Kibble-Zurek Dynamics & Statistics of Topological Defects in Chiral Superfluid ${}^3$He Films

Abstract

In equilibrium, confined films of superfluid ${}^3$He-A have the chiral axis, $\hat{\ell }$, locked normal to the surface of the film. There are two degenerate ground states $\hat{\ell }||\pm \hat{z}$. However, for a temperature quench, i.e. cool down through the phase transition at a finite rate, causally disconnected regions of order parameter fluctuations develop and evolve into an inhomogeneous ordered phase that hosts both domain walls between time-reversed chiral phases as well as vortices with winding numbers $p\in \mathbb{Z}$. We present simulations based on a time-dependent generalization of Ginzburg-Landau theory for strong-coupling ${}^3$He that reveal both types of topological defects to be present following the temperature quench. Results for the dynamics of vortices interacting with anti-vortices as well as domain walls are presented. The vortex number density as a function of quench rate agrees well with the scaling predicted by Kibble and Zurek. We also present results for the number distribution and compare with other theoretical models for full counting statistics of the topological defect density. Finally, we present results for an asymmetry in the post-freeze-out populations of inequivalent vortex core structures that are characteristic of a chiral superfluid.

arXiv comment11 pages, 7 figures, 1 video animation. updated to final accepted manuscript in Physical Reivew B

References in corpus (29)

• Cosmic strings
• Cosmological Experiments in Condensed Matter Systems
• Big bang simulation in superfluid 3He-B -- Vortex nucleation in neutron-irradiated superflow
• Spontaneous vortices in the formation of Bose-Einstein condensates
• The Cosmological Kibble Mechanism in the Laboratory: String Formation in Liquid Crystals
• The Order Parameter for the Superconducting Phases of UPt${}_3$
• Spontaneous creation of Kibble-Zurek solitons in a Bose-Einstein condensate
• Observation of Magnetic Flux Generated Spontaneously During a Rapid Quench of Superconducting Films
• Vortex String Formation in a 3D U(1) Temperature Quench
• Observation of half-quantum vortices in topological superfluid 3He
• Surface States, Edge Currents and the Angular Momentum of Chiral p-wave Superfluids
• Universal Statistics of Topological Defects Formed in a Quantum Phase Transition
• Defect Formation in Quench-Cooled Superfluid Phase Transition
• Nucleation of vortices by rapid thermal quench
• Vortices in chiral, spin-triplet superconductors and superfluids
• Full Counting Statistics of Topological Defects After Crossing a Phase Transition
• The A-B transition in superfluid 3He under confinement in a thin slab geometry
• Suppressing the Kibble-Zurek mechanism by a symmetry-violating bias
• On Nambu's Fermion-Boson Relations for Superfluid ${}^3$He-B
• Multifaceted properties of Andreev bound states: Interplay of symmetry and topology
• Electron bubbles and Weyl Fermions in chiral superfluid ${}^3$He-A
• Strong-coupling and the Stripe phase of ${}^3$He
• The Vortex Phase Diagram of Rotating Superfluid ${}^3$He-B
• Anisotropy and Strong-Coupling Effects on the Collective Mode Spectrum of Chiral Superconductors: Application to Sr${}_2$RuO${}_4$
• Scalar excitation with Leggett frequency in ${}^3$ He-B and the $125$ GeV Higgs particle in top quark condensation models as Pseudo - Goldstone bosons
• A-B transition in superfluid ${}^3$He and cosmological phase transitions
• Weyl Fermions and Broken Symmetry Phases of Laterally Confined ${}^3$He Films
• Competition of vortex core structures in superfluid ${}^3$He-B
• Chiral superfluid helium-3 in the quasi-two-dimensional limit