Mesoscopic Conductance Fluctuations in Class D Superconducting Wires

We study disordered superconducting wires (length L) of class D via supersymmetric sigma-model approach in the critical regime between topological and trivial phases, where delocalization happens and average conductance scales as G ∼ L^-1/2 [1]. In order to calculate the variance of conductance var G in the diffusive regime we introduce n=2 sigma-model and apply the method of transfer-matrix Hamiltonian, studying Laplace-Beltrami operator on the rank two symmetric superspace. We use Iwasawa decomposition to construct eigenbasis on this supermanifold, which appears to consist of three-parametric and one-parametric subsets, with the latter closely related to the eigenfunctions on the n=1 sigma-model manifold. Our approach allows to find var G at arbitrary lengths in the diffusive region with the crossover from the perturbative weak-localisation regime at L << ξ to the regime of a very broad conductance distribution at L >> ξ, where ξ is the correlation length of the wire. Also, we account to the possible back/forward channels imbalance, which is described by a Wess-Zumino-Witten term in the sigma-model action.

[1] A. Altland et. al., Phys. Rev. B 91, 085429 (2015)