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arXiv:1612.01547 · Physical review. B./Physical review. B

Transport in superfluid mixtures

Michael Geracie

Published Apr 14, 2017• 3 citations
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Abstract

We present a general method for constructing effective field theories for nonrelativistic superfluids, generalizing the previous approaches of Greiter, Witten, and Wilczek, and Son and Wingate to the case of several superfluids in solution. We investigate transport in mixtures with broken parity and find a parity-odd ``Hall drag'' in the presence of independent motion as well as a pinning of mass, charge, and energy to sites of nonzero relative velocity. Both effects have a simple geometric interpretation in terms of the signed volumes and directed areas of various subcomplexes of a ``velocity polyhedron'': the convex hull formed by the end points of the velocity vectors of a superfluid mixture. We also provide a simple quasi-one-dimensional model that exhibits nonzero Hall drag.

DOI
10.1103/physrevb.95.134510

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We present a general method for constructing effective field theories for nonrelativistic superfluids, generalizing the previous approaches of Greiter, Witten, and Wilczek, and Son and Wingate to the case of several superfluids in solution. We investigate transport in mixtures with broken parity and find a parity-odd Hall drag'' in the presence of independent motion as well as a pinning of mass, charge, and energy to sites of nonzero relative velocity. Both effects have a simple geometric interpretation in terms of the signed volumes and directed areas of various subcomplexes of a velocity polyhedron'': the convex hull formed by the end points of the velocity vectors of a superfluid mixture. We also provide a simple quasi-one-dimensional model that exhibits nonzero Hall drag.
Dissipationless flows in single-component superfluids have a significant degree of universality. In ^{4}He, the dissipationless mass flow occurs with a superfluid velocity determined by the gradient of the superfluid phase. However, in interacting superfluid mixtures, principally new effects appear. In this Letter, we demonstrate a new kind of dissipationless phenomenon arising in mixtures of interacting bosons in optical lattices. We point out that for a particular class of optical lattices, bosons condense in a state where one of the components' superflow results in dissipationless mass flow of the other component, in a direction different from either of the components' superfluid velocities. The free-energy density of these systems contains a vector productlike interaction of superfluid velocities, producing the dissipationless noncollinear entrainment. The effect represents a superfluid counterpart of the Spin Hall effect.
We study the drag force on objects moving in a Fermi superfluid at velocities on the order of the Landau velocity vL{v}_{L}vL​. The expectation has been that vL{v}_{L}vL​ is the critical velocity beyond which the drag force starts to increase toward its normal-state value. This expectation is challenged by a recent experiment measuring the heat generated by a uniformly moving wire immersed in superfluid 3He^{3}\mathrm{He}3He. We introduce the basis for the calculation of the drag force on a macroscopic object using the Fermi-liquid theory of superfluidity. As a technical tool in the calculations, we propose a boundary condition that describes diffuse reflection of quasiparticles from a surface on a scale that is larger than the superfluid coherence length. We calculate the drag force on steadily moving objects of different sizes. For an object that is small compared to the coherence length, we find a drag force that is in accordance with the expectation. For a macroscopic object, we need to take into account the spatially varying flow field around the object. At low velocities, this arises from ideal flow of the superfluid. At higher velocities, the flow field is modified by excitations that are created when the flow velocity locally exceeds vL{v}_{L}vL​. The flow field causes Andreev reflection of quasiparticles and thus leads to change in the drag force. We calculate multiple limiting cases for a cylinder-shaped object. In the absence of quasiparticle-quasiparticle collisions, we find that the critical velocity is larger than vL{v}_{L}vL​ and the drag force (per cross-sectional area) at 2vL2{v}_{L}2vL​ is reduced by an order of magnitude compared to the case of a small object. In a collision-dominated limit, the flow shows signs of instability at a velocity below vL{v}_{L}vL​.
We study superfluid drag in the two-component Bose-Hubbard model with infinitely strong repulsive interactions. In this system, all transport is mediated by the motion of empty sites, or ``holes", and it is hard to move one component without moving the other. We demonstrate, with a combination of analytic and numeric techniques, that the motion of holes leads to strong dissipationless coupling between currents in the two components. This behavior is attributable to polaronic correlations that emerge in the presence of spin currents, which can be observed in experiments. We derive a closed-form expression for the coupling on various lattices in arbitrary spatial dimensions, which we verify through numerical simulations on two dimensional lattices.
We generalize the Beliaev diagrammatic theory of an interacting spinless Bose-Einstein condensate to the case of a binary mixture. We derive a set of coupled Dyson equations and find analytically the Green's functions of the system. The elementary excitation spectrum consists of two branches, one of which takes the characteristic parabolic form $\ensuremath{\omega}\ensuremath{\propto}{p}^{2}$ in the limit of a spin-independent interaction. We observe renormalization of the magnon mass and the spin-wave velocity due to the Andreev-Bashkin entrainment effect. For a three-dimensional weakly interacting gas the spectrum can be obtained by applying the Bogoliubov transformation to a second-quantized Hamiltonian in which the microscopic two-body potentials in each channel are replaced by the corresponding off-shell scattering amplitudes. The superfluid drag density can be calculated by considering a mixture of phonons and magnons interacting via the effective potentials. We show that this problem is identical to the second-order perturbative treatment of a Bose polaron. In two dimensions the drag contributes to the magnon dispersion already in the first approximation. Our consideration provides a basis for systematic study of emergent phases in quantum degenerate Bose-Bose mixtures.
We construct, to leading orders in the momentum expansion, an effective theory of a chiral (px+ipy{p}_{x}+i{p}_{y}px​+ipy​) two-dimensional fermionic superfluid at zero temperature that is consistent with nonrelativistic general coordinate invariance. This theory naturally incorporates the parity and time-reversal violating effects such as the Hall viscosity and the edge current. The particle number current and stress tensor are computed and their linear response to electromagnetic and gravitational sources is calculated. We also consider an isolated vortex in a chiral superfluid and identify the leading chirality effect in the density depletion profile.
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.