Phase diagrams and collective excitations are investigated for a trapped imbalanced Fermi gas in two dimensions with
s-wave pairing at finite temperatures. The treatment of collective modes is performed within the hydrodynamic approach using the Euler and continuity equations. The equations of state for different phases are simulated by a polytropic law with parameters obtained using a fit to the microscopic equilibrium distributions of the pressure and density. These are determined within the whole range of the BCS-BEC crossover using a path-integral description and taking into account fluctuations about the saddle point. We focus on the case of imbalanced gases, when the number of ``spin-up'' and ``spin-down'' fermions that form the pair is not equal. The superfluid-to-normal transition in the trapped Fermi gas is governed by the Berezinskii-Kosterlitz-Thouless mechanism. The eigenfrequencies of collective modes behave differently from those in the zero-temperature case. They can be used to study a realistic equation of state of a trapped Fermi gas at finite temperatures.
Singlet pairing in a Fermi superfluid is frustrated when the amounts of fermions of each pairing partner are unequal. The resulting ``imbalanced superfluid'' has been realized experimentally for ultracold atomic gases with
s-wave interactions. Inspired by high-temperature superconductivity, we investigate the case of
d-wave interactions and find marked differences from the
s-wave superfluid. Whereas
s-wave imbalanced Fermi gases tend to phase separate in real space, in a balanced condensate and an imbalanced normal halo, we show that the
d-wave gas can phase separate in reciprocal space so that imbalance and superfluidity can coexist spatially. We show that the mechanism explaining this property is the creation of polarized excitations in the nodes of the gap. The Sarma mechanism, present only at nonzero temperatures for the
s-wave case, is still applicable in the temperature zero limit for the
d-wave case. As a result, the
d-wave BCS superfluid is more robust with respect to imbalance and a region of the phase diagram can be identified where the
s-wave BCS superfluidity is suppressed whereas the
d-wave superfluidity is not. When these results are extended into the Bose--Einstein condensate limit of strongly bound molecules, the symmetry of the order parameter matters less. The effects of fluctuations beyond mean field is taken into account in the calculation of the structure factor and the critical temperature. The poles of the structure factor (corresponding to bound molecular states) are less damped in the
d-wave case as compared to that in
s wave. On the BCS side of the unitarity limit, the critical temperature
Tc follows the temperature
T∗ corresponding to the pair binding energy and as such will also be more robust against imbalance. Possible routes for the experimental observation of the
d-wave superfluidity have been discussed.
The shear viscosity has been an important topic in ultracold Fermi gases, and it has served as a diagnostic of various theories. Due to the complicated phase structures of population-imbalanced (polarized) Fermi gases with tunable attraction, past works on the shear viscosity mainly focused on unpolarized Fermi gases. Here we investigate the shear viscosity of homogeneous, population-imbalanced Fermi superfluid at finite temperatures by a pairing fluctuation theory for thermodynamical quantities and a gauge-invariant linear response theory for transport coefficients. The Cooper pairs lead to the anomalous shear viscosity analogous to the shear viscosity. We derive an exact relation connecting certain thermodynamic quantities and transport coefficients at the mean-field level for polarized unitary Fermi superfluids. An approximate relation beyond mean-field is proposed and only exhibits mild deviations from our numerical results. In the unitary and Bose-Einstein condensation (BEC) regimes, the total shear viscosity increases with the polarization because the excess majority fermions cause gapless excitations acting like a normal fluid. Moreover, competition among the excess fermions, noncondensed pairs, and fermionic quasiparticles may lead to non-monotonic behavior of the ratio between the shear viscosity and relaxation time as the polarization increases.