Fulde-Ferrell-Larkin-Ovchinnikov state in d-wave superconductivity

Within the BCS theory of d-wave superconductivity we have analysed $H_{c2}(t, \phi)$ for ${\bf H}$ parallel to the a-b plane in a heavy fermion superconductor CeCoIn$_{5}$. We describe both the angle dependence and the temperature dependence, though the present theory predict the second order phase transition at $H=H_{c2}$. Also we obtain the local quasiparticle density of states $G({\bf r}, E)$ in the vicinity of $H=H_{c2} (t, \phi)$, which can be tested by STM and NMR for example.