Effective theory of vortices in two-dimensional spinless chiral $p$-wave superfluids

Abstract

We propose a $\mathbb{U}(1)\times {\mathbb{Z}}_2$ effective gauge theory for vortices in a $p_x+i{p}_y$ superfluid in two dimensions. The combined gauge transformation binds $\mathbb{U}(1)$ and ${\mathbb{Z}}_2$ defects so that the total transformation remains single-valued and manifestly preserves the the particle-hole symmetry of the action. The ${\mathbb{Z}}_2$ gauge field introduces a complete Chern-Simons term in addition to a partial one associated with the $\mathbb{U}(1)$ 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, $\exp (i\pi /8)$, 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.

8 pages, 3 figures, version published in PRB

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Cited by in corpus (11)

• Odd-frequency superconductivity in a nanowire coupled to Majorana zero modes
• Probing topological superconductors with emergent gravity
• Sound-induced vortex interactions in a zero-temperature two-dimensional superfluid
• Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors
• Boundary central charge from bulk odd viscosity - chiral superfluids
• Phase diagram of superconductivity in the integer quantum Hall regime
• Electromagnetic response of superconductors in the presence of multiple collective modes
• Berezinskii-Kosterlitz-Thouless transition transport in spin-triplet superconductor
• Geometric and computational aspects of chiral topological quantum matter
• How vortex bound states affect the Hall conductivity of a chiral $p\pm ip$ superconductor
• Precise correspondence between the p-wave chiral superfluid and the spinless bosonic superfluid in the lowest Landau level