We investigate pseudogap phenomena in a two-dimensional Fermi gas. Including pairing fluctuations within a selfconsistent T-matrix approximation, we determine the pseudogap temperature T∗ below which a dip appears in the density of states ρ(ω) around the Fermi level. Evaluating T∗, we identify the pseudogap region in the phase diagram of this system. We find that, while the observed Berezinskii-Kosterlitz-Thouless (BKT) transition temperature TexpBKT in a 6Li Fermi gas is in the pseudogap regime, the detailed pseudogap structure in ρ(ω) at TexpBKT still differs from a fullygapped one, indicating the importance of amplitude fluctuations in the Cooper channel there. Since the observed TexpBKT in the weak-coupling regime cannot be explained by the recent BKT theory which only includes phase fluctuations, our results may provide a hint about how to improve this BKT theory. Although ρ(ω) has not been measured in this system, we show that the assessment of our results is still possible by using the observable Tan's contact.
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