  The thermal conductivity of heavy-fermion superconductor CeCoIn$_5$ was
measured with a magnetic field rotating in the tetragonal a-b plane, with the
heat current in the anti-nodal direction, $J$ || [100]. We observe a sharp
resonance in thermal conductivity for the magnetic field at an angle $\theta$
$\sim$ 12$^{\circ}$, measured from the heat current direction [100]. This
resonance corresponds to the reported resonance at an angle $\theta'$ $\sim$
33$^{\circ}$ from the direction of the heat current applied along the nodal
direction, $J$ || [110]. Both resonances, therefore, occur when the magnetic
field is applied in the same crystallographic orientation in the two
experiments, regardless of the direction of the heat current, proving
conclusively that these resonances are due to the structure of the Fermi
surface of CeCoIn$_5$. We argue that the uncondensed Landau quasiparticles,
emerging with field, are responsible for the observed resonance. We support our
experimental results with density-functional-theory model calculations of the
density of states in a rotating magnetic field. Our calculations, using a model
Fermi surface of CeCoIn$_5$, reveal several sharp peaks as a function of the
field direction. Our study demonstrates that the thermal-conductivity
measurement in rotating magnetic field can probe the normal parts of the Fermi
surface deep inside the superconducting state.
