Vortex Mutual Friction in Superfluid 3He

We give a full account of our extensive measurements of vortex mutual friction in rotating superfluid ³He, 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 0.63 Δ is used, but the Justification for such a substitution 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 at 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 ) ħ, consistent with the prediction of the spectral flow theory. We find that the most uniform l texture is obtained by cooling through T_c while rotating, and then stopping rotation. Detailed investigation of textural memory effects shows that the uniform l-up and l-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 in ⁴HeII.     

Topology in superfluid3He: Recent results

We discuss: the topological phase transition in nonsingular vortices in³He-A; vortices in³He-B and solitons terminating on strings; topological defects of the A-B interface: the interaction of continuous A-phase vortices with singular B-phase vortices across the interface; extended degeneracy and topology of Larmor precession; and internal topology in thin³He-A film, responsible for chiral edge states of fermions and QHE.     

Angular momentum of the fields of a few-mode fiber. III. Optical Magnus effect, Berry phase, and topological birefringence

It is shown that, on the one hand, the evolution of the angular rotation of the lines of nodes of the CP₁₁ mode is a manifestation of the optical Magnus effect in a few-mode fiber with a parabolic refractive index profile, and, on the other hand, the additional phase γ _b =±δβ ₂₁ z in CV and IV vortices is the Berry topological phase, which arises as a result of the cyclic change in the orientations of the orthogonal axes of dislocations. The splitting of the propagation velocities of orthogonal circularly polarized CV⁺ and IV⁻ modes in an LV vortex in a parabolic fiber is a manifestation of the phenomenon of topological birefringence of a few-mode fiber. The azimuth of the linear polarization of a vortex undergoes continuous angular rotation. In an optical fiber with a stepped index profile the CP₁₁ mode forms circularly polarized edge dislocation over lengths which are multiples of half the beat length, and over lengths which are odd multiples of the quarter beat length it forms linearly polarized fields with a purely screw dislocation. This transformation of edge and screw dislocations can be regarded formally as conversion of the polarizational angular momentum into orbital angular momentum. The conversion of angular momentum is a reflection of the dynamical unity of the optical Magnus effect and the Berry topological phase in the fields of a few-mode fiber. Pis’ma Zh. Tekh. Fiz. 23, 59–67 (December 12, 1997)     

Majorana Edge Modes of Superfluid 3He A-?and?B-Phases

Motivated by a recent experiment on the superfluid ³He confined in a thin slab, we discuss the Majorana edge modes under the experimental situation. We solve the quasi-classical Eilenberger equation, which is quantitatively reliable, to evaluate several observables, such as local density of states, mass current for the A-phase, and spin current for the B-phase. On the basis of the quantitative calculation, we propose several experiments to check the existence of the Majorana modes.     

Superfluid Rotation Sensor with Helical Laser Trap

The macroscopic quantum states of the dilute bosonic ensemble in helical laser trap at the temperatures about 10^?6 K are considered in the framework of the Gross-Pitaevskii equation. The helical interference pattern is composed of the two counter propagating Laguerre-Gaussian optical vortices with opposite orbital angular momenta ?? and this pattern is driven in rotation via angular Doppler effect. Macroscopic observables including linear momentum and angular momentum of the atomic cloud are evaluated explicitly. It is shown that rotation of reference frame is transformed into translational motion of the twisted matter wave. The speed of translation equals the group velocity of twisted wavetrain V _z =Ω?/k and alternates with a sign of the frame angular velocity Ω and helical pattern handedness ?. We address detection of this effect using currently accessible laboratory equipment with emphasis on the difference between quantum and classical fluids.     

Theory of superconductivity. 3. 2D conduction bands for high Tc. Bose-Einstein condensation transition of the third order

