Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review B

Pseudogap phase in strongly disordered conventional superconductors

Xintian Wu, Ryusuke Ikeda

Published Mar 24, 2011• 7 citations
Publisher

Abstract

Excited states of Bogoliubov--de Gennes equations are examined for a two-dimensional negative-$U$ Hubbard Hamiltonian with on-site disorder. It is shown explicitly that the temperature (pseudogap temperature) when the superconducting gap opens is different from that (the superconducting transition temperature) where the long-range order appears. In the excited-state solutions the system is self-organized into blocks, which behave like superspins and are coupled with their neighbors. Only if the couplings between these blocks become strong enough can the true long-range order be realized.

DOI
10.1103/physrevb.83.104517

Related papers

DISORDERED SUPERCONDUCTORS: A SIMPLE MODEL MANIFESTING PSEUDOGAP AND BCS-BEC CROSSOVER

Poulumi Dey, Saurabh Basu

The effect of random on-site disorder on s-wave (BCS) superconductors described by a two dimensional negative-U Hubbard model is studied using Bogoliubov-de Gennes (BdG) method. The mean field pairing amplitudes become spatially inhomogeneous at large values of disorder where the system breaks up into superconducting islands with large pairing amplitudes, separated by insulating strips. The amplitude fluctuations are correctly accounted for via BdG calculations, however it misses phase fluctuations which are inherent to low dimensions. The phase fluctuations affect superconducting properties strongly, and the effect is more pronounced in the limit of large disorder. We provide a close estimate of the actual transition temperature, Tcby incorporating phase fluctuations about the inhomogeneous BdG state. This is obtained by relating the jump in renormalized Ds(obtained from a self consistent Harmonic approximation on a phase-only Hamiltonian) at the Kosterlitz-Thouless (KT) transition and the KT transition temperature, TKTobtained from Ds(T) = (2/π)TKTas temperature tends to TKTfrom below. This yields opening of a large region sandwiched between [Formula: see text] (obtained by the vanishing of [Formula: see text]) and TKTwhere there is no phase coherence between the pairs, however amplitude correlations continue to exist, reminiscent of a pseudogap phase in high-Tcsuperconductors which is marked by short ranged preformed pairs without any definite phase relation between them. Further, the appearance of the superconducting islands from a homogeneous phase indicates the evolution of a system consisting of large and overlapping pairs to one that contains short and tightly bound pairs - a scenario termed as BCS-BEC crossover. We have investigated in details the crossover phenomenon as a function of disorder and confirmed it's existence at small values of electron concentration, however, absent at larger densities.

International Journal of Modern Physics B•Aug 20, 2009•1 citation

Superconductivity and the Pseudogap in the Two-Dimensional Hubbard Model

Emanuel Gull, Olivier Parcollet, Andrew J. Millis

Recently developed numerical methods have enabled the explicit construction of the superconducting state of the Hubbard model of strongly correlated electrons in parameter regimes where the model also exhibits a pseudogap and a Mott insulating phase. d(x(2)-y(2)) symmetry superconductivity is found to occur in proximity to the Mott insulator, but separated from it by a pseudogapped nonsuperconducting phase. The superconducting transition temperature and order parameter amplitude are found to be maximal at the onset of the normal-state pseudogap. The emergence of superconductivity from the normal state pseudogap leads to a decrease in the excitation gap. All of these features are consistent with the observed behavior of the copper-oxide superconductors.

arXiv:1207.2490•Physical Review Letters•May 22, 2013•318 citations

Evolution of the Density of States Gap in a Disordered Superconductor

Carey Huscroft, Richard T. Scalettar

We determine the effect of a random potential on the density of states $N(\ensuremath{\omega})$ in the attractive Hubbard model. At weak coupling, disorder closes the gap concurrently with the destruction of superconductivity. At larger, but still intermediate coupling, a pseudogap in $N(\ensuremath{\omega})$ remains beyond the point at which off-diagonal long range order vanishes. This change in the elementary excitations of the insulating phase corresponds to a crossover between Fermi and Bose insulators.

