Effects of particle-hole fluctuations on the superfluid transition in two-dimensional atomic Fermi gases

TL;DR

The paper addresses the challenge of understanding the BKT superfluid transition in two-dimensional atomic Fermi gases by incorporating particle-hole fluctuations into a self-consistent pairing-fluctuation framework. By renormalizing the pairing interaction with the full particle-hole T-matrix, the authors demonstrate screening that reduces the pairing gap $\Delta$ and shifts the BKT transition temperature $T_\text{BKT}$ toward the BEC regime, with the effect strongest in the BCS limit and vanishing in the BEC limit. The study shows that including particle-hole fluctuations improves agreement with experimental data and quantum Monte Carlo results in the unitary and BEC regimes, highlighting the importance of these fluctuations in 2D fermionic superfluids. Overall, the work provides a quantitative, self-consistent framework for comparing theory with experiments and simulations across the BCS-BEC crossover in 2D.

Abstract

Proper treatment of the many-body interactions is of paramount importance in our understanding of strongly correlated systems. Here we investigate the effects of particle-hole fluctuations on the Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional Fermi gases throughout the entire BCS-BEC crossover. We include self-consistently in the self energy treatment the entire particle-hole $T$ matrix, which constitutes a renormalization of the bare interaction that appears in the particle-particle scattering $T$ matrix, leading to a screening of the pairing interaction and hence a dramatic reduction of the pairing gap and the transition temperature. The BKT transition temperature $T_\text{BKT}$ is determined by the critical phase space density, for which the pair density and pair mass are determined using a pairing fluctuation theory, which accommodates self-consistently the important self-energy feedback in the treatment of finite-momentum pairing fluctuations. The screening strength varies continuously from its maximum in the BCS limit to essentially zero in BEC limit. In the unitary regime, it leads to an interaction-dependent shift of $T_\text{BKT}$ towards the BEC regime. This shift is crucial in an attempt to explain experimental data quantitatively, which often depends on the interaction strength. Our findings are consistent with available experimental results in the unitary and BEC regimes and with quantum Monte Carlo simulations in the BCS and unitary regimes.

Figures (6)

• Figure 1: Angular average of the on-shell particle-hole susceptibility $\langle\chi_{\text{ph}}(0,|\mathbf{k}+\mathbf{k}'|)\rangle/2m$ with $k=k'$ as a function of momentum $k/k_\text{F}$ at unitarity $\ln(k_\text{F} a_\text{2D}) = 0$ for $T=0$ and $T=T_\text{BKT}$, where $T_\text{BKT}/T_\text{F} = 0.079$ and the corresponding $\Delta$, $\mu$ and $\mu_\text{p}$ are calculated without the particle-hole channel effect.
• Figure 2: $-\langle\chi_{\text{ph}}\rangle / 2m$ at $T=T_\text{BKT}$, averaged at both level 1 (red dashed) and level 2 (black solid line), as a function of $\ln(k_\text{F}a_\text{2D})$ throughout BCS-BEC crossover. The magenta dotted line indicates the BCS limit value, $1/4\pi$, given by $-\langle\chi_{\text{ph}}\rangle = {m}/{2\pi}$.
• Figure 3: (a) Effect of the particle-hole channel contributions on $\Delta$, along with (b) the corresponding $-\langle\chi_{\text{ph}}\rangle / 2m$, at $T=0$, as the function of $\ln(k_\text{F}a_\text{2D})$ throughout the BCS-BEC crossover. Shown are results without (black solid curve) and with particle-hole channel contributions averaged at level 1 (red dashed) and level 2 (blue dot-dashed curve).
• Figure 4: Effect of the particle-hole channel contributions on (a) $T_\text{BKT}$, (b) $\Delta$, (c) $\mu$, (d) $\mu_\text{p}$, (e) $n_\text{B}$ and (f) $M_\text{B}$ versus $\ln(k_\text{F}a_\text{2D})$, with the average $\langle\chi_{\text{ph}}\rangle / 2m$ calculated at level 1 (red dashed) and level 2 (blue dot-dashed curves), respectively. They should be compared with the results without the particle-hole effect (black solid curves).
• Figure 5: Effect of the particle-hole channel contributions on behaviors of $\Delta$ (top row) and $\mu_\text{p}$ (bottom row), as a function of $T/T_\text{BKT}$, with $\ln(k_\text{F}a_\text{2D})=-1,0,2$ from left to right for the BCS, unitary, and BEC regimes, respectively. The black solid curve represents calculations without the particle-hole channel, while the red dashed and green dot-dashed curves include the particle-hole channel effect, using $\langle\chi_{\text{ph}}\rangle / 2m$ under level 1 and level 2 averaging, respectively.