Time-reversal symmetry breaking in frustrated superconductor Re2Hf

Abstract

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 ± -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 Re 2 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 + is -pairing state-consistent with experimental observations. Our investigation demonstrates an alternative SC state which provides a putative setting for both applied and fundamental study.

Superconductivity in breathing kagome-structured C14 Laves phase XOs2(X = Zr, Hf)

“…Magnetization measurement confirms bulk type-II superconductivity with a transition temperature T C = 2.90(3) and 2.69(6) K for ZrOs 2 and HfOs 2 . All physical parameters, as detailed in table 1, are consistent with those observed in the candidate time-reversal symmetry breaking (TRSB) HfRe 2 C14 Laves phase and the recent findings on ROs 2 , where R spans from Sc, Y and Lu in a breathing kagome compound [25,26]. Specific heat data in a zero magnetic field for ZrOs 2 reveal a jump value of 1.66, comparable to the fully gapped superconductors.…”

“…Here, A is a material-dependent quantity, Θ R denotes the Debye temperature, and n generally takes the values 2, 3, and 5 depending on the nature of the interaction [56]. The best fit of the data for n = 5 yielded Debye temperature Θ R = 253(4) K, ρ 0 = 54.4(2) µΩ cm and ρ sat = 409.6(9) µΩ cm for ZrOs 2 and Θ R = 240(3) K, ρ 0 = 87.0(7) µΩ cm and ρ sat = 176.0(3) µΩ cm for ZrOs 2 , respectively, which are comparable to the C14 Re 2 Hf compound [26].…”

“…The curious superconducting pairing mechanism in breathing kagome compounds hints at unconventional pairing through the interplay of geometric frustration-induced nontrivial states and superconductivity [20][21][22]. A recent study on some compounds with a breathing kagome structure [23][24][25] and isostructural Re 2 Hf exhibits unconventional superconductivity with TRSB has drawn attention to superconductivity [26]. Furthermore, distorted kagome variants in RT 3 X 2 systems (R = Y, La, Lu, Th, and T = Ru, Os, Rh, Ir, X = B, Si, Ga) exhibit non-trivial band structures and nodeless moderate coupling superconductivity, showing promise for enhanced superconductivity [27][28][29][30][31][32].…”

“…Superconducting and normal state parameters of ZrOs 2 and HfOs 2 , derived from magnetization, resistivity, and specific heat measurement compared with HfRe 2[26].…”

Spontaneous time-reversal symmetry breaking by disorder in superconductors

“…Such cases are fine tuned, but Fermi surfaces with competing nesting tendencies, for example, are prone to near-degeneracy between several symmetry-distinct superconducting instabilities and may therefore more naturally feature such accidental degenerate superpositions. Examples of these include d + is and d + ig as discussed in the context of ironbased superconductors and Sr 2 RuO 4 (see Figures 1B,C), or the socalled s + is state with nontrivial phases on different bands as displayed in the phase diagram in Figure 1A, which also arises as a result of frustrated pairing interactions which are discussed in view of Fe-based superconductors [64][65][66] and other multiband materials [78]. More recently, accidental degeneracies are also explored for UTe 2 where candidate states include complex spin-triplet superpositions of the form e.g., A u + iB 3u , B 1u + iB 3u or B 3u + iB 2u now expressed directly in terms of the 1D irreps, see Figure 1D.…”