Leggett modes and the Anderson-Higgs mechanism in superconductors without inversion symmetry

TL;DR

This paper develops a microscopic, gauge-invariant theory for collective modes in non-centrosymmetric superconductors, revealing new Leggett modes influenced by spin-orbit coupling and demonstrating the impact of the Anderson-Higgs mechanism.

Contribution

It introduces a novel theoretical framework for collective modes in non-centrosymmetric superconductors, including the derivation of new Leggett modes and analysis of their properties.

Findings

Identification of new Leggett modes with unique properties

Calculation of mode mass and dispersion reflecting spin-orbit coupling

Demonstration of the Anderson-Higgs mechanism's effect on these modes

Abstract

We develop a microscopic and gauge-invariant theory for collective modes resulting from the phase of the superconducting order parameter in non-centrosymmetric superconductors. Considering various crystal symmetries we derive the corresponding gauge mode $\omega_{\rm G}({\bf q})$ and find, in particular, new Leggett modes $\omega_{\rm L}({\bf q})$ with characteristic properties that are unique to non-centrosymmetric superconductors. We calculate their mass and dispersion that reflect the underlying spin-orbit coupling and thus the balance between triplet and singlet superconductivity occurring simultaneously. Finally, we demonstrate the role of the Anderson-Higgs mechanism: while the long-range Coulomb interaction shifts $\omega_{\rm G}({\bf q})$ to the condensate plasma mode $\omega_{\rm P}({\bf q})$, it leaves the mass $\Lambda_0$ of the new Leggett mode unaffected and only slightly modifies its dispersion.