suggesting in fact the validity of Anderson’s theorem, with the account of the general widening of the conduction band due to disorder.
We study the normal (non-superconducting) phase of attractive Hubbard model within dynamical mean field theory (DMFT) using numerical renormalization group (NRG) as impurity solver. Wide range of attractive potentials UUU is considered, from the weak-coupling limit, where superconducting instability is well described by BCS approximation, up to the strong-coupling region, where superconducting transition is described by Bose-condensation of compact Cooper pairs, which are formed at temperatures much exceeding superconducting transition temperature. We calculate density of states, spectral density and optical conductivity in the normal phase for this wide range of UUU, including the disorder effects. Also we present the results on superconducting instability of the normal state dependence on the attraction strength UUU and the degree of disorder. Disorder influence on the critical temperature TcT_cTc​ is rather weak, suggesting in fact the validity of Anderson theorem, with the account of the general widening of the conduction band due to disorder.