Kinetic theory for response and transport in non-centrosymmetric superconductors

TL;DR

This paper develops a comprehensive kinetic theory for non-centrosymmetric superconductors, enabling analysis of their response functions and revealing distinctive spectral features related to their mixed singlet-triplet pairing.

Contribution

It introduces a gauge-invariant, charge-conserving kinetic framework in the band basis for non-centrosymmetric superconductors, including analytical Raman response expressions.

Findings

Predicted a two-peak structure in Raman spectra.

Identified polarization-dependent signatures of singlet-triplet mixing.

Provided analytical Raman vertices for specific materials.

Abstract

We formulate a kinetic theory for non-centrosymmetric superconductors at low temperatures in the clean limit. The transport equations are solved quite generally in spin- and particle-hole (Nambu) space by performing first a transformation into the band basis and second a Bogoliubov transformation to the quasiparticle-quasihole phase space. Our result is a particle-hole-symmetric, gauge-invariant and charge conserving description, which is valid in the whole quasiclassical regime. We calculate the current response, the specific heat capacity, and the Raman response function. For the Raman case, we investigate within this framework the polarization-dependence of the electronic (pair-breaking) Raman response for the recently discovered non-centrosymmetric superconductors at zero temperature. Possible applications include the systems CePt$_3$Si and Li$_2$Pd$_x$Pt$_{3-x}$B, which reflect the two important classes of the involved spin-orbit coupling. We provide analytical expressions for the Raman vertices for these two classes and calculate the polarization-dependence of the electronic spectra. We predict a two-peak structure and different power laws with respect to the unknown relative magnitude of the singlet and triplet contributions to the superconducting order parameter, revealing a large variety of characteristic fingerprints of the underlying condensate.