Symmetry protected topological superfluid (3)He-B

Observation of suppressed viscosity in the normal state of 3He due to superfluid fluctuations

Evidence of fluctuations in transport have long been predicted in 3He. They are expected to contribute only within 100μK of Tc and play a vital role in the theoretical modeling of ordering; they encode details about the Fermi liquid parameters, pairing symmetry, and scattering phase shifts. It is expected that they will be of crucial importance for transport probes of the topologically nontrivial features of superfluid 3He under strong confinement. Here we characterize the temperature and pressure dependence of the fluctuation signature, by monitoring the quality factor of a quartz tuning fork oscillator. We have observed a fluctuation-driven reduction in the viscosity of bulk 3He, finding data collapse consistent with the predicted theoretical behavior.

Vortex-bound solitons in topological superfluid3He

The different superfluid phases of³He are described byp-wave order parameters that include anisotropy axes both in the orbital and spin spaces. The anisotropy axes characterize the broken symmetries in these macroscopically coherent quantum many-body systems. The systems' free energy has several degenerate minima for certain orientations of the anisotropy axes. As a result, spatial variation of the order parameter between two such regions, settled in different energy minima, forms a topological soliton. Such solitons can terminate in the bulk liquid, where the termination line forms a vortex with trapped circulation of mass and spin superfluid currents. Here we discuss possible soliton-vortex structures based on the symmetry and topology arguments and focus on the three structures observed in experiments: solitons bounded by spin-mass vortices in the B phase, solitons bounded by half-quantum vortices (HQVs) in the polar and polar-distorted A phases, and the composite defect formed by a half-quantum vortex, soliton and the Kibble-Lazarides-Shafi wall in the polar-distorted B phase. The observations are based on nuclear magnetic resonance (NMR) techniques and are of three types: first, solitons can form a potential well for trapped spin waves, observed as an extra peak in the NMR spectrum at shifted frequency; second, they can increase the relaxation rate of the NMR spin precession; lastly, the soliton can present the boundary conditions for the anisotropy axes in bulk, modifying the bulk NMR signal. Owing to solitons' prominent NMR signatures and the ability to manipulate their structure with external magnetic field, solitons have become an important tool for probing and controlling the structure and dynamics of superfluid³He, in particular HQVs with core-bound Majorana modes.

Thermoelectric properties of topological chains coupled to a quantum dot

Topological one-dimensional superconductors can sustain zero energy modes protected by different kinds of symmetries in their extremities. Observing these excitations in the form of Majorana fermions is one of the most intensive quests in condensed matter physics. We are interested in another class of one-dimensional topological systems in this work, namely topological insulators. Which present symmetry-protected end modes with robust properties and do not require the low temperatures necessary for topological superconductivity. We consider a device in the form of a single electron transistor coupled to the simplest kind of topological insulators, namely chains of atoms with hybridized sp orbitals. We study the thermoelectric properties of the device in the trivial, non-trivial topological phases and at the quantum topological transition of the chains. We show that the device's electrical conductance and the Wiedemann-Franz ratio at the topological transition have universal values at very low temperatures. The conductance and thermopower of the device with diatomic sp-chains, at their topological transition, give direct evidence of fractional charges in the system. The former has an anomalous low-temperature behavior, attaining a universal value that is a consequence of the double degeneracy of the system due to the presence of zero energy modes. On the other hand, the system can be tuned to exhibit high values of the thermoelectric figure of merit and the power factor at high temperatures.

Direct observation of the specific heat of Majorana quasiparticles in superfluid3He-B

The existence of Majorana quasiparticles was predicted in the edge state in topological insulators, especially in the p-wave superfluid medium [Formula: see text]He-B. Due to its purity and coherent quantum state, [Formula: see text]He-B is an ideal platform for searching for Majorana fermions in condensed matter systems. In the limit of extremely low temperatures, the density of Bogolyubov quasiparticles and the heat capacity of [Formula: see text]He-B decrease exponentially. In this article, we present the first observation of the deviation of its heat capacity from exponential dependence in the limit of record low cooling. We found an additional heat capacity that more than doubled the heat capacity of bulk [Formula: see text]He-B and changes as T[Formula: see text]. The additional heat capacity is in good agreement with the predicted heat capacity of 2D gas of Majorana. This observation is a direct proof of the existence of Majorana quasiparticles in [Formula: see text]He-B.

Multifaceted properties of Andreev bound states: interplay of symmetry and topology

Andreev bound states (ABSs) ubiquitously emerge as a consequence of non-trivial topological structures of the order parameter of superfluids and superconductors and significantly contribute to thermodynamics and low-energy quantum transport phenomena. We here share the current status of our knowledge on their multifaceted properties such as Majorana fermions and odd-frequency pairing. A unified concept behind ABSs originates from a soliton state in the one-dimensional Dirac equation with mass domain wall and interplay of ABSs with symmetry and topology enrich their physical characteristics. We make an overview of ABSs with a special focus on superfluid 3He. The quantum liquid confined to restricted geometries serves as a rich repository of noteworthy quantum phenomena, such as the mass acquisition of Majorana fermions driven by spontaneous symmetry breaking, topological quantum criticality, Weyl superfluidity and the anomalous magnetic response. The marriage of the superfluid 3He and nano-fabrication techniques will take one to a new horizon of topological quantum phenomena associated with ABSs.This article is part of the theme issue 'Andreev bound states'.

Scattering Theory on Surface Majorana Fermions by an Impurity in ^{3}He-B

We have formulated the scattering theory on Majorana fermions emerging in the surface bound state of the superfluid ^{3}He B phase (^{3}He-B) by an impurity. By applying the theory to the electron bubble, which is regarded as the impurity, trapped below a free surface of ^{3}He-B, the observed mobility of the electron bubble [J. Phys. Soc. Jpn. 82, 124607 (2013)JUPSAU0031-901510.7566/JPSJ.82.124607] is quantitatively reproduced. The mobility is suppressed in low temperatures from the expected value in the bulk ^{3}He-B by the contribution from the surface Majorana fermions. By contrast, the mobility does not depend on the trapped depth of the electron bubble in spite of the spatial variation of the wave function of the surface Majorana fermions. Our formulated theory demonstrates the depth-independent mobility by considering intermediate states in the scattering process. Therefore, we conclude that the experiment has succeeded in observing Majorana fermions in the surface bound state.

Critical Velocity in the Presence of Surface Bound States in Superfluid ^{3}He-B

A microelectromechanical oscillator with a gap of 1.25  μm was immersed in superfluid ^{3}He-B and cooled below 250  μK at various pressures. Mechanical resonances of its shear motion were measured at various levels of driving force. The oscillator enters into a nonlinear regime above a certain threshold velocity. The damping increases rapidly in the nonlinear region and eventually prevents the velocity of the oscillator from increasing beyond the critical velocity which is much lower than the Landau critical velocity. We propose that this peculiar nonlinear behavior stems from the escape of quasiparticles from the surface bound states into the bulk fluid.

Observation of Half-Quantum Vortices in Topological Superfluid ^{3}He

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 ^{3}He-A but have never been resolved there. Here we report an observation of half-quantum vortices (HQVs) in the polar phase of superfluid ^{3}He. The vortices are created with rotation or by the Kibble-Zurek mechanism and identified based on their nuclear magnetic resonance signature. This discovery provides a pathway for studies of unpaired Majorana modes bound to the HQV cores in the polar-distorted A phase.

Lifshitz Transition in the Double-Core Vortex in ^{3}He-B

We study the spectrum of fermion states localized within the vortex core of a weak-coupling p-wave superfluid. The low energy spectrum consists of two anomalous branches that generate a large density of states at the locations of the half cores of the vortex. Fermi liquid interactions significantly stretch the vortex structure, which leads to a Lifshitz transition in the effective Fermi surface of the vortex core fermions. We apply the results to the rotational dynamics of vortices in superfluid ^{3}He-B and find an explanation for the observed slow mode.