  Angular dependent magnetothermal conductivity experiments on CeCoIn_5
indicate that this compound is a d-wave superconductor. In this study, the
low-temperature behavior of the upper critical field is measured in a single
crystal of CeCoIn_5 along the directions H parallel a and H parallel c. The
data is compared with model calculations of the upper critical field in a
d-wave superconductor. It is found that the observed H_c2(T) along H parallel a
is consistent with a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state at low
temperatures, T < 0.7K, whereas for H parallel c the FFLO state appears to be
absent in CeCoIn_5. Furthermore, it is predicted that the quasiparticle density
of states in the FFLO state exhibits a complex peak structure which should be
observable by scanning tunneling microscopy.
