TY - JOUR

T1 - Conductance fluctuations in disordered superconductors with broken time-reversal symmetry near two dimensions

AU - Ryu, S.

AU - Furusaki, A.

AU - Ludwig, A. W.W.

AU - Mudry, C.

N1 - Funding Information:
C.M. and A.F. acknowledge hospitality of the Kavli Institute for Theoretical Physics at Santa Barbara during the completion of the manuscript. This research was supported in part by the National Science Foundation under Grants No. DMR-00-75064 (A.W.W.L.) and No. PHY99-07949 (S.R., A.F., C.M.).

PY - 2007/10/1

Y1 - 2007/10/1

N2 - 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 + ε{lunate}) dimensions (symmetry classes C and D of Altland and Zirnbauer). Using a perturbative renormalization group analysis of the corresponding non-linear sigma model (NLσM) 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 ε{lunate} = (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 Kähler type, and suggests that this is a generic property of the perturbative treatment of NLσMs defined on Riemannian symmetric target spaces.

AB - 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 + ε{lunate}) dimensions (symmetry classes C and D of Altland and Zirnbauer). Using a perturbative renormalization group analysis of the corresponding non-linear sigma model (NLσM) 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 ε{lunate} = (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 Kähler type, and suggests that this is a generic property of the perturbative treatment of NLσMs defined on Riemannian symmetric target spaces.

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U2 - 10.1016/j.nuclphysb.2007.03.027

DO - 10.1016/j.nuclphysb.2007.03.027

M3 - Article

AN - SCOPUS:34547948584

VL - 780

SP - 105

EP - 142

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -