Probing the superconducting ground state of ZrIrSi: A muon spin rotation and relaxation study

The superconducting ground state of recently discovered ZrIrSi is probed by means of muon spin rotation and relaxation ($\mu \mathrm{SR}$) and resistivity measurements. The occurrence of superconductivity at $T_{\mathrm{C}}=1.7$ K is confirmed by resistivity measurements. Zero field $\mu \mathrm{SR}$ study revealed that below $T_{\mathrm{C}}$ there is no spontaneous magnetic field in the superconducting state, which indicates time-reversal symmetry is preserved in the case of ZrIrSi. From transverse field $\mu \mathrm{SR}$ measurement, we have estimated the superfluid density as a function of temperature, which is described by an isotropic $s$-wave model with a superconducting gap $2\mathrm{\Delta }\left(0\right)/k_{\mathrm{B}}{T}_{\mathrm{C}}=5.10\left(2\right)$ and indicates the presence of strong coupling superconductivity. Ab initio electronic structure calculation indicates that there are four bands passing through the Fermi level, forming four Fermi surface pockets. We find that the low-energy bands are dominated by the $4d$ orbitals of the transition metal Zr, with substantially less weight from the $5d$ orbitals of the Ir atoms.

Figure 1

(a) The crystal structure of ZrIrSi which crystallizes in the orthorhombic structure with the space group $Pnma$, where the spheres represent the Zr (green), Ir (red), and Si (blue) atoms. (b) Temperature variation of resistivity in zero field. Time dependence TF-$\mu \mathrm{SR}$ asymmetry spectra for ZrIrSi recorded at (c) $T=0.1$ K and (d) $T=1.9$ K in the presence of the applied field ${\mu }_{0}H=10$ mT and at (e) $T=0.1$ K and (f) $T=2.0$ K in the applied field ${\mu }_{0}H=30$ mT. The red solid line shows the fittings to the data using Eq. (1) described in the text.

Figure 2

(a) The superconducting depolarization rate ${\sigma }_{\mathrm{sc}}\left(T\right)$ as a function of temperature in the presence of an applied field of $10\le {\mu }_{0}H\le 40$ mT. (b) The magnetic field dependence of the muon spin depolarization rate is shown for a range of different temperatures. The solid lines are the results of fitting the data using Brandt's equation as discussed in Eq. (2). (c) The inverse magnetic penetration depth squared as a function of temperature is shown here. The lines show the fits using $s$-wave (solid) and $d$-wave (dashed) gap functions.

Figure 3

ZF-$\mu \mathrm{SR}$ asymmetry time spectra for ZrIrSi at 0.05 K (black circles) and 2 K (dark yellow squares) are shown together. The lines are the least-squares fits to the data using Eq. (4).

Figure 4

(a) Computed DFT band structure is plotted along the standard high-symmetric directions for the orthorhombic crystal structure of ZrIrSi. The bands are colored with the difference in the $d$-orbital weight of the Zr and Ir atoms, where red color gives stronger Zr $d$-orbital weight while blue color dictates Ir $d$-orbital weight. Four bands which pass through the Fermi level are indicated by 1, 2, 3, 4 numbers. (b) Corresponding Fermi surfaces are plotted in the full three-dimensional Brillouin zone. We find that Fermi surface 1 and 2 form pockets around the X point, while Fermi surface 3 and 4 constitute pockets centering the $\mathrm{\Gamma }$ point. The colors on the Fermi surface only aid visualization.