arXiv:cond-mat/9804122•Physical Review Letters•Sep 28, 1998•32 citations

Interplay of superconductivity and spin-dependent disorder

Ravindra Nanguneri, Mi Jiang, Tyler Cary +2 more

The finite-temperature phase diagram for the two-dimensional attractive fermion Hubbard model with spin-dependent disorder is considered within Bogoliubov--de Gennes mean-field theory. Three types of disorder are studied. In the first, only one species is coupled to a random site energy; in the second, the two species both move in random site energy landscapes which are of the same amplitude but different realizations; and finally, in the third, the disorder is in the hopping rather than the site energy. For all three cases, we find that, unlike the case of spin-symmetric randomness, where the energy gap and average order parameter do not vanish as the disorder strength increases, a critical disorder strength exists separating distinct phases. In fact, the energy gap and the average order parameter vanish at distinct transitions, ${V}_{c}^{\mathrm{gap}}$ and ${V}_{c}^{\mathrm{op}}$, allowing for a gapless superconducting (gSC) phase. The gSC phase becomes smaller with increasing temperature until it vanishes at a temperature ${T}^{*}$.

arXiv:1308.2200•Physical Review B•Apr 9, 2012•12 citations

Phase Fluctuations in Strongly Coupled d -Wave Superconductors

Matthias Mayr, Gonzalo Álvarez, Cengiz Şen +1 more

We present a numerically exact solution for the BCS Hamiltonian at any temperature, including the degrees of freedom associated with classical phase, as well as amplitude fluctuations via a Monte Carlo integration. This allows for an investigation over the whole range of couplings: from weak attraction, as in the well-known BCS limit, to the mainly unexplored strong-coupling regime of pronounced phase fluctuations. In the latter, two characteristic temperatures T(*) and T(c), associated with short- and long-range ordering, respectively, can be identified in a mean-field-motivated Hamiltonian. T(*) at the same time corresponds to the opening of a gap in the excitation spectrum. In addition to introducing a novel procedure to study strongly coupled d-wave superconductors, our results indicate that classical phase fluctuations are not sufficient to explain the pseudogap features of high-temperature superconductors.

arXiv:cond-mat/0511023•Physical Review Letters•Jun 3, 2005•59 citations

Superfluid Density and Phase Relaxation in Superconductors with Strong Disorder

G. Seibold, Lara Benfatto, Claudio Castellani +1 more

We consider the attractive Hubbard model with on-site disorder as a prototype of a disordered superconductor. We solve the Bogoliubov-de Gennes equations on two-dimensional finite clusters at zero temperature and evaluate the electromagnetic response to a vector potential. We find that the standard decoupling between transverse and longitudinal response does not apply in the presence of disorder. Moreover, the superfluid density is strongly reduced by the relaxation of the phase of the order parameter already at mean-field level when disorder is large. We also find that the anharmonicity of the phase fluctuations is strongly enhanced by disorder. Beyond mean field, this provides an enhancement of quantum fluctuations inducing a zero-temperature transition to a nonsuperconducting phase of disordered preformed pairs. Finally, the connection of our findings with the glassy physics for extreme dirty superconductors is discussed.

