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arXiv:cond-mat/0206267 · Physical review. B, Condensed matter

Effect of disorder on superconductivity in the boson-fermion model

T. Domański, Karol Izydor Wysokiński

Published Aug 20, 2002• 11 citations
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Abstract

We study how a randomness of either boson or fermion site energies affects the superconducting phase of the boson fermion model. We find that, contrary to what is expected for s-wave superconductors, the nonmagnetic disorder is detrimental to the s-wave superconductivity. However, depending on which subsystem the disorder is located, we can observe different channels being affected. Weak disorder of the fermion subsystem is mainly responsible for the renormalization of the single-particle density of states, while disorder in the boson subsystem leads directly to fluctuations of the strength of the effective pairing between fermions.

DOI
10.1103/physrevb.66.064517

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We study how a randomness of either boson or fermion site energies affects the superconducting phase of the boson fermion model. We find that, contrary to what is expected for s-wave superconductors, the nonmagnetic disorder is detrimental to the s-wave superconductivity. However, depending on which subsystem the disorder is located, we can observe different channels being affected. Weak disorder of the fermion subsystem is mainly responsible for the renormalization of the single-particle density of states, while disorder in the boson subsystem leads directly to fluctuations of the strength of the effective pairing between fermions.
We show that weak nonmagnetic impurities in a two-dimensional d-wave superconductor introduce a nontrivial exponent in the energy dependence of the single-particle density of states: \ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\sim}\ensuremath{\Vert}\ensuremath{\omega}${\mathrm{\ensuremath{\Vert}}}^{\mathrm{\ensuremath{\alpha}}}$. The exponent \ensuremath{\alpha}>0 is exactly calculated for two types of disorder. We argue that the appearance of a finite \ensuremath{\rho}(0) would be equivalent to breaking of a continuous symmetry, prohibited in two dimensions. The method we use is based on the Abelian and non-Abelian bosonization of the effective model of 1D interacting fermions.
We study the influence of the repulsive Coulomb interactions on the thermodynamic properties of the boson-fermion model with an anisotropic (d(d(d-wave and extended s-wave) order parameter. Superconductivity is induced in this model from the anisotropic charge exchange interaction between the conduction-band fermions (electrons or holes) and the immobile hard-core bosons (the localized electron pairs). The on-site Coulomb repulsion competes with this pairing interaction and hence is expected to have a detrimental influence on superconductivity. We analyze this effect in some detail, considering the two opposite limits of the weak and strong repulsion. A possible crossover between both these regimes is also discussed.
The half-filled attractive Hubbard model exhibits a simultaneous charge-density wave and superconducting order in its ground state. In this paper we use approximation-free quantum Monte Carlo techniques to explore the effect of disorder in the site energies on this degeneracy. We find that superconducting order survives randomness out to a critical amount of disorder, but charge ordering is immediately destroyed. This settles the issue as to whether disordered site energies, which do not break time-reversal invariance, can destroy pairing correlations. We also locate the precise ratio of disorder to bandwidth required for the disorder-driven transition from the superconducting state. We explore the validity of a strong-coupling picture which maps the system onto a Heisenberg model in a random magnetic field.
We study the interplay between on-site disorder and fermion pairing on the quasi-one-dimensional flat-band Creutz lattice. Both disorder and flat bands localize particles, but an attractive interaction results in pair formation and delocalization giving rise to superconductivity. In this work, we examine the attractive Hubbard model on the Creutz lattice to study the competition between these two effects and elucidate the properties of the superconducting phase and the localization quantum phase transition as the disorder strength is increased. Our main result is that flat-band superconductivity is robust against disorder: The critical disorder strength Wc{W}_{c}Wc​ required to localize the fermion pairs and destroy superconductivity is finite at any interaction strength UUU and is proportional to the superconducting weight Ds{D}_{s}Ds​ of the clean system. Using large-scale density matrix renormalization group computations, we show that this transition is of the Berezinskii-Kosterlitz-Thouless form. In addition, even at very small interaction strength, the localization is not due to single-fermion localization but to pair localization. For completeness, we briefly study this disorder-induced localization with mean field theory and show that Wc{W}_{c}Wc​ can be accurately determined by using an appropriate scaling function.
The effect of nonmagnetic impurities on 2D sss-wave superconductors is studied beyond the weak disorder regime. Within the Bogoliubov--de Gennes (BdG) framework, the local pairing amplitude develops a broad distribution with significant weight near zero with increasing disorder. Surprisingly, the density of states continues to show a finite spectral gap. The persistence of the spectral gap at large disorder is shown to arise from the breakup of the system into superconducting ``islands.'' Superfluid density and off-diagonal correlations show a substantial reduction at high disorder. A simple analysis of phase fluctuations about the highly inhomogeneous BdG state is shown to lead to a transition to a nonsuperconducting state.