Time-reversal symmetry breaking in the noncentrosymmetric ${\mathrm{Zr}}_3\mathrm{Ir}$ superconductor

We report the discovery of ${\mathrm{Zr}}_3\mathrm{Ir}$ as a structurally different type of unconventional noncentrosymmetric superconductor (with $T_c=2.3$ K), here investigated mostly via muon-spin rotation/relaxation ($\mu \mathrm{SR}$) techniques. Its superconductivity was characterized using magnetic susceptibility, electrical resistivity, and heat capacity measurements. The low-temperature superfluid density, determined via transverse-field $\mu \mathrm{SR}$ and electronic specific heat, suggests a fully gapped superconducting state. The spontaneous magnetic fields, revealed by zero-field $\mu \mathrm{SR}$ below $T_c$, indicate the breaking of time-reversal symmetry in ${\mathrm{Zr}}_3\mathrm{Ir}$ and hence the unconventional nature of its superconductivity. By using symmetry arguments and electronic-structure calculations we obtain a superconducting order parameter that is fully compatible with the experimental observations. Hence, our results clearly suggest that ${\mathrm{Zr}}_3\mathrm{Ir}$ represents a structurally different member of noncentrosymmetric superconductors with broken time-reversal symmetry.

Figure 1

(a) Temperature-dependent zero-field-cooled (ZFC) and field-cooled (FC) magnetic susceptibilities, measured in an applied field of 1 mT for ${\mathrm{Zr}}_3\mathrm{Ir}$. (b) Estimated ${\mu }_0{H}_{c1}$ values vs temperature; the solid line represents a fit to ${\mu }_0{H}_{c1}\left(T\right)={\mu }_0{H}_{c1}\left(0\right)[1-{(T/T_c)}^2]$. The inset shows the field-dependent magnetization $M\left(H\right)$ recorded at various temperatures. ${\mu }_0{H}_{c1}$ was identified with the deviation of $M\left(H\right)$ from linearity (dashed-dotted line).

Figure 2

(a) Time-domain TF-$\mu \mathrm{SR}$ spectra in the superconducting (0.02 K) and the normal (4 K) phase of ${\mathrm{Zr}}_3\mathrm{Ir}$ measured in a field of ${\mu }_0{H}_{\mathrm{appl}}=30$ mT. (b) Normalized superfluid density and (c) zero-field electronic specific heat vs the reduced temperature ($T/T_c$). The $\mu \mathrm{SR}$ data sets collected on GPS and LTF spectrometers are highly consistent. The inset in (c) shows the raw $C/T$ data measured in a 0.5-T applied field as a function of $T^2$. The dashed line is a fit to $C/T={\gamma }_{\mathrm{n}}+\beta T^2$, from which the phonon contribution was evaluated. The solid black lines in (b) and (c) represent fits using a fully gapped $s$-wave model, while the red dashed-dotted line in (b) is a fit to a dirty-limit model.

Figure 3

Representative zero-field $\mu \mathrm{SR}$ spectra in the superconducting (0.02 K) and the normal (3 K) phase of ${\mathrm{Zr}}_3\mathrm{Ir}$, together with longitudinal field data, collected at 0.02 K and 10 mT. The solid lines are fits to Eq. (3). (b) Derived relaxation rate $\mathrm{\Lambda }$ vs temperature. The dashed lines are guides to the eye. The data sets collected on GPS and LTF spectrometers are highly consistent.

Figure 4

(a) High-symmetry points of the ${\mathrm{Zr}}_3\mathrm{Ir}$ unit cell. (b) Electronic band structure with (dotted blue lines) and without SOC (solid red lines), within $\pm 0.5$ eV from the Fermi energy.