Broken time-reversal symmetry in superconducting Pr${}_{1-x}$La${}_x$Pt${}_4$Ge${}_{12}$

Abstract

The superconducting state of the filled skutterudite alloy series Pr${}_{1-x}$La${}_x$Pt${}_4$Ge${}_{12}$ has been systematically studied by specific heat, zero-field muon spin relaxation ($\hat{I}¼$SR), and superconducting critical field measurements. An additional inhomogeneous local magnetic field, indicative of broken time-reversal symmetry (TRS), is observed in the superconducting states of the alloys. For $x\lesssim 0.5$ the broken-TRS phase sets in below a temperature $T_m$ distinctly lower than the superconducting transition temperature $T_c$. For $x\gtrsim 0.5$ $T_m\approx T_c$. The local field strength decreases as $x\to 1$, where LaPt${}_4$Ge${}_{12}$ is characterized by conventional pairing. The lower critical field $H_{c1}(T)$ of PrPt${}_4$Ge${}_{12}$ shows the onset of a second quadratic temperature region below $T_q\sim T_m$. Upper critical field $H_{c2}(T)$ measurements suggest multiband superconductivity, and point gap nodes are consistent with the specific heat data. In Pr${}_{1-x}$La${}_x$Pt${}_4$Ge${}_{12}$ only a single specific heat discontinuity is observed at $T_c$, in contrast to the second jump seen in PrOs${}_4$Sb${}_{12}$ below $T_c$. These results suggest that superconductivity in PrPt${}_4$Ge${}_{12}$ is characterized by a complex order parameter.