Superfluid Density and Energy Gap Function of Superconducting ${\mathrm{PrPt}}_4{\mathrm{Ge}}_{12}$

The filled skutterudite superconductor ${\mathrm{PrPt}}_4{\mathrm{Ge}}_{12}$ was studied in muon-spin rotation ($\mu \mathrm{SR}$), specific heat, and electrical resistivity experiments. The continuous increase of the superfluid density with decreasing temperature and the dependence of the magnetic penetration depth $\lambda$ on the magnetic field obtained by means of $\mu \mathrm{SR}$, as well as the observation of a $T^3$ dependence of the electronic specific heat indicate the presence of pointlike nodes in the superconducting energy gap. The gap and the specific heat are found to be well described by two models with point nodes, similar to results obtained for the unconventional heavy fermion skutterudite superconductor ${\mathrm{PrOs}}_4{\mathrm{Sb}}_{12}$.

Figure 1

Inset: specific heat $C-C_{\mathrm{ph}}$ of ${\mathrm{PrPt}}_4{\mathrm{Ge}}_{12}$ (corrected for the phonon term) and normal-state electronic ${\gamma }_N$ (horizontal line). Main panel: data $(C_{\mathrm{el}}+C_{\mathrm{nucl}})$ below 1.4 K and data $C_{\mathrm{el}}$ corrected for the nuclear Schottky contribution $C_{\mathrm{nucl}}$ of Pr (see text).

Figure 2

(a) The magnetic field distribution $P(B)$ at $T=1.55\mathrm{K}$ and applied fields $B_a=75$, 200, and 400 mT obtained by means of fast Fourier transform. The solid lines are fits to the data (see text for details). (b) Temperature dependence of the upper critical field $B_{c2}$ obtained in specific heat (squares) and resistivity (dots) experiments compared with fit results of $\mu \mathrm{SR}$ time spectra (see text). Panels (c) and (d) show correlation plots ${\chi }^2(\lambda ,\xi )$ for $B_a=400\mathrm{mT}$ and 50 mT, respectively.

Figure 3

Field dependence of the superfluid density ${\rho }_s\propto ⟨|\psi {|}^2⟩/{\lambda }^2$. The solid line is the power law fit ${\rho }_s(T)/{\rho }_s(T=0)=1-(B/B_{c2}{)}^{\alpha }$ with $\alpha =0.26(2)$. The dashed line represents the case when $\lambda$ does not depend on the magnetic field. The inset shows $\lambda (B/B_{c2})$ at $T=1.55\mathrm{K}$.

Figure 4

(a) Temperature dependence of ${\rho }_s\propto ⟨|\psi (\mathbf{r}){|}^2⟩/{\lambda }^2$ normalized to its value ${\rho }_s(0)$ at $T=30\mathrm{mK}$. The lines represent the fits by using six different gap models as illustrated in panel (b). The inset shows the low-temperature region between $T=0$ and $T=0.3T_c$. The panel (b) illustrates the gap functions listed in Table .