Abelian Chern-Simons Term in Superfluid 3He-A

One of the most sought-after objects in topological quantum matter systems is a vortex carrying half a quantum of circulation. They were originally predicted to exist in superfluid 3He-A, but have never been resolved there. Here we report an observation of half-quantum vortices (HQVs) in the polar phase of superfluid 3He. The vortices are created with rotation or by the Kibble-Zurek mechanism and identified based on their nuclear magnetic resonance signature. This discovery p...

We construct the effective field theory for the A-phase of superfluid $^3$He up to the next-to-leading order in the derivative expansion. To this end, we gauge the internal global symmetries of the theory on the curved space by introducing the background gauge fields and spatial metric so as to expose a hidden local symmetry known as the nonrelativistic diffeomorphism. The nonrelativistic diffeomorphism is particularly useful to yield an additional constraint on the effective...

We theoretically investigate the role of surface Andreev bound states (SABSs) on the phase diagram and spin susceptibilities of superfluid 3He confined to a restricted geometry. We first explicitly derive the dispersion of the SABS in 3He-B in the presence of a magnetic field, where the Majorana Ising spin and the spin susceptibility contributed from the SABS are associated with the SO(3) order parameter manifold. Subsequently, based on the quasiclassical Eilenberger theory w...

Superfluid 3He-A displays the largest variety in vortex structure among the presently known coherent quantum systems. The experimentally verified information comes mostly from NMR measurements on the rotating fluid, from which the order-parameter texture can often be worked out. The various vortex structures differ in the topology of their order-parameter field, in energy, critical velocity, and in their response to temporal variations in the externally applied flow. They req...

Exploiting analogies between spin-orbit coupled spin superfluids and non-Abelian Yang-Mills theory, we argue that machines can be built capable of trapping a quantized amount of electric linear charge density, while the line charge quantum itself is surprisingly large. The required conditions might well hold in superfluid 3He-B, for which we propose an experimental realization of this phenomenon.

We discuss the general properties of periodic vortex arrangements in rotating superfluids. The different possible structures are classified according to the symmetry space-groups and the circulation number. We calculate numerically several types of vortex structures in superfluid 3He-A. The calculations are done in the Ginzburg-Landau region, but the method is applicable at all temperatures. A phase diagram of vortices is constructed in the plane formed by the magnetic field ...

In this article, we give a comprehensive review of recent progress in research on symmetry-protected topological superfluids and topological crystalline superconductors, and their physical consequences such as helical and chiral Majorana fermions. We start this review article with the minimal model that captures the essence of such topological materials. The central part of this article is devoted to the superfluid $^3$He, which serves as a rich repository of novel topologica...

We report the first observation of superfluid $\beta$ phase of $^3$He. This phase is realized in $^3$He in nematic aerogel in presence of high magnetic field right below the superfluid transition temperature. We use a vibrating aerogel resonator to detect the transition to the $\beta$ phase and measure the region of existence of this phase.

Superfluid 3He-A gives example of how chirality, Weyl fermions, gauge fields and gravity appear in low energy corner together with corresponding symmetries, including Lorentz symmetry and local SU(N). This supports idea that quantum field theory (Standard Model or GUT) is effective theory describing low-energy phenomena. * Momentum space topology of fermionic vacuum provides topological stability of universality class of systems, where above properties appear. * BCS scheme fo...

In this paper we propose the quantized spin Hall effect (SHE) in the vortex state of a rotating p-wave paired Fermi system in an inhomogeneous magnetic field and in a weak periodic potential. It is the three dimensional extension of the spin Hall effect for a 3He-A superfluid film studied in Ref. [1]. It may also be considered as a generalization of the 3D quantized charge Hall effect of Bloch electrons in Ref. [2] to the spin transport. The A-phase of 3He or, more generally,...