Nodeless superconductivity in Ca${}_3$Ir${}_4$Sn${}_{13}$: Evidence from quasiparticle heat transport

We report resistivity $\rho$ and thermal conductivity $\kappa$ measurements on Ca${}_3$Ir${}_4$Sn${}_{13}$ single crystals, in which superconductivity with $T_c\approx 7$ K was claimed to coexist with ferromagnetic spin fluctuations. Among three crystals, only one crystal shows a small hump in resistivity near 20 K, which was previously attributed to the ferromagnetic spin fluctuations. The other two crystals show the $\rho \sim T^2$ Fermi-liquid behavior at low temperature. For both single crystals with and without the resistivity anomaly, the residual linear term ${\kappa }_0/T$ is negligible in zero magnetic field. In low fields, ${\kappa }_0\left(H\right)/T$ shows a slow field dependence. These results demonstrate that the superconducting gap of Ca${}_3$Ir${}_4$Sn${}_{13}$ is nodeless and thus rule out a nodal gap caused by ferromagnetic spin fluctuations.

Figure 1

(a) The typical dc magnetic susceptibility of Ca${}_3$Ir${}_4$Sn${}_{13}$ single crystals measured in $H=20$ Oe both parallel and perpendicular to the (110) plane, with zero field cooled. (b) Resistivity of three samples in zero magnetic field. (c) Low-temperature data of the resistivities in (b). The data sets are offset for clarity. Samples S2 and S3 both show $\rho \sim T^2$ Fermi-liquid behavior at low temperature, as indicated by the solid lines.

Figure 2

(a) Resistivity of Ca${}_3$Ir${}_4$Sn${}_{13}$ single crystal S1 in $H=0$, 1, 2, 3, 4, 5, 6, and 7 T. The normal-state $\rho$(7 T) curve is quite flat, extrapolating to residual resistivity ${\rho }_0$(7 T) $\approx$ 114 $\mu \Omega$ cm. (b) Temperature dependence of the upper critical field $H_{c2}$, defined by $\rho =0$. The dashed line is a guide to the eye, which points to $H_{c2}\left(0\right)\approx 7$ T.

Figure 3

(a) Low-temperature thermal conductivity of Ca${}_3$Ir${}_4$Sn${}_{13}$ single crystals S1 and S2 in zero magnetic field. The solid lines are $\kappa /T=a+b{T}^{\alpha -1}$ fits below 250 mK, respectively. (b) Thermal conductivity of S1 in magnetic fields. The dashed line is the normal-state Wiedemann-Franz law expectation $L_0$/${\rho }_0$(7 T), with $L_0$ the Lorenz number $2.45\times {10}^{-8}$ W $\Omega$ K${}^{-2}$ and ${\rho }_0$(7 T) $=$ 114.0 $\mu \Omega$ cm.

Figure 4

Normalized residual linear term ${\kappa }_0/T$ of Ca${}_3$Ir${}_4$Sn${}_{13}$ plotted as a function of $H/H_{c2}$. For comparison, similar data are shown for the clean $s$-wave superconductor Nb,[17] the dirty $s$-wave superconducting alloy InBi,[18] the multiband $s$-wave superconductor NbSe${}_2$,[19] and an overdoped sample of the $d$-wave superconductor Tl-2201.[15]