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arXiv:cond-mat/9804122 · Physical Review Letters

Evolution of the Density of States Gap in a Disordered Superconductor

Carey Huscroft, Richard T. Scalettar

Published Sep 28, 1998• 32 citations
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Abstract

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.

DOI
10.1103/physrevlett.81.2775

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We determine the effect of a random potential on the density of states N(\ensuremathω)N(\ensuremath{\omega})N(\ensuremathω) 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(\ensuremathω)N(\ensuremath{\omega})N(\ensuremathω) 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.
We investigate the effect of site disorder on the superconducting state in the attractive Hubbard model within the framework of dynamical mean field theory. For a fixed interaction strength (U), the superconducting order parameter decreases monotonically with increasing disorder (x), while the single-particle spectral gap decreases for small x, reaches a minimum and keeps increasing for larger x. Thus, the system remains gapped beyond the destruction of the superconducting state, indicating a disorder-driven superconductor-insulator transition. We investigate this transition in depth considering the effects of weak and strong disorder for a range of interaction strengths. In the clean case, the order parameter is known to increase monotonically with increasing interaction, saturating at a finite value asymptotically for U→∞. The presence of disorder results in destruction of superconductivity at large U, thus drastically modifying the clean case behaviour. A physical understanding of our findings is obtained by invoking particle-hole asymmetry and the probability distributions of the order parameter and spectral gap.
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Using the generalized DMFT+Σ approach, we study the influence of disorder on single-particle properties of the normal phase and the superconducting transition temperature in the attractive Hubbard model. A wide range of attractive potentials U is studied, from the weak coupling region, where both the instability of the normal phase and superconductivity are well described by the BCS model, to the strong-coupling region, where the superconducting transition is due to Bose-Einstein condensation (BEC) of compact Cooper pairs, formed at temperatures much higher than the superconducting transition temperature. We study two typical models of the conduction band with semi-elliptic and flat densities of states, respectively appropriate for three-dimensional and two-dimensional systems. For the semi-elliptic density of states, the disorder influence on all single-particle properties (e.g., density of states) is universal for an arbitrary strength of electronic correlations and disorder and is due to only the general disorder widening of the conduction band. In the case of a flat density of states, universality is absent in the general case, but still the disorder influence is mainly due to band widening, and the universal behavior is restored for large enough disorder. Using the combination of DMFT+Σ and Nozieres-Schmitt-Rink approximations, we study the disorder influence on the superconducting transition temperature T c for a range of characteristic values of U and disorder, including the BCS-BEC crossover region and the limit of strong-coupling. Disorder can either suppress T c (in the weak-coupling region) or significantly increase T c (in the strong-coupling region). However, in all cases, the generalized Anderson theorem is valid and all changes of the superconducting critical temperature are essentially due to only the general disorder widening of the conduction band.
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.
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