We derive a low-energy effective field theory for chiral superfluids, which accounts for both spontaneous symmetry breaking and fermionic ground-state topology. Using the theory, we show that the odd (or Hall) viscosity tensor, at small wave vector, contains a dependence on the chiral central charge
c of the boundary degrees of freedom, as well as additional nonuniversal contributions. We identify related bulk observables which allow for a bulk measurement of
c. In Galilean invariant superfluids, only the particle current and density responses to strain and electromagnetic fields are required. To complement our results, the effective theory is benchmarked against a perturbative computation within a canonical microscopic model.
We develop a low-energy effective field theory of a two-dimensional bosonic superfluid on the lowest Landau level at zero temperature and identify a Berry term that governs the dynamics of coarse-grained superfluid degrees of freedom. For an infinite vortex crystal we compute how the Berry term affects the low-energy spectrum of soft collective Tkachenko oscillations and nondissipative Hall responses of the particle number current and stress tensor. This term gives rise to a quadratic in momentum term in the Hall conductivity, but does not generate a nondissipative Hall viscosity.
Using boson-vortex duality, we formulate a low-energy effective theory of a two-dimensional vortex lattice in a bosonic Galilean-invariant compressible superfluid. The excitation spectrum contains a gapped Kohn mode and an elliptically polarized Tkachenko mode that has quadratic dispersion relation at low momenta. External rotation breaks parity and time-reversal symmetries and gives rise to Hall responses. We extract the particle number current and stress tensor linear responses and investigate the relations between them that follow from Galilean symmetry. We argue that elementary particles and vortices do not couple to the spin connection which suggests that the Hall viscosity at zero frequency and momentum vanishes in a vortex lattice.
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 construct an effective field theory description of relativistic superfluids with nonzero angular momentum density. At first order in the derivative expansion, the effective action contains a term with a quantized coefficient, which encodes the Berry phase for the angular momentum of the superfluid condensate. From this single term we derive a number of physical effects, including the relativistic Mermin-Ho relation, an anomalous Ettingshausen effect (exchangeable for an anomalous Hall effect), and an anomalous Hall viscosity.
We study the orbital angular momentum (OAM)
Lz of two-dimensional chiral
(px+ipy)ν-wave superfluids (SFs) in the presence of an axisymmetric multiply quantized vortex (MQV) with vorticity
k on a disk at zero temperature, in the framework of Bogoliubov-de Gennes (BdG) theory. Focusing on spectral asymmetry (or spectral flow), we find that
Lz=(k+ν)N/2 for any integer
ν and
k in the Bose-Einstein Condensation (BEC) regime, where
N is the total number of fermions. While in the weak-pairing Bardeen-Cooper-Schrieffer (BCS) regime, only for chiral
p+ip-wave SF with
k=±1,
Lz=(k+ν)N/2 still holds. For chiral SFs with
ν≥2 or
∣k∣≥2 in the BCS regime, the OAM
Lz is remarkably reduced from its ``full" value in the BEC regime. However, the deviations differ in these two cases. For chiral SFs with
ν≥2,
Lz is sharply suppressed in this ideal setting with a specular wall, while the suppression caused by the
∣k∣≥2 vortex is moderate, which is core-size dependent. Furthermore, for
p+ip-wave SF with
k=−1, the total OAM
Lz is zero, but the distribution
Lz(r) is nontrivial compared with that of vortex-free
s-wave SF, in which the total OAM is zero as well. For chiral SFs with
ν≥2 and
∣k∣≥2, the effects of circulation due to vortex and chiral pairing can coexist, and hence depress the OAM simultaneously. These observations can be explained by spectral asymmetry and unpaired fermions in the ground state of the BdG Hamiltonian. We also investigate the spatial distribution of particle density, OAM, by solving the BdG equation.