Abelian Chern-Simons Term in Superfluid 3He-A

We present a short review of the current and recent development in the field of superfluid 3He and 4He. The review is based on the topics discussed at the NSF sponsoredWorkshop on Grand Challenges in Quantum Fluids and Solids chaired by Moses Chan from Pennsylvania State University and held at University of Buffalo in August, 2015.

The low-energy physics of a superfluid 3He-B is governed by Nambu-Goldstone bosons resulting from its characteristic symmetry breaking pattern. Here we construct an effective field theory at zero temperature consistent with all available symmetries in curved space, which are the U(1) phase x SU(2) spin x SO(3) orbital gauge invariance and the nonrelativistic general coordinate invariance, up to the next-to-leading order in a derivative expansion. The obtained low-energy effec...

In the theory of the chiral anomaly in relativistic quantum field theories (RQFT) some results depend on regularization scheme at ultraviolet. In the chiral superfluid 3He-A, which contains two Weyl points and also experiences the effects of chiral anomaly, the "trans-Planckian" physics is known and the results can be obtained without regularization. We discuss this on example of the chiral magnetic effect (CME), which has been observed in 3He-A in 90's. There are two forms o...

Theoretical developments during the past several years have shown that large scale properties of the Quantum Hall system can be successfully described by effective field theories which use the Chern-Simons interaction. In this article, we first recall certain salient features of the Quantum Hall Effect and their microscopic explanation. We then review one particular approach to their description based on the Chern-Simons Lagrangian and its variants.

We have used torsional oscillators, containing disk-shaped slabs of superfluid 3He-A, to probe the chiral orbital textures created by cooling into the superfluid state while continuously rotating. Comparing the observed flow-driven textural transitions with numerical simulations of possible textures shows that an oriented monodomain texture with l antiparallel to the angular velocity Omega_0 is left behind after stopping rotation. The bias towards a particular chirality, whil...

It is well-known that (2+1)-dimensional Chern-Simons term may lead to topological Meissner effect. However, we show that 3-dimensional Chern-Simons term, which is different from (2+1)-dimensional Chern-Simons term, will instead destroy traditional Meissner effect. This means that the presence of a 3-dimensional Chern-Simons term naturally guarantees the validity of "pre-formed pairs" picture explaining high-T_c superconductivity, because such a term breaks Meissner effect ind...

Owing to the richness of symmetry and well-established knowledge on the bulk superfluidity, the superfluid $^3$He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in understanding the topological superfluidity of $^3$He in a multifaceted manner, including symmetry consideration, the Jackiw-Rebbi's index theorem, and the quasiclassical theory. Special focus is placed on the symmetry protected topological sup...

Motivated by a recent experiment on superfluid 3He-A confined in narrow parallel plates using a rotating cryostat, we explore possible vortices stable under magnetic field applied to arbitrary angle relative to the plates in order to seek vortices which can accommodate the Majorana zero mode in the core. After proving that the singular vortex with the unit winding number provides the Majorana mode in the spinful situation, we establish the phase diagram in the plane; the rota...

It is established theoretically that an ordered state with continuous symmetry is inherently unstable to arbitrarily small amounts of disorder [1, 2]. This principle is of central importance in a wide variety of condensed systems including superconducting vortices [3, 4], Ising spin models [5] and their dynamics [6], and liquid crystals in porous media [7, 8], where some degree of disorder is ubiquitous, although its experimental observation has been elusive. Based on these i...

The magnetic field dependence of the $A\to B$ transition temperature $T_{AB}$ in the superfluid $^3He$ is reconsidered in order to take into account the linear-in-field contribution beyond the approximation used in Ref.[7]. In the high field region, where the quadratic-in-field contribution prevails, the well known answer is restored. On the other hand,it is pointed out that the Fermi liquid effects shift the observability of the linear-in-field region to rather low magnetic ...