A general theory of superconductivity is developed, starting with a BCS Hamiltonian in which the interaction strengths (V ₁₁,V ₂₂,V ₁₂) among and between “electron” (1) and “hole” (2) Cooper pairs are differentiated, and identifying “electrons” (“holes”) with positive (negative) masses as those Bloch electrons moving on the empty (filled) side of the Fermi surface. The supercondensate is shown to be composed of equal numbers of “electron” and “hole” ground (zero-momentum) Cooper pairs with charges ±2e and different masses. This picture of a neutral supercondensate naturally explains the London rigidity and the meta-stability of the supercurrent ring. It is proposed that for a compound conductor the supercondensate is formed between “electron” and “hole” Fermi energy sheets with the aid of optical phonons having momenta greater than the minimum distance (momentum) between the two sheets. The proposed model can account for the relatively short coherence lengthsξ observed for the compound superconductors including intermetallic compound, organic, and cuprous superconductors. In particular, the model can explain why these compounds are type II superconductors in contrast with type I elemental superconductors whose condensate is mediated by acoustic phonons. A cuprous superconductor has 2D conduction bands due to its layered perovskite lattice structure. Excited (nonzero momentum) Cooper pairs (bound by the exchange of optical phonons) aboveT _c are shown to move like free bosons with the energy-momentum relation?=1/2v_Fq. They undergo a Bose-Einstein condensation atT _c = 0.977?v _F k _b ^?1 n ^1/2, wheren is the number density of the Cooper pairs. The relatively high value ofT _c (～100 K) arises from the fact that the densityn is high:n ^1/2～ξ^?1 ～10⁷ cm^?1. The phase transition is of the third order, and the heat capacity has a reversed lambda (λ)-like peak atT _c .     

Modified BCS Mechanism of Cooper Pair Formation in Narrow Energy Bands of Special Symmetry I. Band Structure of Niobium

The superconductor niobium possesses a narrow, roughly half-filled energy band with Bloch functions, which can be unitarily transformed into optimally localized spin-dependent Wannier functions belonging to a double-valued representation of the space group O ⁹ _h of Nb. The special symmetry of this superconducting band can be interpreted within a nonadiabatic extension of the Heisenberg model of magnetism. While the original Heisenberg model assumes that there is exactly one electron at each atom, the nonadiabatic model postulates that the Coulomb repulsion energy in narrow, partly filled energy bands is minimum when the balance between the bandlike and atomiclike behavior is shifted as far as possible toward the atomiclike behavior. Within this nonadiabatic Heisenberg model, the electrons of the superconducting band form Cooper pairs at zero temperature. Just as in the BCS theory of superconductivity, this formation of Cooper pairs is mediated by phonons. However, there is an important difference: within the nonadiabatic Heisenberg model, the electrons in a narrow superconducting band are constrained to form Cooper pairs because the conservation of spin angular momentum would be violated in any normal conducting state. There is great evidence that these constraining forces are responsible for superconducting eigenstates. This means that an attractive electron–electron interaction alone is not able to produce stable Cooper pairs. In addition, the constraining forces established within the nonadiabatic Heisenberg model must exist in a superconductor.     

Photoelectric and electrical properties of a reverse-biased p-Si/n-CdS/n +-CdS heterostructure

We have demonstrated a photosensitive p-Si/n-CdS/n ⁺-CdS structure. A reverse bias voltage applied to this structure leads to electron injection from the narrow-band-gap material p-Si to the high-resistivity, wide-band-gap semiconductor n-CdS. Evidence is presented for mutual compensation of opposite drift and diffusion flows of charge carriers in this structure. At current densities in the range I ～ 10^?8 to 10^?7 A/cm², the opposite drift and diffusion flows of nonequilibrium minority charge carriers cause the photosensitivity of the structure to change sign in both the short- and long-wavelength regions of the spectrum. The mutual compensation of the opposite drift and diffusion flows at current densities on the order of ～10⁶ A/cm² leads to sublinear behavior of the reverse current-voltage characteristic in a wide range of bias voltages.     

A laminar walljet on a moving wall

Summary The laminar wall jet from a momentum source at the leading edge on a wall which is moving in the same direction with uniform velocity is considered. It is shown that a solution is possible starting at the leading edge and proceeding all the way downstream. For smallx (x measures distance along the wall) we find the solution by using a natural coordinate expansion in powers ofx ^1/2. For largex, the asymptotic solution is approached through eigensolutions and the two coordinate expansions are then joined by a numerical solution of the full equations.With 2 Figures     

Enhancement of Magnetization in Liquid 3He at Aerogel Interface

A novel feature of condensate state in liquid ³He is predicted theoretically, which consists of spin triplet s-wave Cooper pairs (Higashitani et al. in J. Low. Temp. Phys. 155:83–97, 2009). Such a spin triplet s-wave state will appear inside aerogel near the surface boundary contacting with superfluid ³He-B, and the enhancement of magnetization due to s-wave state is theoretically expected (Nagato et al. in J. Phys. Soc. Jpn. 78:123603, 2009; Higashitani et al. in Phys. Rev. B 85:024524, 2012). In order to detect this proximity effect, we made the interface in columnar glass tube which coated with 2.5 layer ⁴He, and set a saddle shape NMR coil very near the interface. At 7 bar, we found that superfluidity in liquid ³He inside aerogel never occurred, even at considerably low temperatures. At 24 bar below T/T _c =0.392, we observed no decrease of magnetization with decreasing temperatures. This phenomenon might be due to spin triplet s-wave Cooper pairs.     

