  Recently, the statistical effect of fermionic superradiance is approved by
series of experiments both in free space and in a cavity. The Pauli blocking
effect can be visualized by a 1/2 scaling of Dicke transition critical pumping
strength against particle number Nat for fermions in a trap. However, the Fermi
surface nesting effect, which manifests the enhancement of superradiance by
Fermi statistics is still very hard to be identified. Here we studied the
influence of localized fermions on the trap edge when both pumping optical
lattice and the trap are presented. We find due to localization, the
statistical effect in superradiant transition is enhanced. Two new scalings of
critical pumping strength are observed as 4/3, and 2/3 for mediate particle
number, and the Pauli blocking scaling 1/3 (2d case) in large particle number
limit is unaffected. Further, we find the 4/3 scaling is subject to a power law
increasing with rising ratio between recoil energy and trap frequency in
pumping laser direction. The divergence of this scaling of critical pumping
strength against $N_{\rm at}$ in $E_R/\omega_x\rightarrow+\infty$ limit can be
identified as the Fermi surface nesting effect. Thus we find a practical
experimental scheme for visualizing the long-desired Fermi surface nesting
effect with the help of trap induced localization in a two-dimensional Fermi
gas in a cavity.
