Nonlinear σ model for localization in superconductors: Role of order-parameter phase fluctuations

V. E. Kravtsov; R. Oppermann

doi:10.1103/PhysRevB.43.10865

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Nonlinear σ model for localization in superconductors: Role of order-parameter phase fluctuations

V. E. Kravtsov, R. Oppermann

DOI 10.1103/PhysRevB.43.10865 · Physical Review B

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Abstract

The phenomenon of Anderson localization of normal excitations in dirty superconductors is considered using the functional representation in terms of the nonlinear σ model. The derivation of the effective functional allows for the slow spatial variations of the superconducting order-parameter phase. The thermal fluctuations of the order-parameter phase are shown to violate the equivalence between particle-particle and particle-hole diffusion propagators due to the broken time-reversal symmetry in the presence of random local supercurrents. As a result, a new characteristic length lf∝T−1/2 appears in a system. If the correlation length lc∝‖n-nc‖−ν connected with the Anderson transition is larger than lf, the transport properties of normal excitations are the same as in normal metals in a weak magnetic field. At lc≪ξ (ξ is a superconducting coherence length) they are the same as in normal metals without magnetic field. The behavior of diffusion propagators in a crossover region ξ≪lc≪lf is discussed, and a crossover exponent is calculated.