arXiv:1107.3839•Physical Review Letters•May 17, 2012•60 citations
Excited states of Bogoliubov--de Gennes equations are examined for a two-dimensional negative-UUU Hubbard Hamiltonian with on-site disorder. It is shown explicitly that the temperature (pseudogap temperature) when the superconducting gap opens is different from that (the superconducting transition temperature) where the long-range order appears. In the excited-state solutions the system is self-organized into blocks, which behave like superspins and are coupled with their neighbors. Only if the couplings between these blocks become strong enough can the true long-range order be realized.
The effect of random on-site disorder on s-wave (BCS) superconductors described by a two dimensional negative-U Hubbard model is studied using Bogoliubov-de Gennes (BdG) method. The mean field pairing amplitudes become spatially inhomogeneous at large values of disorder where the system breaks up into superconducting islands with large pairing amplitudes, separated by insulating strips. The amplitude fluctuations are correctly accounted for via BdG calculations, however it misses phase fluctuations which are inherent to low dimensions. The phase fluctuations affect superconducting properties strongly, and the effect is more pronounced in the limit of large disorder. We provide a close estimate of the actual transition temperature, Tcby incorporating phase fluctuations about the inhomogeneous BdG state. This is obtained by relating the jump in renormalized Ds(obtained from a self consistent Harmonic approximation on a phase-only Hamiltonian) at the Kosterlitz-Thouless (KT) transition and the KT transition temperature, TKTobtained from Ds(T) = (2/π)TKTas temperature tends to TKTfrom below. This yields opening of a large region sandwiched between [Formula: see text] (obtained by the vanishing of [Formula: see text]) and TKTwhere there is no phase coherence between the pairs, however amplitude correlations continue to exist, reminiscent of a pseudogap phase in high-Tcsuperconductors which is marked by short ranged preformed pairs without any definite phase relation between them. Further, the appearance of the superconducting islands from a homogeneous phase indicates the evolution of a system consisting of large and overlapping pairs to one that contains short and tightly bound pairs - a scenario termed as BCS-BEC crossover. We have investigated in details the crossover phenomenon as a function of disorder and confirmed it's existence at small values of electron concentration, however, absent at larger densities.
Recently developed numerical methods have enabled the explicit construction of the superconducting state of the Hubbard model of strongly correlated electrons in parameter regimes where the model also exhibits a pseudogap and a Mott insulating phase. d(x(2)-y(2)) symmetry superconductivity is found to occur in proximity to the Mott insulator, but separated from it by a pseudogapped nonsuperconducting phase. The superconducting transition temperature and order parameter amplitude are found to be maximal at the onset of the normal-state pseudogap. The emergence of superconductivity from the normal state pseudogap leads to a decrease in the excitation gap. All of these features are consistent with the observed behavior of the copper-oxide superconductors.
We determine the effect of a random potential on the density of states $N(\ensuremath{\omega})$ in the attractive Hubbard model. At weak coupling, disorder closes the gap concurrently with the destruction of superconductivity. At larger, but still intermediate coupling, a pseudogap in $N(\ensuremath{\omega})$ remains beyond the point at which off-diagonal long range order vanishes. This change in the elementary excitations of the insulating phase corresponds to a crossover between Fermi and Bose insulators.
The finite-temperature phase diagram for the two-dimensional attractive fermion Hubbard model with spin-dependent disorder is considered within Bogoliubov--de Gennes mean-field theory. Three types of disorder are studied. In the first, only one species is coupled to a random site energy; in the second, the two species both move in random site energy landscapes which are of the same amplitude but different realizations; and finally, in the third, the disorder is in the hopping rather than the site energy. For all three cases, we find that, unlike the case of spin-symmetric randomness, where the energy gap and average order parameter do not vanish as the disorder strength increases, a critical disorder strength exists separating distinct phases. In fact, the energy gap and the average order parameter vanish at distinct transitions, Vcgap{V}_{c}^{\mathrm{gap}}Vcgap​ and Vcop{V}_{c}^{\mathrm{op}}Vcop​, allowing for a gapless superconducting (gSC) phase. The gSC phase becomes smaller with increasing temperature until it vanishes at a temperature T∗{T}^{*}T∗.
We present a numerically exact solution for the BCS Hamiltonian at any temperature, including the degrees of freedom associated with classical phase, as well as amplitude fluctuations via a Monte Carlo integration. This allows for an investigation over the whole range of couplings: from weak attraction, as in the well-known BCS limit, to the mainly unexplored strong-coupling regime of pronounced phase fluctuations. In the latter, two characteristic temperatures T(*) and T(c), associated with short- and long-range ordering, respectively, can be identified in a mean-field-motivated Hamiltonian. T(*) at the same time corresponds to the opening of a gap in the excitation spectrum. In addition to introducing a novel procedure to study strongly coupled d-wave superconductors, our results indicate that classical phase fluctuations are not sufficient to explain the pseudogap features of high-temperature superconductors.
We consider the attractive Hubbard model with on-site disorder as a prototype of a disordered superconductor. We solve the Bogoliubov-de Gennes equations on two-dimensional finite clusters at zero temperature and evaluate the electromagnetic response to a vector potential. We find that the standard decoupling between transverse and longitudinal response does not apply in the presence of disorder. Moreover, the superfluid density is strongly reduced by the relaxation of the phase of the order parameter already at mean-field level when disorder is large. We also find that the anharmonicity of the phase fluctuations is strongly enhanced by disorder. Beyond mean field, this provides an enhancement of quantum fluctuations inducing a zero-temperature transition to a nonsuperconducting phase of disordered preformed pairs. Finally, the connection of our findings with the glassy physics for extreme dirty superconductors is discussed.