Anisotropy of thermal conductivity and possible signature of the Fulde-Ferrell-Larkin-Ovchinnikov state in CeCoIn₅

We have measured the thermal conductivity of the heavy-fermion superconductor CeCoIn₅ in the vicinity of the upper critical field, with the magnetic field perpendicular to the c axis. Thermal conductivity displays a discontinuous jump at the superconducting phase boundary below critical temperature T_c ≈ 1 K, indicating a change from a second- to first-order transition and confirming the recent results of specific heat measurements on CeCoIn₅. In addition, the thermal conductivity data as a function of field display a kink at a field H_k below the superconducting critical field, which closely coincides with the recently discovered anomaly in specific heat, tentatively identified with the appearance of the spatially inhomogeneous Fulde-Ferrell-Larkin-Oychinnikov (FFLO) superconducting state. Our results indicate that the thermal conductivity is enhanced within the FFLO state, and call for further theoretical investigations of the order parameter's real-space structure (and, in particular, the structure of vortices) and of the thermal transport within the inhomogeneous FFLO state.