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Local density of states and its mesoscopic fluctuations near the transition to a superconducting state in disordered systems

I. S. Burmistrov, I. V. Gornyi, and A. D. Mirlin
Phys. Rev. B 93, 205432 – Published 20 May 2016

Abstract

We develop a theory of the local density of states (LDOS) of disordered superconductors, employing the nonlinear sigma-model formalism and the renormalization-group framework. The theory takes into account the interplay of disorder and interaction couplings in all channels, treating the systems with short-range and Coulomb interactions on equal footing. We explore two-dimensional systems that would be Anderson insulators in the absence of interaction and two- or three-dimensional systems that undergo an Anderson transition in the absence of interaction. We evaluate both the average tunneling density of states and its mesoscopic fluctuations which are related to the LDOS multifractality in normal disordered systems. The obtained average LDOS shows a pronounced depletion around the Fermi energy, both in the metallic phase (i.e., above the superconducting critical temperature Tc) and in the insulating phase near the superconductor-insulator transition (SIT). The fluctuations of the LDOS are found to be particularly strong for the case of short-range interactions, especially, in the regime when Tc is enhanced by Anderson localization. On the other hand, the long-range Coulomb repulsion reduces the mesoscopic LDOS fluctuations. However, also in a model with Coulomb interaction, the fluctuations become strong when the systems approach the SIT.

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  • Received 9 March 2016
  • Revised 5 May 2016

DOI:https://doi.org/10.1103/PhysRevB.93.205432

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

I. S. Burmistrov1,2, I. V. Gornyi3,4,5,1, and A. D. Mirlin3,5,6,1

  • 1L. D. Landau Institute for Theoretical Physics, Kosygina street 2, 117940 Moscow, Russia
  • 2Moscow Institute of Physics and Technology, 141700 Moscow, Russia
  • 3Institut für Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
  • 4A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia
  • 5Institut für Theorie der kondensierten Materie, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
  • 6Petersburg Nuclear Physics Institute, 188300 St. Petersburg, Russia

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Issue

Vol. 93, Iss. 20 — 15 May 2016

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