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Physical Review B

Superconductivity in multiband disordered systems: A vector recursion approach

Shreemoyee Ganguly, Indra Dasgupta, Abhijit Mookerjee

Published Nov 10, 2011• 2 citations
Publisher

Abstract

We present a vector recursion based approach to study the effect of disorder on superconductivity in a system modeled by the two-band attractive Hubbard model. We use the augmented space formalism for the disorder averaging. In the presence of only intraband pairing in a two-band disordered system with disorder in either or both bands, our calculations reveal that the gap survives in the quasiparticle spectrum; similar to single band systems. However, for interband pairing the gap in the quasiparticle spectrum ceases to exist beyond a critical value of the disorder strength. In the presence of both interband and intraband pairing interaction, depending on the relative magnitude of the pairing strength, only a particular kind of pairing is possible for a half filled two-band system.

DOI
10.1103/physrevb.84.174508

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We present a vector recursion based approach to study the effect of disorder on superconductivity in a system modeled by the two-band attractive Hubbard model. We use the augmented space formalism for the disorder averaging. In the presence of only intraband pairing in a two-band disordered system with disorder in either or both bands, our calculations reveal that the gap survives in the quasiparticle spectrum; similar to single band systems. However, for interband pairing the gap in the quasiparticle spectrum ceases to exist beyond a critical value of the disorder strength. In the presence of both interband and intraband pairing interaction, depending on the relative magnitude of the pairing strength, only a particular kind of pairing is possible for a half filled two-band system.
Phase diagram of the two-band Fermi gas with repulsive intraband and interband interactions is obtained with the bosonization technique. In the forward-scattering model, there is a region for the superconductivity (SC) within a band due to charge fluctuations in the accompanying band. When the backward scattering is relevant the SC region becomes wider, while when the umklapp scattering is relevant the system is renormalized into two independent single bands, which is considered to cover the regime where superconductivity a\ifmmode\acute\else\textasciiacute\fi{} la single-band attractive Hubbard model is found from quantum Monte Carlo results in the multiband model on discrete lattices.
We present a real-space approach to study the effect of disorder on superconductivity. The method is based on augmented space formalism that goes beyond mean-field approximations for configuration averaging and effectively deals with the influence of configuration fluctuations of the neighborhood of an atom. In the regime of validity of Anderson's theorem our results for sss- and ddd-wave dirty superconductors have excellent agreement with existing results. The formalism is extended and tested for random negative UUU Hubbard model. Having verified the reliability of our method we use it to study environment-dependent inhomogeneous randomness in disordered superconducting systems.
The phase diagram for spin 1/2 fermions with attractive interband interactions (- V ) is obtained for the two-band Hubbard model in the space of - V , intraband repulsion ( U ), and the band filling from the quantum Monte Carlo calculation along with the mean-field theory in one dimension. The competition of an off-diagonal long-range order with diagonal orders (CDW and SDW) is shown to result in a superconducting ground state arising from interband pairing (i) in the presence of U of right magnitude ( ∼ V ) and (ii) in non-half-filled bands.
A renormalization group treatment is applied to a model of (quasi)-two-dimensional semiconductor with a small band gap. Phase diagrams are derived based on the numerical solutions of the scaling equations. In the purely two-dimensional case, we find the singlet superconducting phase is induced by the repulsive interband interaction in the presence of the attractive intraband interaction. We also find the ferromagnetism and/or the ferroelectricity are stabilized in the presence of the repulsive interband and intraband interactions. The effects of the other kinds of interband and interplanar interactions are also discussed.
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.