[Paper Review] Interaction Effects on Quasiparticle Localization in Dirty Superconductors

M. S. Jeng, Arne Ludwig+2 more|arXiv (Cornell University)|Dec 4, 2001

Physics of Superconductivity and Magnetism3 citations

TL;DR

This paper investigates quasiparticle localization in dirty superconductors with broken time-reversal symmetry, focusing on interaction effects via a renormalization group approach. It shows that in two-dimensional class D superconductors—lacking both spin-rotation and time-reversal symmetry—quasiparticle interactions are irrelevant, stabilizing a metallic phase even with disorder and interactions.

ABSTRACT

We study how quasiparticle interactions affect their localization properties in dirty superconductors with broken time reversal symmetry -- for example in a magnetic field. For SU(2) spin-rotation invariant (class C) systems, the only important coupling is the spin-spin triplet interaction, which we study within a renormalization group approach. Either an additional Zeeman coupling or a complete breaking of spin rotation symmetry renders all interactions irrelevant. These two situations realize, respectively, the non-interacting unitary Anderson and the ``thermal'' (class D) universality class. Our results imply a stable metallic phase in 2D for class D. Experimental implications are discussed.

Motivation & Objective

• To understand how quasiparticle interactions affect localization in dirty superconductors with broken time-reversal symmetry.
• To determine whether interaction effects alter the universality class of thermal metal-insulator transitions in disordered superconductors.
• To identify physical conditions under which interactions become irrelevant, enabling clean observation of localization transitions.
• To assess the stability of metallic phases in two-dimensional superconductors under combined disorder and interaction effects.
• To clarify the role of spin-triplet interactions and Zeeman coupling in determining the relevance of interactions in the renormalization group framework.

Proposed method

• Applies a renormalization group (R.G.) approach to analyze the stability of quasiparticle localization in dirty superconductors with broken time-reversal symmetry.
• Focuses on the SU(2) spin-rotation invariant (class C) case, where the dominant interaction is spin-spin triplet, and evaluates its relevance via one-loop R.G. equations.
• Analyzes the case of full spin-rotation symmetry breaking (class D), showing that all Finkelstein-type interaction terms vanish due to the absence of spin indices in the diffusion mode matrix.
• Uses the replica trick and nonlinear sigma model formulation to derive the effective field theory for quasiparticle transport in the presence of disorder and interactions.
• Evaluates the spin and thermal conductivity corrections using the 1-loop result for the conductivity, incorporating interaction effects through the parameter $U_{tz}$.
• Assesses renormalizability and potential generation of long-range interactions via R.G. flow, concluding that short-range interactions do not generate such terms.

Experimental results

Research questions

• RQ1 Are quasiparticle interactions relevant for the thermal metal-insulator transition in two-dimensional dirty superconductors with broken time-reversal symmetry?
• RQ2 How does the presence of spin-triplet interactions affect the localization properties in class C superconductors?
• RQ3 What is the role of Zeeman coupling and spin-orbit scattering in determining the universality class of the transition?
• RQ4 Can a metallic phase survive in two dimensions when both disorder and interactions are present in superconductors?
• RQ5 Do short-range quasiparticle interactions generate long-range terms under renormalization group flow in these systems?

Key findings

• In two-dimensional class D superconductors—lacking both spin-rotation and time-reversal symmetry—quasiparticle interactions are irrelevant, stabilizing a metallic phase.
• The absence of spin-rotation symmetry eliminates all Finkelstein-type interaction terms, as the diffusion mode matrix lacks spin indices and antisymmetry suppresses interaction terms.
• For class C systems, the spin-triplet interaction $U_{tz}$ is marginal at the non-interacting fixed point to one-loop order, requiring higher-loop analysis to determine relevance.
• In class D, the thermal and spin conductivity are unmodified by interactions, and the metallic phase remains stable even with strong interactions.
• The 1-loop expression for spin conductivity shows that repulsive triplet interactions reduce the weak localization correction, while attractive interactions enhance it.
• The result implies that the 3D thermal metal-insulator transition in class D is also unmodified by interactions, consistent with the absence of marginal interaction terms.