Conductance fluctuations in disordered superconductors with broken time-reversal symmetry near two dimensions

Details Conductance fluctuations in disordered superconductors with broken time-reversal symmetry near two dimensions Conductance fluctuations in disordered superconductors with broken time-reversal symmetry near two dimensions

2006-12-06

arxiv.org/abs/cond-mat/0612134v1

Nucl. Phys. B 780, 105 (2007)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

23 pages

Scientific paper

10.1016/j.nuclphysb.2007.03.027

We extend the analysis of the conductance fluctuations in disordered metals by Altshuler, Kravtsov, and Lerner (AKL) to disordered superconductors with broken time-reversal symmetry in $d=(2+\epsilon)$ dimensions (symmetry classes C and D of Altland and Zirnbauer). Using a perturbative renormalization group analysis of the corresponding non-linear sigma model (NL$\sigma$M) we compute the anomalous scaling dimensions of the dominant scalar operators with $2s$ gradients to one-loop order. We show that, in analogy with the result of AKL for ordinary, metallic systems (Wigner-Dyson classes), an infinite number of high-gradient operators would become relevant (in the renormalization group sense) near two dimensions if contributions beyond one-loop order are ignored. We explore the possibility to compare, in symmetry class D, the $\epsilon=(2-d)$ expansion in $d<2$ with exact results in one dimension. The method we use to perform the one-loop renormalization analysis is valid for general symmetric spaces of K\"ahler type, and suggests that this is a generic property of the perturbative treatment of NL$\sigma$Ms defined on Riemannian symmetric target spaces.

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