The entrainment theorem for wall driven boundary layer flows

Boundary layer flows driven by permeable plane surfaces, stretching with power–law velocities are considered in the presence of an applied lateral mass flux. The relationship between the wall shear stress and the entrainment velocity (the transversal velocity at the outer edge of the boundary layer) as a function of the mass transfer parameter f _w is examined analytically by using the Merkin transformation method. It is shown that at the value of f _w where the wall shear stress vanishes, the entrainment velocity reaches a minimum or maximum value. This relationship between two characteristic quantities at the outer and inner edge of the boundary layer, respectively, is referred to as entrainment theorem. Its physical content is analyzed in the paper in some detail.     

Quasiparticle scattering amplitude for normal liquid3He

The quasiparticle scattering amplitude is calculated from a semimicroscopic model by analytically solving a generalization of Landau's integral equation to momentum transfers up to 2 _PF. This solution in general does not obey exchange symmetry for a given particle-hole irreducible vertex partf _pp′(q). We establish conditions for and explicitly construct exchange-symmetric scattering amplitudes by adding higher angular momentum components. Results using certain models forf _pp′(q) are compared with transport properties of liquid³He.     

A new model of the erase process in single layer direct overwritemagneto-optical recording media

The effects of angular momentum compensation on domain wall motion are considered. Particular attention is paid to the dynamic parameters of the wall in response to effects brought about by the approach to the angular momentum compensation temperature. When the wall gets close to the angular momentum compensation point, the net angular momentum is effectively lowered, thus causing the mobility of the wall to increase markedly. This unusual behavior is believed to be responsible for the erase process in single-layer direct-overwrite magnetooptical recording media     

Azimuthally unidirectional transport of energy in magnetoelectric fields: topological Lenz’s effect

Magnetic-dipolar modes (MDMs) in a quasi-2D ferrite disc are microwave energy-eigenstate oscillations with topologically distinct structures of rotating fields and unidirectional power-flow circulations. At the first glance, this might seem to violate the law of conservation of an angular momentum, since the microwave structure with an embedded ferrite sample is mechanically fixed. However, an angular momentum is seen to be conserved if topological properties of electromagnetic fields in the entire microwave structure are taken into account. In this paper, we show that due to the topological action of the azimuthally unidirectional transport of energy in a MDM-resonance ferrite sample there exists the opposite topological reaction on a metal screen placed near this sample. We call this effect topological Lenz’s effect. The topological Lenz’s law is applied to opposite topological charges: one in a ferrite sample and another on a metal screen. The MDM-originated near fields – the magnetoelectric (ME) fields – induce helical surface electric currents and effective charges on a metal. The fields formed by these currents and charges will oppose their cause.     

Angular momentum of the fields of a few-mode fiber: I. A perturbed optical vortex

This paper presents the results of studies of the physical nature of the electrodynamic angular momentum of a stable CV ₊₁ ⁺ vortex in a few-mode fiber. It shows that the angular momentum of a CV ₊₁ ⁺ vortex can be conventionally divided into orbital and spin angular momenta. The longitudinal component of the fundamental HE ₁₁ ⁺ mode on the axis of the fiber has a pure screw dislocation with a topological charge of e=+1. The longitudinal component of a CV ₊₁ ⁺ vortex also has a pure screw dislocation on the axis of the fiber with a topological charge of e=+2. Therefore, perturbation of a CV ₊₁ ⁺ vortex by the field of the fundamental HE ₁₁ ⁺ mode removes the degeneracy of the pure screw dislocations of the longitudinal and transverse components of the field and breaks down the structural stability of the CV ₊₁ ⁺ vortex. As a result, an additional azimuthal flux of energy with an angular momentum opposite to that of the fundamental flux is induced. An analogy is drawn between the stream lines of a perturbed CV vortex and the stream lines of an inviscid liquid flowing around a rotating cylinder. Studies of the evolution of a CV vortex in a parabolic fiber show that they are structurally stable when acted on by the perturbing field of the HE ₁₁ ⁺ mode. However, perturbing a CV ₊₁ ⁺ 1 vortex of a stepped fiber with the field of the HE ₁₁ ⁺ mode destroys the structural stability of the vortex. It is found that the propagation of a circularly polarized CV vortex can be represented as a helical wavefront screwing into the medium of the fiber. The propagation of a linearly polarized vortex in free space is characterized by the translational displacement (without rotation) of a helical wavefront. Pis’ma Zh. Tekh. Fiz. 23, 74–81 (November 12, 1997)     

