Quantum criticality near the upper critical field of Ce${}_2$PdIn${}_8$

We report low-temperature specific heat measurements in magnetic fields up to 12 T applied parallel and perpendicular to the tetragonal c-axis of the heavy fermion superconductor Ce${}_2$PdIn${}_8$. In contrast to its quasi-two-dimensional (2D) relative CeCoIn${}_5$, the system displays an almost isotropic upper critical field. While there is no indication for a FFLO phase in Ce${}_2$PdIn${}_8$, the data suggest a smeared weak first-order superconducting transition close to $H_{c2}\approx 2$ T. The normal state electronic specific heat coefficient displays logarithmically divergent behavior, comparable to CeCoIn${}_5$ and in agreement with 2D quantum criticality of spin-density-wave type.