  We investigate theoretically the many-body pairing of a strongly correlated
two-dimensional Fermi gas with and without negative confinement-induced
effective range. Using a strong-coupling effective field theory in the normal
state, we show that the specific heat at constant volume can be used as a
characteristic indicator of the crossover from the normal Fermi liquid to the
pseudogap state in two dimensions. We calculate the pseudogap formation
temperature through the specific heat at constant volume, examining the role of
a negative confinement-induced effective range on many-body pairing above the
superfluid transition. We compare our results with and without effective range
to the recent experimental measurement performed with radio-frequency
spectroscopy in Murthy et al.[Science359, 452-455 (2018)]. Although a good
qualitative agreement is found, we are not able to discriminate the effect of
the confinement-induced effect range in the experimental data.