BCS-BEC Crossover and Chiral Anomaly in p-Wave Superfluids with the Symmetry of A1-Phase

We solve the Leggett equations for BCS-BEC crossover in the 3D resonance p-wave superfluid with the symmetry of A1-phase. We calculate sound velocity, normal density and specific heat for the BCS-domain (μ>0), BEC-domain (μ<0) as well as close to important point μ=0 in 100% polarized case. We find the indications of quantum phase-transition close to the point μ(T=0)=0. Deep in BCS and BEC-domains the crossover ideas of Leggett and Nozieres, Schmitt-Rink work pretty well. We discuss the spectrum of orbital waves, the paradox of intrinsic angular momentum and complicated problem of chiral anomaly in BCS A1-phase at T=0. We present two different approaches to a chiral anomaly: one based on supersymmetric hydrodynamics, another one on the formal analogy with Dirac equation in quantum electrodynamics (QED theory). We evaluate the damping of nodal fermions due to different decay processes in superclean case at T=0 and find that we are in a ballistic regime ω τ?1. We propose to use aerogel or nonmagnetic impurities to reach hydrodynamic regime ω τ?1 at T=0. We discuss the concept of spectral flow and exact cancellations between time-derivatives of anomalous and quasiparticle currents in the equation for the conservation of total linear momentum. We propose to derive and solve a kinetic equation for nodal quasiparticles both in the hydrodynamic and in the ballistic regimes to demonstrate this cancellation explicitly. We briefly discuss the role of the other residual interactions different from damping and invite experimentalists to measure the spectrum and damping of orbital waves in A-phase of ³He at low temperatures.     

Energy supply to the region of colliding plasma flows with opposite polarization fields

The interaction of two colliding deuterium plasma flows propagating in opposite directions across the magnetic field and having opposite directions of the polarization fields has been experimentally studied. The plasma flows with densities up to 10¹⁶ cm^?3 and a velocity of up to 2 × 10⁷ cm/s were formed using discharges initiated in crossed E × H fields. Each discharge operated at an electric power of up to 300 mW and a discharge current up to 100 kA. The results of measurements of the equivalent capacitance of polarized plasma flows were used to estimate the transverse permittivity of plasma. The rate of depolarization in colliding flows was determined. The frequency and energy characteristics of a plasma LC circuit formed by colliding flows were estimated. The temporal modulation of plasma density in the flows was measured.     

Quasiclassical Green's function in the BCS pairing theory

We study a generalization of the quasiclassical Green's function which allows us to include the transfer of momentum to the particles. In this approach, we may handle Galilei transformations, rotations, and gauge transformations in a systematic way. As an example, we calculate the quasiparticle flow pattern which arises during the motion of the orbital vector in the ABM phase, and discuss the meaning of the intrinsic angular momentum of the Cooper pairs. Finally, we consider charged particles in a magnetic field, and derive a Boltzmann equation for a superconductor which applies to the Hall effect in the case of moving vortices.On leave from Institut für Théorie der Kondensierten Materie, Universität Karlsruhe.     

Electromigration-induced cracks in eutectic SnPb solder reaction couple at room temperature

Electromigration (EM) of 63Sn–37Pb solder reaction couple was studied under high current density of 5 × 10³ A/cm² at room temperature. There was non-uniform distribution of current density across the linear specimen, and the dissimilar interface of two different materials could trigger current crowding especially at the edge of the interface. Though the atoms/ions of Sn and Pb would migrate along the direction of electron flow pushed by electron wind force, the Sn atoms were observed to be the principal diffusion entities at room temperature. Depletion of mass at cathode side induced the tensile stress along parallel direction of the specimen cross-section, while the accumulation of mass at anode side induced the compressive stress along the perpendicular direction of the specimen cross-section. Crack initiation and propagation in both cathode and anode side was found to be strongly dependent on the current density distribution.