Chiral symmetry breaking in superfluid 3He-A

Surface State Dissipation in Confined ^{3}He-A

We have studied the power dependence of superfluid Helmholtz resonators in flat (750 and 1800 nm) rectangular channels. In the A phase of superfluid ^{3}He, we observe a nonlinear response for velocities larger than a critical value. The small size of the channels stabilizes a static uniform texture that eliminates dissipative processes produced by changes in the texture. For such a static texture, the lowest velocity dissipative process is due to the pumping of surface bound states into the bulk liquid. We show that the temperature dependence of the critical velocity observed in our devices is consistent with this surface-state dissipation. Characterization of the force-velocity curves of our devices may provide a platform for studying the physics of exotic surface bound states in superfluid ^{3}He.

Broken Inversion Symmetry in Van Der Waals Topological Ferromagnetic Metal Iron Germanium Telluride

Inversion symmetry breaking is critical for many quantum effects and fundamental for spin-orbit torque, which is crucial for next-generation spintronics. Recently, a novel type of gigantic intrinsic spin-orbit torque is established in the topological van der Waals (vdW) magnet iron germanium telluride. However, it remains a puzzle because no clear evidence exists for interlayer inversion symmetry breaking. Here, the definitive evidence of broken inversion symmetry in iron germanium telluride directly measured by the second harmonic generation (SHG) technique is reported. The data show that the crystal symmetry reduces from centrosymmetric P63/mmc to noncentrosymmetric polar P3m1 space group, giving the threefold SHG pattern with dominant out-of-plane polarization. Additionally, the SHG response evolves from an isotropic pattern to a sharp threefold symmetry upon increasing Fe deficiency, mainly due to the transition from random defects to ordered Fe vacancies. Such SHG response is robust against temperature, ensuring unaltered crystalline symmetries above and below the ferromagnetic transition temperature. These findings add crucial new information to the understanding of this interesting vdW metal, iron germanium telluride: band topology, intrinsic spin-orbit torque, and topological vdW polar metal states.

Weyl Fermions and broken symmetry phases of laterally confined3He films

Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D)3He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum,Lz=(N/2)ℏ, forN/2Cooper pairs. The power law suppression of the angular momentum,Lz(T)≃(N/2)ℏ[1-23(πT/Δ)2]for0⩽T≪Tc, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid3He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry atDc2∼16ξ0. The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement lengthD→Dc2. The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral 'polar phase' atDc1∼9ξ0, in which a single p-wave orbital state of Cooper pairs is aligned along the channel.

Intrinsic Anomalous Hall Effect in a Bosonic Chiral Superfluid

The anomalous Hall effect has had a profound influence on the understanding of many electronic topological materials but is much less studied in their bosonic counterparts. We predict that an intrinsic anomalous Hall effect exists in a recently realized bosonic chiral superfluid, a p-orbital Bose-Einstein condensate in a 2D hexagonal boron nitride optical lattice [Wang et al., Nature (London) 596, 227 (2021)NATUAS0028-083610.1038/s41586-021-03702-0]. We evaluate the frequency-dependent Hall conductivity within a multi-orbital Bose-Hubbard model that accurately captures the real experimental system. We find that in the high frequency limit, the Hall conductivity is determined by finite loop current correlations on the s-orbital residing sublattice, the latter a defining feature of the system's chirality. In the opposite limit, the dc Hall conductivity can trace its origin back to the noninteracting band Berry curvature at the condensation momentum, although the contribution from atomic interactions can be significant. We discuss available experimental probes to observe this intrinsic anomalous Hall effect at both zero and finite frequencies.

Geometric Induction in Chiral Superfluids

We explore the properties of chiral superfluid thin films coating a curved surface. Because of the vector nature of the order parameter, a geometric gauge field emerges and leads to a number of observable effects such as anomalous vortex-geometric interaction and curvature-induced mass and spin supercurrents. We apply our theory to several well-known phases of chiral superfluid ^{3}He and derive experimentally observable signatures. We further discuss the cases of flexible geometries where a soft surface can adapt itself to compensate for the strain from the chiral superfluid. The proposed interplay between geometry and chiral superfluid order provides a fascinating avenue to control and manipulate quantum states with strain.

Spin-Nernst Effect in Time-Reversal-Invariant Topological Superconductors

We investigate the spin-Nernst effect in time-reversal-invariant topological superconductors, and show that it provides smoking-gun evidence for helical Cooper pairs. The spin-Nernst effect stems from asymmetric, in spin space, scattering of quasiparticles at nonmagnetic impurities, and generates a transverse spin current by the temperature gradient. Both the sign and the magnitude of the effect sensitively depend on the scattering phase shift at impurity sites. Therefore the spin-Nernst effect is uniquely suitable for identifying time-reversal-invariant topological superconducting orders.

Cryogen-free one hundred microkelvin refrigerator

A temperature below 100 µK is achieved in a customized cryogen-free dilution refrigerator with a copper-nuclear demagnetization stage. The lowest temperature of conduction electrons of the demagnetization stage is below 100 µK as measured by using a pulsed platinum nuclear magnetic resonance thermometer, and the temperature can remain below 100 µK for over 10 h. A demagnetization magnetic field of up to 9 T and a research magnetic field of up to 12 T can be controlled independently, provided by a coaxial room-temperature-bore cryogen-free magnet.

