Pair Correlations in the Two-Dimensional Fermi Gas

We consider the two-dimensional Fermi gas at finite temperature with attractive short-range interactions. Using the virial expansion, which provides a controlled approach at high temperatures, we determine the spectral function and contact for the normal state. Our calculated spectra are in qualitative agreement with recent photoemission measurements [M. Feld et al., Nature (London) 480, 75 (2011).], thus suggesting that the observed pairing gap is a feature of the high-temperature gas rather than being evidence of a pseudogap regime just above the superfluid transition temperature. We further argue that the strong pair correlations result from the fact that the crossover to bosonic dimers occurs at weaker interactions than previously assumed.

Figure 1

(a) Diagramatic representation of the virial expansion of the bare propagator. The number of vertical dashes indicates the power of fugacity of the corresponding term in Eq. (4). (b) Second order contribution to density due to interactions. $t_1$ and $t_2$ represent intervals on the imaginary time axis.

Figure 2

The contribution from interactions to the second and third virial coefficients of the uniform 2D Fermi gas.

Figure 3

The contact calculated within the second (solid) and third (dashed) order of the virial expansion for $\ln (k_F{a}_{2\mathrm{D}})=-0.5$, 0, 0.5, 1 (top to bottom). The filled circles are the results of zero-temperature QMC calculations [14]. Inset: Contact from $T=0$ QMC (solid), the virial expansion up to second order at $T={ϵ}_F$ (dashed), and at $T=3{ϵ}_F$ (dotted).

Figure 4

(a) The occupied part of the spectral function for various values of the interaction parameter $\ln (k_F{a}_{2\mathrm{D}})$ near the crossover. They all correspond to expansion parameter $z{e}^{\beta {ϵ}_B/2}\simeq 0.7$. The (black) dotted line corresponds to the free particle dispersion shifted by the binding energy, i.e., ${\epsilon }_{\mathbf{k}}-{ϵ}_B$, while the (white) solid line depicts the position of the peak in the incoherent part of the spectrum at negative energies. The (white) dashed line is the peak position predicted for a thermal gas of bosonic dimers. (b) Slices of the spectra at $\mathbf{k}=0$ for two different temperatures. The vertical dotted lines indicate the two-body binding energy $-{ϵ}_B$.