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Europhysics Letters (EPL)

Viscous friction and inertia of domain walls in chiral p-wave superfluids

Kirill V. Samokhin

Published Oct 1, 2011• 2 citations
Publisher

Abstract

Two-fold degeneracy of the ground state in chiral p -wave superfluids or superconductors makes it possible for domain walls separating regions of opposite chirality to exist. In addition to affecting the quasiparticle spectrum in the bulk, the domain walls also carry localized low-energy fermionic excitations, whose spectrum is determined by the phase difference between the domains. In this letter we show how a moving domain wall acquires inertia and friction due to transitions between different quasiparticle states.

DOI
10.1209/0295-5075/96/27012

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Two-fold degeneracy of the ground state in chiral p -wave superfluids or superconductors makes it possible for domain walls separating regions of opposite chirality to exist. In addition to affecting the quasiparticle spectrum in the bulk, the domain walls also carry localized low-energy fermionic excitations, whose spectrum is determined by the phase difference between the domains. In this letter we show how a moving domain wall acquires inertia and friction due to transitions between different quasiparticle states.
We consider a spinless fermionic $p\ifmmode\pm\else\textpm\fi{}ip$ superfluid living on a two-dimensional sphere. Using superfluid hydrodynamics, we show that the ground state necessarily exhibits topological defects: either a pair of elementary vortices or a domain wall between $p\ifmmode\pm\else\textpm\fi{}ip$ phases. In the topologically nontrivial BCS phase we identify the chiral fermion modes localized on the topological defects and compute their low-energy spectrum.
We have used torsional oscillators, containing disk-shaped slabs of superfluid (3)He-A, to probe the chiral orbital textures created by cooling into the superfluid state while continuously rotating. Comparing the observed flow-driven textural transitions with numerical simulations of possible textures shows that an oriented monodomain texture with l antiparallel to the angular velocity Ω(0) is left behind after stopping rotation. The bias toward a particular chirality, while in the vortex state, is due to the inequivalence of energies of vortices of opposite circulation. When spun-up from rest, the critical velocity for vortex nucleation depends on the sense of rotation relative to that of l. A different type of vorticity, apparently linked to the slab's rim by a domain wall, appears when the angular velocity, Ω, is parallel to l.
We have used torsional oscillators, containing disk-shaped slabs of superfluid 3 He-A, to probe the chiral orbital textures created by cooling into the superfluid state while continuously rotating.Comparing the observed flow-driven textural transitions with numerical simulations of possible textures shows that an oriented monodomain texture with l antiparallel to the angular velocity 0 is left behind after stopping rotation.The bias toward a particular chirality, while in the vortex state, is due to the inequivalence of energies of vortices of opposite circulation.When spun-up from rest, the critical velocity for vortex nucleation depends on the sense of rotation relative to that of l.A different type of vorticity, apparently linked to the slab's rim by a domain wall, appears when the angular velocity, , is parallel to l.
We show that in the collision of two superfluid fermionic atomic clouds one observes the formation of quantum shock waves as discontinuities in the number density and collective flow velocity. Domain walls, which are topological excitations of the superfluid order parameter, are also generated and exhibit abrupt phase changes by π and slower motion than the shock waves. The domain walls are distinct from the gray soliton train or number density ripples formed in the wake of the shock waves and observed in the collisions of superfluid bosonic atomic clouds. Domain walls with opposite phase jumps appear to collide elastically.
The chiral spin liquid is a canonical state of quantum spins combining topological and symmetry-breaking order, and possible experimental realizations have attracted growing interest. We examine the physics at interfaces between chiral spin liquid domains of opposite chirality. We show that a self-consistent mean-field description of spinons remains possible in the vicinity of a domain wall and use this to formulate a Ginzburg-Landau theory of the domain wall. The bulk of a chiral spin liquid contains gapped spinon excitations and gauge fluctuations, set by a finite spinon mass and a nonzero spinon Chern number. A third class of excitations consists of amplitude fluctuations of the spinon hoppings, which admit a geometric interpretation in terms of effective vielbein fields. These fluctuations are usually neglected because they are irrelevant for a homogeneous chiral spin liquid and are suppressed in standard large-[Formula: see text] treatments. Going beyond the purely topological Chern-Simons limit, we incorporate these fluctuations into an effective field theoretic framework and show that they generate momentum-dependent corrections, including Chern-Simons-like linear terms and higher-order contributions, beyond the universal topological limit. We then analyze nontopological properties, including domain wall tension and edge velocity, and explain how they modify observables relative to the uniform case. These results connect measurable, nonuniversal quantities such as domain wall width, domain wall tension, and edge velocity to microscopic parameters and provide concrete targets for experiments.
For hardcore bosons on honeycomb lattice ribbons with zigzag edges, charge domain walls are energetically favorable, in sharp contrast to the more typical occupation of a set of sites on a single sublattice of the bipartite geometry at $\ensuremath{\rho}=\frac{1}{2}$ filling. This self-organized domain wall separates two charge-density-wave regions with opposite Berry curvatures. Associated with the change of topological properties, superfluid transport occurs down the domain wall.