We use the Bogoliubov--de Gennes formalism and study the ground-state phases of trapped spin-orbit-coupled Fermi gases in two dimensions. Our main finding is that the presence of a symmetric (Rashba-type) spin-orbit coupling spontaneously induces counterflowing mass currents in the vicinity of the trap edge, i.e., $\ensuremath{\uparrow}$ and $\ensuremath{\downarrow}$ particles circulate in opposite directions with equal speed. These currents flow even in noninteracting systems, but their strength decreases toward the molecular Bose-Einstein-condensate limit, which can be achieved by increasing either the spin-orbit coupling or the interaction strength. These currents are also quite robust against the effects of asymmetric spin-orbit couplings in the
x and
y directions, gradually reducing to zero as the spin-orbit coupling becomes one dimensional. We compare our results with those of chiral
p-wave superfluids and superconductors.
Abstract The superconductors can have a Fermi surface even below the transition temperature, which is known as the Bogoliubov Fermi surface. Focusing on the degrees of freedom at low energies, which are described by the spinless Bogoliubov particles for the case without time-reversal symmetry, we consider the self-energy from the impurity scattering on the Bogoliubov Fermi surfaces. The physical quantities such as the density of states are evaluated based on the single-particle Green’s functions. We systematically compare these results with those of the conventional s-wave spin-singlet pairing state, to illuminate the characteristic features of the Bogoliubov particles located at the Fermi level.
We investigate collective modes in charge-neutral altermagnetic superconductors with
d-wave spin-split bands, focusing on the impact of emergent Bogoliubov Fermi surfaces. In the absence of a magnetic field, the BCS state supports collective modes that inherit the underlying
d-wave symmetry, resulting in pronounced momentum-space anisotropy. The broken time-reversal symmetry further couples these modes to spin-density fluctuations, allowing their signatures to emerge in the spin dynamical structure factor. Upon applying a magnetic field, Bogoliubov Fermi surfaces emerge and qualitatively reshape the collective-mode dynamics through gapless particle-hole excitations and strongly anisotropic Landau damping. The damping is strongest along the momentum-space diagonal, where it can suppress the low-energy phonon mode at small momenta. Remarkably, the suppressed phonon is accompanied by the emergence of an in-gap structure in the Higgs mode and an associated pronounced enhancement of the spin response. These results establish Bogoliubov Fermi surfaces as a mechanism for generating highly anisotropic collective-mode dynamics and identify spin response as a sensitive probe of in-gap Higgs excitations in altermagnetic superconductors.