Effective theory of vortices in two-dimensional spinless chiralp-wave superfluids

Abstract

We propose a U(1)×Z2 effective gauge theory for vortices in a px+ipy superfluid in two dimensions. The combined gauge transformation binds U(1) and Z2 defects so that the total transformation remains single-valued and manifestly preserves the the particle-hole symmetry of the action. The Z2 gauge field introduces a complete Chern-Simons term in addition to a partial one associated with the U(1) gauge field. The theory reproduces the known physics of vortex dynamics such as a Magnus force proportional to the superfluid density. More importantly, it predicts a universal Abelian phase, exp(iπ/8), upon the exchange of two vortices. This phase is modified by non-universal corrections due to the partial Chern-Simon term, which are nevertheless screened in a charged superfluid at distances that are larger than the penetration depth.

Boundary central charge from bulk odd viscosity: Chiral superfluids

“…The authors thank Daniel Ariad for sharing and explaining the Mathematica code used in [41]. We also benefited from discussions with Ady Stern, Andrey Gromov, Barry…”

“…In particular, the relativistic limit misses most of the physics of the Goldstone field [25]. Analysis of the Goldstone physics in CSFs was undertaken in [40,41]. More recently, Refs.…”

Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors

“…In the absence of vortices it is customary at this point to transform to electrically neutral fermions, ψ i = exp(−iϕτ z )ψ i , which eliminates the phase ϕ from the gap term [6]. Importantly, in the presence of vortices this transformation is not single-valued [46], and instead one should perform a single-valued transformation [47] (see also [48] for a general discussion) The presence of these neutral fermions, that braid trivially with all other quasiparticles, will be reflected in the fermionic nature of the K-matrices discussed in Sec.V. After performing the transformation with the minus sign in Eq.…”

Effective theory of two-dimensional chiral superfluids: Gauge duality and Newton-Cartan formulation

“…For this reason q v = ν b = 0 for the conventional superfluid. On the other hand, vortices are known to be abelian anyons in a chiral superfluid [40], which implies ν b = 0. In addition, in the weakly coupled BCS phase they accommodate gappless Majorana fermionic modes which can be included in the effective theory [41,42].…”