Weak localization of disordered quasiparticles in the mixed superconducting state

Abstract

Starting from a random matrix model, we construct the low-energy effective field theory for the noninteracting gas of quasiparticles of a disordered superconductor in the mixed state. The theory is a nonlinear σ model, with the order parameter field being a supermatrix whose form is determined solely on symmetry grounds. The weak localization correction to the field-axis thermal conductivity is computed for a dilute array of s-wave vortices near the lower critical field Hc1. We propose that weak localization effects, cut off at low temperatures by the Zeeman splitting, are responsible for the field dependence of the thermal conductivity seen in recent high-Tc experiments by Aubin et al.

Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions

“…Such models have arisen in various contexts: the integer quantum Hall (IQH) effect [1][2][3][4][5][6][7][8], and recent generalizations [9][10][11][12][13][14][15][16][17][18][19][20][21][22], as well as other problems of fermions with quenched disorder [23][24][25][26][27][28]; percolation, polymers, and other statistical mechanics problems (Refs. [29,13] and this paper); and strings in anti-de Sitter space (reviewed in Ref.…”

Absence of a metallic phase in random-bond Ising models in two dimensions: Applications to disordered superconductors and paired quantum Hall states

“…Note that this result is independent of the coupling g. When n → 0, we obtain r m 2 /8 , a positive power of distance. In the full non-linear sigma model, g 2 approaches zero logarithmically with distance when n = 0 [7,5,8]. From standard perturbative renormalization group arguments, we expect that the nonconstancy of the coupling produces at worst a factor of the form exp[C ′ (m)(ln r ij ) α(m) ] on the right hand side, where α(m) < 1 is an m-dependent exponent.…”

“…In that case, calculations can be done without domain walls as in other sigma models, but with a sum over the two phases. In fact, all existing proposals for a metallic phase in class D/B/BD [7,5,8] neglect domain walls. Alternative phases where domain walls proliferate may exist, but have not been identified, and may not be metallic.…”

“…The claim about the metallic phase is that, in that phase, the partition function Z, and correlation functions, can be represented at large distances by those of the nonlinear sigma model for class D [7,5,8]. In replica language, this model contains a field that takes values in the target manifold O(2n)/U(n).…”

“…The symmetries are the same as those of the fermion problem in the two-dimensional (2D) random-bond Ising models (RBIM), and "energy" for the fermions of the Ising model corresponds to excitation energy for the fermions in the superconductor. The nonlinear sigma model for class D [6], which in effect defines this ensemble for dimensions greater than zero, has been shown, in the 2D case, to flow under the renormalization group to weaker values of the coupling constant [7,5,8,9]. The coupling constant is related to the inverse of the thermal conductivity of the superconductor, and this flow implies that there is a phase in which there is a nonzero density of extended fermion eigenstates at zero excitation energy, and a superconductor described by this model would be in a thermal metal phase.…”