Anomalous superfluid response in the layered heavy fermion compound Ce$_2$PdIn$_8$ near a magnetic quantum critical point

The recently discovered layered heavy fermion superconductor Ce$_2$PdIn$_8$ ($T_c$ = 0.7 K) has attracted a great interest because of the appearance of unconventional superconductivity near a quantum critical point. Here we report high-precision measurements of magnetic penetration depth $\lambda$ down to 60 mK ($\sim0.1T/T_c$) by using a tunnel diode oscillator operating at $\sim$13 MHz. A strong power-law temperature dependence of $\lambda$ demonstrates low-energy excitations of quasiparticles, which is consistent with recent thermal conductivity measurements indicative of nodal superconductivity. The observed $T^{1.5}$ behavior at low temperatures, which is commonly seen in superconductors with line nodes near a magnetic quantum critical point such as CeCoIn$_5$ or organics, can be attributed to the enhancement of effective mass towards zero temperature due to quantum magnetic fluctuations even in the superconducting state.