Superconductivity from repulsive interactions on the kagome lattice

TL;DR

This paper provides a microscopic theoretical analysis of superconducting instabilities on the kagome lattice, considering repulsive interactions, and explores the complex pairing symmetries relevant to $A$V$_3$Sb$_5$ materials.

Contribution

It introduces a detailed study of competing superconducting pairing states on the kagome lattice with repulsive Coulomb interactions, relevant for understanding $A$V$_3$Sb$_5$ superconductors.

Findings

Multiple nearly degenerate pairing symmetries near van Hove filling

Presence of both spin-singlet and spin-triplet pairing states

Complex gap structures with multiple nodes on the Fermi surface

Abstract

The discovery of superconductivity in layered vanadium-based kagome metals $A$V$_3$Sb$_5$ ($A$: K, Rb, Cs) has added a new family of materials to the growing class of possible unconventional superconductors. However, the nature of the superconducting pairing in these materials remains elusive. We present a microscopic theoretical study of the leading superconducting instabilities on the kagome lattice based on spin- and charge-fluctuation mediated Cooper pairing. The applied methodology includes effects of both on-site and nearest-neighbor repulsive Coulomb interactions. Near the upper van Hove filling -- relevant for the $A$V$_3$Sb$_5$ materials -- we find a rich phase diagram with several pairing symmetries being nearly degenerate. In particular, while a substantial fraction of the phase diagram is occupied by a spin-singlet order parameter transforming as a two-dimensional irreducible representation of the point group, several nodal spin-triplet pairing states remain competitive. We compute the band and interaction parameter-dependence of the hierarchy of the leading superconducting instabilities, and determine the detailed momentum dependence of the resulting preferred gap structures. Crucially, for moderate values of the interaction parameters, the individual pairing states depend strongly on momentum and exhibit multiple nodes on the Fermi surface. We discuss the properties of these superconducting gap structures in light of recent experimental developments of the $A$V$_3$Sb$_5$ materials.