Multiband superconductivity in PrPt${}_4$Ge${}_{12}$ single crystals

We report measurements of the London penetration depth $\Delta \lambda \left(T\right)$ and the electronic specific heat $C_e\left(T\right)$ on high-quality single crystals of the filled skutterudite superconductor PrPt${}_4$Ge${}_{12}$ ($T_c\simeq$ 8 K). Both quantities show a weak temperature dependence at $T\ll T_c$, following $\Delta \lambda \sim T^n$ ($n=3.2\pm 0.1$) and $C_e/T\sim T^{2.8}$. Such temperature dependences deviate from both conventional $s$-wave-type and nodal superconductivity. A detailed analysis indicates that the superfluid density ${\rho }_s\left(T\right)$, derived from the penetration depth, as well as the electronic specific heat can be consistently described in terms of a two-gap model, providing strong evidence of multiband superconductivity for PrPt${}_4$Ge${}_{12}$.

Figure 1

(a)–(f) Single crystals obtained from the samples after recrystallization heat treatment performed close to the melting point. For crystals (e) and (f), an enlarged fragment of their surfaces is shown, where the detected phases are indicated.

Figure 2

Temperature dependence of the electrical resistivity $\rho \left(T\right)$ for PrPt${}_4$Ge${}_{12}$. Insets (a) and (b) show the superconducting transitions in the electrical resistivity $\rho \left(T\right)$ and magnetic susceptibility $\chi \left(T\right)$, respectively.

Figure 3

Temperature dependence of the penetration depth $\Delta \lambda \left(T\right)$ for PrPt${}_4$Ge${}_{12}$. Solid, dash-dotted, and dashed lines represent the fits of $\Delta \lambda \sim T^{3.2}$, $\Delta \lambda \sim T^2$ (point node), and the single-gap BCS model, respectively. The inset shows $\Delta \lambda \left(T\right)$ over the entire temperature range.

Figure 4

Superfluid density ${\rho }_s\left(T\right)$ vs normalized temperature $T/T_c$. The inset expands the low-temperature region. Circles and diamonds display the experimental data derived from TDO measurements (this study) and $\mu$SR experiments (from Ref. 12), respectively. Lines shows theoretical fits of various gap functions as listed in Table .

Figure 5

Temperature dependence of the electronic specific heat $C_e\left(T\right)/T$ of a PrPt${}_4$Ge${}_{12}$ single crystal at zero field. Dash-dotted lines (green and blue) and the solid line show the individual and total contributions of the two gaps to the specific heat $C_e\left(T\right)/T$, respectively. Inset (a) shows the total specific heat, $C_p\left(T\right)/T$, plotted as a function of $T^2$. Inset (b) shows the electronic specific heat $C_e\left(T\right)/T$ at low temperatures, fitted by $C_e/T\sim T^{2.8}$ (dotted line). The dashed line refers to the standard BCS model.