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 CeCoIn_5 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_0 ~ 1 K, indicating a change from a second to first order transition and confirming the recent results of specific heat measurements on CeCoIn_5. 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-Ovchinnikov (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.