Low-energy effective field theory of superfluid 3He-B and its gyromagnetic and Hall responses

Abstract

The low-energy physics of a superfluid 3 He-B is governed by Nambu-Goldstone bosons resulting from its characteristic symmetry breaking pattern. Here we construct an effective field theory at zero temperature consistent with all available symmetries in curved space, which are the U(1) phase × SU(2)spin × SO(3) orbital gauge invariance and the nonrelativistic general coordinate invariance, up to the next-to-leading order in a derivative expansion. The obtained low-energy effective field theory is capable of reproducing gyromagnetic responses of the superfluid 3 He-B, such as a magnetization generated by a rotation and an orbital angular momentum density generated by a magnetic field, in a model-independent and nonperturbative way. We furthermore show that the stress tensor exhibits a dissipationless Hall viscosity with coefficients uniquely fixed by the orbital angular momentum density, which manifests itself as an elliptical polarization of sound wave with an induced transverse component.

Topological Waves in Fluids with Odd Viscosity

“…For instance, microscopic Coriolis or Lorentz forces are sufficient to induce a non-zero odd viscosity [23,24], in addition to the corresponding body forces. Odd viscosity has been studied theoretically in various systems (see SI for a partial review) including polyatomic gases [25], magnetized plasmas [24,26], flu-ids of vortices [27][28][29][30], chiral active fluids [31], quantum Hall states and chiral superfluids/superconductors [32][33][34][35][36][37][38][39][40][41][42]. Its presence has been experimentally reported in polyatomic gases [43][44][45] (where both positive and negative odd viscosities were observed under the same magnetic field, for different molecules), electron fluids subject to a magnetic field [46], and spinning colloids [47].Here, we show that the presence of odd viscosity fundamentally affects the topological properties of linear waves in the fluid.…”

Nonrelativistic Hydrodynamics from Quantum Field Theory: (I) Normal Fluid Composed of Spinless Schrödinger Fields

“…systems interacting through the Lennard-Jones potential-by the use of auxiliary massless field living in extra dimensions (See e.g. [53,54] for such a treatment). The essential point here is that we assume that S int [φ; j] respects diffeomorphism, gauge, and Milne boost invariance as is the case of for the above two examples.…”

Hall viscosity in the A-phase of superfluid $^3$He

“…We here employ the effective field theory based on the symmetries and the systematic derivative expansion following Refs. [20,23,42]. This approach is valid at zero temperature and thus applicable to the A-phase under a sufficiently large magnetic field.…”

“…It is related to an adiabatic response to deformations of the spatial geometry [6,7] and attracts considerable attention as an analogous index to the Hall conductivity that can distinguish topological phases. Theoretical studies have been performed in various systems, such as integer [6,8] and fractional quantum Hall systems [9][10][11][12][13][14][15], topological insulators [16][17][18][19], chiral superfluids and superconductors [20][21][22], the superfluid 3 He B-phase (Balian-Werthamer state) [23], and so on [24][25][26][27][28][29][30]. Although a number of its observable signatures has been proposed [31][32][33][34][35][36][37][38], the Hall viscosity has rarely been measured in experiments except for colloidal chiral fluid [39] and graphene [40].…”

“…Thanks to their intrinsic angular momentum, the ground state spontaneously breaks the time-reversal and space-rotation symmetries, so that the A-phase naturally satisfies the conditions for a nonvanishing Hall viscosity. Therefore, one may expect a larger Hall viscosity in the A-phase compared to the B-phase, where the above conditions are satisfied only by applying an external magnetic field [23]. * furusawa@stat.phys.titech.ac.jp…”