The Josephson relation for the superfluid density is derived for a Fermi superfluid in the BCS-BEC crossover. This identity extends the original Josephson relation for Bose superfluids. It gives a simple exact relation between the superfluid density $ρ_s$ and the broken-symmetry Cooper pair order parameter $Δ_0$ in terms of the infrared limit of the pair fluctuation propagator. The same expression holds through the entire BCS-BEC crossover, describing the superfluid density of a weak-coupling BCS superfluid as well as the superfluid density of a Bose condensate of dimer molecules.
Pairing fluctuations and the superfluid density through the BCS-BEC crossover
我们推导了一个表达式的超流密度的均匀的两个组件的费米气体通过BCS-BEC交叉的热力学势在存在一个强加的超流。按照Nozières和Schmitt-Rink的方法处理高斯近似中的配对涨落，我们使用$ρ_s$的这个定义来获得在有限温度下和在完整的BCS-BEC交叉上有效的明确结果。BCS能隙$Δ$、化学势$μ$和$ρ_s$都以自洽的方式包括相同水平的波动效应，这一点至关重要。我们发现，正常的流体密度$ρ_n \equiv n - ρ_s$自然分离成费米BCS准粒子（$ρ^F_{n}$）和玻色集体模（$ρ^B_{n}$）的贡献之和。$ρ^F_{n}$的表达式只是BCS费米超流体的朗道公式，但现在是在BCS-BEC交叉上计算的。玻色贡献的表达式$ρ^B_{n}$更复杂，并且仅在极端BEC极限下简化为玻色超流体的朗道公式，其中所有费米子都形成了稳定的玻色对，并且相关分子玻色凝聚体的Bogoliubov激发是无阻尼的。在一个配套文件中，我们提出了数值计算的$ρ_s$使用一个表达式相当于本文推导出的，在BCS-BEC交叉，包括么正性，并在有限的温度。
We systematically study relativistic two-species fermions with tunable attractive interactions and number-density asymmetry at zero temperature. In general, a Bardeen-Cooper-Schrieffer (BCS) - Bose-Einstein Condensation (BEC) - relativistic BEC (RBEC) crossover is observed. A generalized BCS ground state and its stability are analyzed. The homogeneous superfluid phase can become unstable and we consider phase separation in real space for neutral systems. In the nonrelativistic limit, our results are consistent with well-known results. In addition to a BCS-BEC crossover similar to that in the n…
We present a stability analysis on a driven-dissipative electron-hole condensate in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein-condensation)-crossover region. Extending the combined BCS-Leggett theory with the generalized random phase approximation (GRPA) to the non-equilibrium case by employing the Keldysh formalism, we show that the pumping-and-decay of carriers causes a depairing effect on excitons. This phenomenon gives rise to an attractive interaction between excitons in the BEC regime, as well as a supercurrent that anomalously flows anti-parallel to $\nabla θ({\bf r})$ (whe…