Impurity-Induced Anomalous Thermal Hall Effect in Chiral Superconductors

Chiral superconductors exhibit novel transport properties that depend on the topology of the order parameter, topology of the Fermi surface, the spectrum of bulk and edge Fermionic excitations, and the structure of the impurity potential. In the case of electronic heat transport, impurities induce an anomalous (zero-field) thermal Hall conductivity that is easily orders of magnitude larger than the quantized edge contribution. The effect originates from branch-conversion scattering of Bogoliubov quasiparticles by the chiral order parameter, induced by potential scattering. The former transfers angular momentum between the condensate and the excitations that transport heat. The anomalous thermal Hall conductivity is shown to depend to the structure of the electron-impurity potential, as well as the winding number ν of the chiral order parameter Δ(p)=|Δ(p)|e^{iνϕ_{p[over ^]}}. The results provide quantitative formulas for interpreting heat transport experiments seeking to identify broken T and P symmetries, as well as the topology of the order parameter for chiral superconductors.

Spin transfer torque and exchange coupling in Josephson junctions with ferromagnetic superconductor reservoirs

In this paper, the spin transfer torque (STT) and the exchange coupling of the Josephson junctions containing the interesting cases of diffusive/ballistic-triplet/singlet ferromagnetic superconductor (FS) materials are investigated. First, the diffusive FS₁/F _c /FS₂ structures with F _c being a junction consisting of ferromagnetic and normal metal parts as well as insulating barriers are investigated. Secondly, the ballistic Josephson junction containing the triplet chiral p/wave FS reservoirs is studied. Using the Nazarov quantum circuit theory for the diffusive structures, it is found that the antiparallel/parallel or vice versa parallel/antiparallel transition of the favorable exchange coupling takes place due to the appearance of the only out-of-plane STT. Furthermore, the analyze of the phase difference interval in which an interlayer length-induced antiparallel/parallel transition can be occurred, is performed. Afterward, the mentioned ballistic structure is dealt with solving the 16 [Formula: see text] 16 Bogoliubov-de-Gennes equation. It is found that although the exchange fields of the FS are laid in the z and y  direction, the STT interestingly exists in all three directions of x, y  and z. This exciting finding suggests that the favorable equilibrium configuration concerning the least exchange coupling occurs in the relative exchange field direction different from 0 or [Formula: see text].

Dynamics of the Vortex-Particle Complexes Bound to the Free Surface of Superfluid Helium

We present an experimental and theoretical study of the 2D dynamics of electrically charged nanoparticles trapped under a free surface of superfluid helium in a static vertical electric field. We focus on the dynamics of particles driven by the interaction with quantized vortices terminating at the free surface. We identify two types of particle trajectories and the associated vortex structures: vertical linear vortices pinned at the bottom of the container and half-ring vortices traveling along the free surface of the liquid.

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'.

Chiral Domain Structure in Superfluid ^{3}He-A Studied by Magnetic Resonance Imaging

The existence of a spatially varying texture in superfluid ^{3}He is a direct manifestation of the complex macroscopic wave function. The real space shape of the texture, namely, a macroscopic wave function, has been studied extensively with the help of theoretical modeling but has never been directly observed experimentally with spatial resolution. We have succeeded in visualizing the texture by a specialized magnetic resonance imaging. With this new technology, we have discovered that the macroscopic chiral domains, of which sizes are as large as 1 mm, and corresponding chiral domain walls exist rather stably in ^{3}He-A film at temperatures far below the transition temperature.

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.

New perspectives for Rashba spin-orbit coupling

In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain the peculiarities of electron spin resonance in two-dimensional semiconductors. Over the past 30 years, Rashba spin-orbit coupling has inspired a vast number of predictions, discoveries and innovative concepts far beyond semiconductors. The past decade has been particularly creative, with the realizations of manipulating spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and the discovery of new topological classes of materials. This progress has reinvigorated the interest of physicists and materials scientists in the development of inversion asymmetric structures, ranging from layered graphene-like materials to cold atoms. This Review discusses relevant recent and ongoing realizations of Rashba physics in condensed matter.

Orbital angular momentum and spectral flow in two-dimensional chiral superfluids

We study the orbital angular momentum (OAM) L_{z} in two-dimensional chiral (p_{x}+ip_{y})^{ν}-wave superfluids (SFs) of N fermions on a disk at zero temperature, in terms of spectral asymmetry and spectral flow. It is shown that L_{z}=νN/2 for any integer ν, in the Bose-Einstein condensation regime. In contrast, in the BCS limit, while the OAM is L_{z}=N/2 for the p+ip-wave SF, for chiral SFs with ν≥2, the OAM is remarkably suppressed as L_{z}=N×O(Δ_{0}/ϵ_{F})≪N, where Δ_{0} is the gap amplitude and ϵ_{F} is the Fermi energy. We demonstrate that the difference between the p+ip-wave SF and the other chiral SFs in the BCS regimes originates from the nature of edge modes and related depairing effects.