2. GRAVITY 7. MICROSCOPIC PHYSICS 13. TOPOLOGY OF DEFECTS 18. ANOMALOUS NON-CONSERVATION OF FERMIONIC CHARGE 22. EDGE STATES AND FERMION ZERO MODES ON SOLITON 26. LANDAU CRITICAL VELOCITY 29. CASIMIR EFFECT AND VACUUM ENERGY

The Universe in a Helium Droplet

Weyl semimetals are three-dimensional crystalline systems where pairs of bands touch at points in momentum space, termed Weyl nodes, that are characterized by a definite topological charge: the chirality. Consequently, they exhibit the Adler-Bell-Jackiw anomaly, which in this condensed-matter realization implies that the application of parallel electric (E) and magnetic (B) fields pumps electrons between nodes of opposite chirality at a rate proportional to E⋅B. We argue that this pumping is measurable via nonlocal transport experiments, in the limit of weak internode scattering. Specifically, we show that as a consequence of the anomaly, applying a local magnetic field parallel to an injected current induces a valley imbalance that diffuses over long distances. A probe magnetic field can then convert this imbalance into a measurable voltage drop far from source and drain. Such nonlocal transport vanishes when the injected current and magnetic field are orthogonal and therefore serves as a test of the chiral anomaly. We further demonstrate that a similar effect should also characterize Dirac semimetals—recently reported to have been observed in experiments—where the coexistence of a pair of Weyl nodes at a single point in the Brillouin zone is protected by a crystal symmetry. Since the nodes are analogous to valley degrees of freedom in semiconductors, the existence of the anomaly suggests that valley currents in three-dimensional topological semimetals can be controlled using electric fields, which has potential practical “valleytronic” applications.

https://link.aps.org/pdf/10.1103/PhysRevX.4.031035

Probing the Chiral Anomaly with Nonlocal Transport in Three-Dimensional Topological Semimetals

http://cds.cern.ch/record/383983/files/9904229.pdf

Semilocal and electroweak strings

Superfluid analogies of cosmological phenomena

Topological superconductors are novel classes of quantum condensed phases, characterized by topologically nontrivial structures of Cooper pairing states. On the surfaces of samples and in vortex co...

Majorana Fermions and Topology in Superconductors

We show that recent 3He experiments at Manchester demonstrate the creation of excitation momentum (momentogenesis) by quantized vortices, a process analogous to baryogenesis within cosmic strings. Since superfluid 3He is the most complex field theoretic system available in the laboratory, this experiment gives a firmer foundation to chiral anomaly calculations for baryogenesis on non-trivial backgrounds of the Higgs field such as cosmic strings.

Momentum creation by vortices in 3He experiments as a model of primordial baryogenesis

The Universe contains much more matter than antimatter, which is probably the result of processes in the early Universe in which baryon number was not conserved. These processes may have occurred during the electroweak phase transition, when elementary particles first acquired mass1–4. It is impossible to study directly processes relevant to the early Universe, because of the extreme energies involved. One is therefore forced to investigate laboratory systems with analogous phase transitions. Much of the behaviour of superfluid 3He is analogous to that predicted within the standard model of the electroweak interaction5. Superfluids and liquid crystals have already been used to investigate cosmic string production6–11; here we describe experiments on 3He that demonstrate the creation of excitation momentum (which we call momentogenesis) by quantized vortices in the superfluid. The underlying physics of this process is similar to that associated with the creation of baryons within cosmic strings, and our results provide quantitative support for this type of baryogenesis.

Momentum creation by vortices in superfluid 3He as a model of primordial baryogenesis

We give a full account of our extensive measurements of vortex mutual friction in rotating superfluid3He, in both the A- and B-phases. The B-phase results are in qualitative agreement with a theory based on the concept of “spectral flow”; the agreement becomes quantitative if an effective energy gap of 0.63Δ is used, but the justification for such a subtitution is not clear. The vortex core transition, at first not seen because of metastability and hysteresis, has now been observed. Detailed investigation suggests that the high temperature vortex state is a temperature dependent mixture of least two vortex types. The A-phase mutual friction is found to be well described by two hydrodynamic coefficients, the orbital viscosity and the orbital inertia. The latter corresponds to an orbital angular momentum per Cooper pair of (0.0015±0.0017) h, consistent with the prediction of the spectral flow theory. We find that the most uniforml texture is obtained by cooling through Tc while rotating, and then stopping rotation. Detailed investigation of textural memory effects shows that the uniforml-up andl-down textures are associated with opposite directions of rotation. We discuss the various types of texture that may be formed in our experiments. Finally, we compare our mutual friction results with those found in4Hell.

Vortex mutual friction in superfluid3He

A vibrating wire viscometer has been constructed using superconducting wire of diameter 58 µm in the form of a semicircular loop of radius 1.4 cm fixed at both ends and oscillating in a direction perpendicular to the plane of the loop. The use of the viscometer to measure the viscosity of normal phase3He is described and the corrections that have been applied to the data to allow for the finiteQ of the resonance, a quasiparticle mean free path comparable to the wire diameter, and a viscous penetration depth comparable to the size of the channel containing the wire are discussed. The measured viscosities show small departures from the ηT
2=const law of Fermi liquid theory similar to those observed in some but not all previous measurements. The values of the viscosity at the superfluid transition temperature agree with those obtained in other measurements.

Vibrating wire measurements in liquid 3 He. I. The normal state

The Manchester rotating cryostat has been used to measure the longitudinal and transverse coefficients of vortex mutual friction in the A and B phases of superfluid3He. In the B phase the dominant contribution to the mutual friction is scattering of excitations off occupied bound states in the vortex core. The A phase results are explained quantitatively by assuming that doubly quantised continuous vortices are created with a dynamics determined by the equation of motion of the orbital vectorI; the measurements enable us to put an upper limit on the orbital inertia of less than 0.01h per Cooper pair. History-dependent textural effects which had to be overcome in order to make meaningful measurements in the A phase are explained by noting that for a given rotation direction the most stable vortices can be formed more easily from one direction of uniformI texture than the other.

J. R. Hook

Papers

Momentum creation by vortices in 3He experiments as a model of primordial baryogenesis

Momentum creation by vortices in superfluid 3He as a model of primordial baryogenesis

Vortex mutual friction in superfluid3He

Vibrating wire measurements in liquid 3 He. I. The normal state

Vortex Mutual Friction in Rotating Superfluid 3He-B.