Time-reversal symmetry breaking in frustrated superconductor Re$_2$Hf

TL;DR

This paper reports the discovery of a time-reversal symmetry breaking superconducting state in Re$_2$Hf caused by Fermi surface nesting frustration, supported by experimental evidence and first-principles calculations indicating an $s+is'$ pairing symmetry.

Contribution

It provides the first experimental observation of a time-reversal symmetry breaking state induced by Fermi surface nesting frustration in a superconductor, supported by theoretical calculations.

Findings

Observation of time-reversal symmetry breaking in Re$_2$Hf

Evidence of a fully gapped pairing symmetry from experiments

First-principles calculations indicating an $s+is'$ pairing state

Abstract

Geometrical frustration leads to novel quantum phenomena such as the spin-liquid phase in triangular and Kagom\'e lattices. Intra-band and inter-band Fermi surface (FS) nesting can drive unique superconducting (SC) ground states with $d$-wave and $s^{\pm}$ pairing symmetries, respectively, according to the criterion that the SC gap changes sign across the nesting wavevector. For an odd number of FSs, when multiple inter-band nesting is of comparable strength, the sign-reversal criterion between different FS sheets can leads to frustration, which promotes novel SC order parameters. Here we report the experimental observation of a time-reversal symmetry breaking pairing state in Re$_2$Hf resulting from FS nesting frustration. Furthermore, our electronic specific heat and transverse-field $\mu$SR experiments suggest a fully gaped pairing symmetry. The first-principle electronic structure calculation reveals multiple Fermi surface sheets with comparable inter-band nesting strength. Implementing the {\it ab-initio} band structure, we compute spin-fluctuation mediated SC pairing symmetry which reveals a $s+is'$-pairing state - consistent with experimental observations. Our investigation demonstrates a novel SC state which provides a putative setting for both applied and fundamental study.