Time-reversal symmetry breaking in frustrated superconductor Re2Hf

Geometrical frustration leads to novel quantum phenomena such as the spin-liquid phase in triangular and kagome lattices. Intraband and interband Fermi surface (FS) nesting can drive unique superconducting (SC) ground states with $d$-wave and ${s}^{\ifmmode\pm\else\textpm\fi{}}$-pairing symmetries, respectively, according to the criterion that the SC gap changes sign across the nesting wave vector. For an odd number of FSs, when multiple interband nesting is of comparable strength, the sign-reversal criterion between different FS sheets can lead to frustration, which promotes novel SC order parameters. Here, we report the experimental observation of a time-reversal symmetry breaking pairing state in ${\mathrm{Re}}₂\mathrm{Hf}$ resulting from FS nesting frustration. Furthermore, our electronic specific heat and transverse-field muon spin rotation experiments suggest a fully gapped pairing symmetry. The first-principles electronic structure calculation reveals multiple Fermi surface sheets with comparable interband nesting strength. Implementing the ab initio band structure, we compute spin-fluctuation mediated SC pairing symmetry which reveals an $s+i{s}^{\ensuremath{'}}$-pairing state---consistent with experimental observations. Our investigation demonstrates an alternative SC state which provides a putative setting for both applied and fundamental study.