Interplay of superconductivity and charge-density-wave order in kagome materials

TL;DR

This paper develops a phenomenological Ginzburg-Landau framework to explore how charge density waves influence the symmetry and properties of superconductivity in kagome materials, aiding experimental and theoretical understanding.

Contribution

It introduces a comprehensive Ginzburg-Landau model for the interplay of superconductivity and charge density waves, considering various pairing symmetries and symmetry-breaking effects.

Findings

Superconducting states reflect the broken symmetries of the charge density wave.

The framework guides experimental identification of pairing symmetries.

It provides a basis for future microscopic and experimental studies.

Abstract

In the $\textit{A}$V$_{3}$Sb$_{5}$ ($\textit{A}$ $=$ K, Rb, Cs) kagome materials, superconductivity coexists with a charge density wave (CDW), constituting a new platform to study the interplay of these two orders. Despite extensive research, the symmetry of the superconducting order parameter remains disputed, with experiments seemingly supporting different conclusions. As key aspects of the physics might lie in the intertwining of electronic orders, a better understanding of the impact of the CDW on superconductivity is crucial. In this work, we develop a phenomenological framework to study the interplay of superconductivity and CDW order. In particular, we derive a Ginzburg-Landau free energy for both superconducting and CDW order parameters. Given the unclear nature of the superconducting state, we discuss general pairing symmetries with a focus on $s$-wave, $d$-wave, and pair-density-wave order parameters. Motivated by experiments, we consider the additional breaking of time-reversal or point-group symmetries of the CDW and determine in detail the consequences for the superconducting state. Our results show how the superconducting state mimics the broken symmetries of the CDW and can guide future microscopic calculations, as well as the experimental identification of the superconducting state in the $\textit{A}$V$_{3}$Sb$_{5}$ compounds.