Investigation of superconducting gap structure in HfIrSi using muon spin relaxation/rotation

We have investigated the superconducting state of HfIrSi using magnetization, specific heat, muon spin rotation and relaxation (μSR) measurements. Superconductivity was observed at TC = 3.6(1)K in both specific heat and magnetization measurements. From an analysis of the transverse-field μSR data, it is clear that the temperature variation of superfluid density is well fitted by an isotropic Bardeen-Cooper-Schrieffer (BCS) type s-wave gap structure. The superconducting carrier density n_s = 6.6(1) × 10²⁶ m^-3, the magnetic penetration depth, λL(0) = 259(4) nm, and the effective mass, m^∗ = 1.57(3)m_e, were calculated from the TF-μSR data. Zero-field μSR data for HfIrSi reveal the absence of any spontaneous magnetic moments below TC, indicating that time-reversal symmetry (TRS) is preserved in the superconducting state of HfIrSi. Theoretical investigations suggest that the Hf and Ir atoms hybridize strongly along the c-axis, and that this is responsible for the strong three-dimensionality of this system which screens the Coulomb interaction. As a result, despite the presence of d-electrons in HfIrSi, these correlation effects are weakened, making the electron-phonon coupling more important.