Half-quantum vortices and walls bounded by strings in the polar-distorted phases of topological superfluid 3He

Abstract

Symmetries of the physical world have guided formulation of fundamental laws, including relativistic quantum field theory and understanding of possible states of matter. Topological defects (TDs) often control the universal behavior of macroscopic quantum systems, while topology and broken symmetries determine allowed TDs. Taking advantage of the symmetry-breaking patterns in the phase diagram of nanoconfined superfluid 3He, we show that half-quantum vortices (HQVs)—linear topological defects carrying half quantum of circulation—survive transitions from the polar phase to other superfluid phases with polar distortion. In the polar-distorted A phase, HQV cores in 2D systems should harbor non-Abelian Majorana modes. In the polar-distorted B phase, HQVs form composite defects—walls bounded by strings hypothesized decades ago in cosmology. Our experiments establish the superfluid phases of 3He in nanostructured confinement as a promising topological media for further investigations ranging from topological quantum computing to cosmology and grand unification scenarios.

Regularized big bang singularity

“…1 in Ref. [17]). The combined process in superfluid 3 He (two phase transitions and the intermediate polar phase) is analogous to the spacetime defect of the regularized big bang singularity, which has a vanishing determinant of the spacetime metric.…”

“…I. In superfluid 3 He experiments, there occur phase transitions between different topological phases [16,17]. In one of these phases-the polar phase-the determinant of the effective tetrad field vanishes.…”

“…Degenerate effective metrics also appear in the context of condensed matter physics and are perhaps accessible by experiment [16,17].…”

50 years in the Landau Institute environment

“…4 discussed by Schwarz [42], who collaborated with Belavin and Polyakov in the instanton problem [43]. Experimentally the halfquantum vortices were observed only 40 years later, first in the time-reversal symmetric polar phase of 3 He [44], and finally in the chiral 3 He-A [45]. Moreover, it was found that they survive the phase transition to 3 He-B, where the half-quantum vortex is topologically unstable: it becomes the termination line of the nontopological domain wall -the analog of Kibble cosmic wall [46].…”

Observation of Wall-Vortex Composite Defects in a Spinor Bose-Einstein Condensate

“…In cosmology, it has been noted that such composite defects can be nucleated through successive phase transitions with different symmetry breaking in grand unification theories; furthermore, composite defect formation has been proposed as a possible mechanism for galaxy formation [1,2] and baryogenesis [3] in the early Universe.Spinful superfluid systems with multiple symmetry breaking provide an experimental platform for studying the physics of composite defects and, thus, to examine the cosmological scenario. In superfluid 3 He-B, it has been observed that a spin-mass vortex, on which a planar soliton terminates, can survive after phase transitions by being pinned on the vortex lattice [4,5] or nafen [6]. Composite defects have also been theoretically studied in the atomic Bose-Einstein condensate (BEC) system.…”