Strong interactions that favor chiral p-wave pairing, combined with strong pair breaking by confining boundaries, are shown to lead to new equilibrium states with different broken symmetries. Based on a strong-coupling extension of the Ginzburg-Landau theory that accurately accounts for the thermodynamics and phase diagram of the bulk phases of superfluid ^{3}He, we predict new phases of superfluid ^{3}He for confined geometries that spontaneously break rotational and translational symmetry in combination with parity and time-reversal symmetry. One of the newly predicted phases exhibits a unique combination of chiral and helical order that is energetically stable in cylindrical channels of radius approaching the Cooper pair coherence length, e.g., R∼100 nm. Precise numerical minimization of the free energy yields a broad region of stability of the helical phase as a function of pressure and temperature, in addition to three translationally invariant phases with distinct broken spin and orbital rotation symmetries. The helical phase is stable at both high and low pressures and favored by boundaries with strong pair breaking. We present calculations of transverse NMR frequency shifts as functions of rf pulse tipping angle, magnetic field orientation, and temperature as signatures of these broken symmetry phases.
We report theoretical results for the stability of half-quantum vortices (HQVs) in the superfluid phases of
3He confined in highly anisotropic Nafen aerogel. Superfluidity of
3He confined in Nafen is the realization of a ``nematic superfluid'' with Cooper pairs condensed into a single
p-wave orbital aligned along the anisotropy axis of the Nafen aerogel. In addition to the nematic phase, we predict a second ``chiral'' phase that onsets at a lower transition temperature. This chiral phase spontaneously breaks time-reversal symmetry and is a topological superfluid. Both superfluid phases are equal-spin pairing condensates that host arrays of HQVs as equilibrium states of rotating superfluid
3He. We present results for the structure of HQVs, including magnetic and topological signatures of HQVs in both the nematic and chiral phases of
3He-Nafen.
This paper reports the discovery of a new breaking of symmetry of the quantized vortex lines in superfluid
3B: Vortices with broken axisymmetry are found energetically more favorable than any of the axisymmetric ones in the weak-coupling limit. Based on our extensive numerical minimization of the vortex free-energy functional, we identify the vortices occurring in rotating
3B at low pressures as v vortices having---in addition to broken space parity P---also broken axisymmetry Q with the nonaxisymmetry quantum number \ensuremath{\Vert}Q\ensuremath{\Vert}=2, and with superfluid core in the axiplanar state.
In conventional superfluid hydrodynamics the velocity field v_s is irrotational except at the cores of quantized vortices, implying a single scalar phase field. We propose that in addition to the ordinary superfluid velocity there exists a hidden rotational mode represented by an effective vorticity field Omega_h that is not directly observable through conventional probes. This hidden mode emerges naturally from the multi-component order parameter structure when internal symmetries are spontaneously broken. By constructing a generalized Ginzburg–Landau functional that includes both the conventional phase gradient and an auxiliary vector potential associated with internal gauge fields, we derive coupled equations of motion that reveal the coexistence of a standard mass current and a hidden rotational current. The hidden vorticity Omega_h satisfies a conservation law analogous to Kelvin's theorem but is confined to subspaces of the internal symmetry group, thereby evading direct detection. We analyze the stability conditions for such hidden modes, showing that they are energetically favorable in regimes of rapid rotation or strong spin–orbit coupling, typical of ultracold atomic gases. The existence of Omega_h implies an additional set of collective excitations—hidden Kelvin waves—that modify the low-energy spectrum of the superfluid. We discuss how these excitations influence the response to external perturbations and outline potential signatures in density–density correlation functions and in the dynamical structure factor. Our theoretical framework provides a unified description of hidden rotational degrees of freedom in superfluid systems and opens a pathway for discovering new quantum fluid phases with exotic angular momentum textures.
The spectra of fermionic excitations, pairing correlations, and edge currents confined near the boundary of a chiral
p-wave superfluid are calculated to leading order in $\ensuremath{\hbar}/{p}_{f}\ensuremath{\xi}$. Results for the energy- and momentum-resolved spectral functions, including the spectral current density, of a chiral
p-wave superfluid near a confining boundary are reported. The spectral functions reveal the subtle role of the chiral edge states in relation to the edge current and the angular momentum of a chiral
p-wave superfluid, including the rapid suppression of
Lz(T) for $0\ensuremath{\lesssim}T\ensuremath{\ll}{T}_{c}$ in the fully gapped two-dimensional chiral superfluid. The edge current and ground-state angular momentum are shown to be sensitive to boundary conditions, and as a consequence the topology and geometry of the confining boundaries. For perfect specular boundaries, the edge current accounts for the ground-state angular momentum, ${L}_{z}=(N/2)\ensuremath{\hbar}$, of a cylindrical disk of a chiral superfluid with
N/2 fermion pairs. Nonspecular scattering can dramatically suppress the edge current. In the limit of perfect retroreflection, the edge states form a flat band of zero modes that are nonchiral and generate no edge current. For a chiral superfluid film confined in a cylindrical toroidal geometry, the ground-state angular momentum is, in general, nonextensive, and can have a value ranging from ${L}_{z}>(N/2)\ensuremath{\hbar}$ to ${L}_{z}<\ensuremath{-}(N/2)\ensuremath{\hbar}$ depending on the ratio of the inner and outer radii and the degree of backscattering on the inner and outer surfaces. Nonextensive scaling of
Lz, and the reversal of the ground-state angular momentum for a toroidal geometry, would provide a signature of broken time-reversal symmetry of the ground state of superfluid
3He-
A, as well as direct observation of chiral edge currents.
We describe the emergence of superfluid phases of ultracold dipolar fermions in optical lattices for two-dimensional systems. Considering the many-body screening of dipolar interactions at intermediate and larger filling factors, we show that several superfluid phases with distinct pairing symmetries naturally arise in the singlet channel: local s-wave
(sl), extended s-wave
(se), d-wave
(d) or time-reversal-symmetry breaking
(sl+se±id)-wave. We obtain the temperature versus filling factor phase diagram and show that d-wave pairing is favored near half-filling, that
(sl+se)-wave is favored near zero or full filling, and that time-reversal-breaking
(sl+se±id)-wave is favored in between. The inclusion of a harmonic trap reveals that a sequence of phases can coexist in the cloud depending on the filling factor at the center of the trap. Most notably in the spatial region where the
(sl+se±id)-wave superfluid occurs, spontaneous currents are generated, and may be detected using velocity sensitive Bragg spectroscopy.
As in between liquid and crystal phases lies a nematic liquid crystal, which breaks rotation with preservation of translation symmetry, there is a nematic superfluid phase bridging a superfluid and a supersolid. The nematic order also emerges in interacting electrons and has been found to largely intertwine with multiorbital correlation in high-temperature superconductivity, where Ising nematicity arises from a four-fold rotation symmetry C_{4} broken down to C_{2}. Here, we report an observation of a three-state (Z_{3}) quantum nematic order, dubbed "Potts-nematicity", in a system of cold atoms loaded in an excited band of a hexagonal optical lattice described by an sp^{2}-orbital hybridized model. This Potts-nematic quantum state spontaneously breaks a three-fold rotation symmetry of the lattice, qualitatively distinct from the Ising nematicity. Our field theory analysis shows that the Potts-nematic order is stabilized by intricate renormalization effects enabled by strong interorbital mixing present in the hexagonal lattice. This discovery paves a way to investigate quantum vestigial orders in multiorbital atomic superfluids.