Level statistics inside the core of a superconductive vortex
Skvortsov M.A., Kravtsov V.E., Feigel'man M.V.
PACS: 73.23.-b, 74.40.+k
Microscopic theory of the type of Efetov's supermatrix sigma-model is constructed for the low-lying electron states in a mixed superconductive-normal system with disorder. This technique is used for the study of the localized states in the core of a vortex in a moderately clean superconductor with τ-1 ^ ωο ~ Δ2/Ερž . At low energies e <C ”C ijJth ~ (ωο/τ)1/2, the energy level statistics is described by the "zero-dimensional" limit of this supermatrix theory, and the result for the density of states is equivalent to that obtained within Altland-Zirnbauer random matrix model. Nonzero modes of the sigma-model increase the mean interlevel distance by the relative amount [21η(1/ωοτ)]_1.
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![](/ps/961/article_14674_800_head.png "<b>Microscopic theory of the type of Efetov's supermatrix sigma-model is constructed for the low-lying electron states in a mixed superconductive-normal system with disorder. This technique is used for the study of the localized states in the core of a vortex in a moderately clean superconductor with τ<sup>-1</sup> ^ ωο ~ <i>Δ<sup>2</sup>/Ερž . </i>At low energies e <C ”C </b><b><i>ijJth </i></b><b>~ (ωο/τ)<sup>1</sup>/<sup>2</sup>, the energy level statistics is described by the "zero-dimensional" limit of this supermatrix theory, and the result for the density of states is equivalent to that obtained within Altland-Zirnbauer random matrix model. Nonzero modes of the sigma-model increase the mean interlevel distance by the relative amount [21η(1/ωοτ)]<sup>_1</sup>.</b>")