  In this letter we consider spinless Fermi gases placed inside a cavity and
study the critical strength of pumping field for driving a superradiance
transition. We emphasize that Fermi surface nesting effect strongly enhances
the superradiance tendency. Around certain fillings, when the Fermi surface is
nearly nested with a relevant nesting momentum, the susceptibility of the
system toward a checkboard density-wave ordered state is strongly enhanced,
because of which a much smaller (sometime even vanishingly small) critical
pumping field strength can lead to superradiance. This leads to interesting
reentrance behavior and topologically distinct structure in the phase diagram.
Away from these fillings, the Pauli exclusion principle brings about the
dominant effect for which the critical pumping strength is lowered in the
low-density regime and increased in the high-density regime, in comparison to a
Bose gas with same density. These results open the prospect of studying rich
phenomena of degenerate Fermi gases in cavity.
