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

Detecting Fermi Surface Nesting Effect for Fermionic Dicke Transition by Trap Induced Localization