Time-reversal-symmetry breaking and unconventional pairing in the noncentrosymmetric superconductor ${\mathrm{La}}_7{\mathrm{Rh}}_3$

Noncentrosymmetric superconductors have sparked significant research interests due to their exciting properties, such as the admixture of spin-singlet and spin-triplet pairing. Here we report on the muon spin rotation and relaxation and thermodynamic measurements on the noncentrosymmetric superconductor ${\mathrm{La}}_7{\mathrm{Rh}}_3$, which show an isotropic superconducting gap but also spontaneous time-reversal-symmetry breaking occurring at the onset of superconductivity. We show that our results pose severe constraints on any microscopic theory of superconductivity in this system. A symmetry analysis identifies ground states compatible with time-reversal-symmetry breaking, and the resulting gap functions are discussed. Furthermore, general energetic considerations indicate the relevance of electron-electron interactions for the pairing mechanism, in accordance with hints of spin fluctuations revealed in susceptibility measurements.

Figure 1

(a) Superconductivity appears around $T_c=2.65\mathrm{K}$ with the onset of strong diamagnetic signal in the zero-field-cooled warming (ZFCW) and field-cooled cooling (FCC) magnetization measurements. (b) Low-temperature specific heat data in the superconducting regime fit well for the BCS $s$-wave model for a fitting parameter $\mathrm{\Delta }\left(0\right)/k_B{T}_c=1.74$.

Figure 2

(a) $\mathrm{TF}\text{−}\mu \mathrm{SR}$ spectra collected in an applied magnetic field of 30 mT at temperatures 3.5 K ($>T_c$) and 0.1 K ($<T_c$). The solid lines are fits using Eq. (). (b) Temperature dependence of the muon spin relaxation rate at different applied magnetic fields from 15 to 50 mT.

Figure 3

(a) Muon spin depolarization rate as a function of field at various temperatures. The data were fitted using Eq. () to extract the temperature dependence of the inverse magnetic penetration depth squared. (b) Temperature dependence of ${\lambda }^{-2}$, where the solid line represents the best fit using Eq. (3).

Figure 4

(a) $\mathrm{ZF}\text{−}\mu \mathrm{SR}$ spectra at 0.1 and 3.5 K. The orange circles refer to measurements in the presence of a small LF of 10 mT. (b) The temperature dependence of the electronic relaxation rate $\mathrm{\Lambda }$ shows a systematic increase below $T=2.64$ K, which is close to $T_c$. (c) The temperature dependence of the nuclear relaxation rate ${\sigma }_{\text{ZF}}$ shows no appreciable change at $T_c$.

Figure 5

The location of symmetry-imposed zeros of the single-band gap function $|{\tilde{\mathrm{\Delta }}}_{\mathit{k}a}|$ in the Brillouin zone is shown in red for the TRS-breaking candidate states (a) $E_1(1,i)$ and (b) $E_2(1,i)$. Nondegenerate Fermi surfaces crossing these lines/planes lead to symmetry-protected point/line nodes. Bands are expected to be nondegenerate for generic momentum points (invariant only under the identity operation of the point group), including generic points in the planes $k_z=0,\pi /c$; however, at the high-symmetry lines parallel to the $k_z$ axis and going through the indicated high-symmetry points, this will not necessarily be the case.

Figure 6

Temperature dependence of the magnetic susceptibility measured at 1 T. The solid line is a fit to the indicated function form [61] for $\chi \left(T\right)$.