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.
A (
2+1)-dimensional superfluid in a rapidly rotating trap forms an array of vortices, with collective excitations called Tkachenko modes. Du et al. [Phys. Rev. Res. 6, L012040 (2024)] argued from an effective field theory viewpoint that these excitations are described by a field theory living on a noncommutative space. We elucidate the microscopic origin of these noncommutative fields, and present a derivation of the effective field theory for this superfluid using a lowest Landau level projected coherent state path-integral approach. Aside from conceptual clarity, this approach makes quantitative predictions about the long-wavelength, low-energy behavior in terms of the microscopic parameters of the short-range interacting lowest Landau level superfluid, relevant to trapped Bose-Einstein condensate experiments.
We investigate the microscopic theory of collective excitations and vortex dynamics in superfluid systems. We derive an effective Gross-Pitaevskii Lagrangian for the vortex and collective excitations and obtain the dynamical equations governing their motion. We solve these equations without assuming adiabaticity of vortex motion and show that the vortex has a natural cyclotron frequency. This frequency allows us to identify the vortex mass which turns out to be finite. We also conclude that this implies the existence of a length scale due to the Berry phase associated to the vortex and that it acts as an infrared cutoff.
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.
The complete low-energy collective-excitation spectrum of vortex lattices is discussed for rotating Bose-Einstein condensates by solving the Bogoliubov-de Gennes equation, yielding, e.g., the Tkachenko mode recently observed at JILA. The totally symmetric subset of these modes includes the transverse shear, common longitudinal, and differential longitudinal modes. We also solve the time-dependent Gross-Pitaevskii equation to simulate the actual JILA experiment, obtaining the Tkachenko mode and identifying a pair of breathing modes. Combining both approaches allows one to unambiguously identify every observed mode.
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.