Ca${}_3$Ir${}_4$Sn${}_{13}$: A weakly correlated nodeless superconductor

We report detailed Seebeck coefficient, Hall resistivity, as well as specific heat measurement on Ca${}_3$Ir${}_4$Sn${}_{13}$ single crystals. The Seebeck coefficient exhibits a peak corresponding to the anomaly in resistivity at $T^{*}$, and the carrier density is suppressed significantly below $T^{*}$. This indicates a significant Fermi surface reconstruction and the opening of the charge density wave gap at the superlattice transition. The magnetic field induced enhancement of the residual specific heat coefficient $\gamma \left(H\right)$ exhibits a nearly linear dependence on magnetic field, indicating a nodeless gap. In the temperature range close to $T_c$ the Seebeck coefficient can be described well by the diffusion model. The zero-temperature extrapolated thermoelectric power is very small, implying large normalized Fermi temperature. Consequently the ratio $\frac{T_c}{T_F}$ is very small. Our results indicate that Ca${}_3$Ir${}_4$Sn${}_{13}$ is a weakly correlated nodeless superconductor.

Figure 1

(a) Powder XRD patterns and structural refinement results. (b) Magnetic susceptibility $4\pi \chi$ for a single crystal around a superconducting transition temperature $T_c=7$ K in 100 Oe field. Inset in (b) shows the crystal crystal structure of Ca${}_3$Ir${}_4$Sn${}_{13}$.

Figure 2

(a) Temperature dependence of the resistivity $\rho \left(T\right)$ (a), Seebeck coefficient $S\left(T\right)$ (b), and magnetization $M\left(T\right)$ (c) for a Ca${}_3$Ir${}_4$Sn${}_{13}$ single crystal in different magnetic fields, respectively. Insets in (c) shows the magnetization-magnetic field curve at 8 K.

Figure 3

Temperature dependence of the the Hall coefficient $R_H$ (a), the carrier density $n$, and mobility ${\mu }_H$ for a Ca${}_3$Ir${}_4$Sn${}_{13}$ crystal. Inset in (a) shows the Hall resistivity ${\rho }_{xy}$ at four different temperatures.

Figure 4

(a) Temperature dependence of the specific heat $C_p$ of a Ca${}_3$Ir${}_4$Sn${}_{13}$ single crystal in 0 T (squares) and 9 T (circles), respectively. (b) The difference in the specific heat data between 0 and 9 T, $\Delta C_p/T=C_p\left(H\right)-C_p\left(0\right)$. The blue solid lines here are just to show determining the height of the specific heat anomaly. (c) Low-temperature specific heat $C_p/T$ vs $T^2$ in different magnetic fields up to a 4 T Ca${}_3$Ir${}_4$Sn${}_{13}$ single crystal. The lines are the fitting results below the superconducting transition temperature $T_c$ using $C_p(T,H)=\gamma \left(H\right)T+\beta T^2+\eta T^5$. (d) Field dependence of the Sommerfeld coefficient $\Delta \gamma \left(H\right)=\gamma \left(H\right)-\gamma \left(0\right)$ for crystal.

Figure 5

The temperature dependence of the Seebeck coefficient divided by $T$, $S/T$ under 0 T for a Ca${}_3$Ir${}_4$Sn${}_{13}$ crystal. The open squares are the experimental data and the solid line is the linear fitting result within normal phase. Inset: $T_c$ as a function of Fermi temperature $T_F$ in a few superconductors. The black circle and arrow show the position of Ca${}_3$Ir${}_4$Sn${}_{13}$. Adapted from Refs. 32 and 35.