Transverse force on a vortex and vortex mass: effects of free bulk and vortex-core bound quasiparticles

The paper reassesses the old but still controversial problem of the transverse force on a vortex and the vortex mass. The transverse force from free bulk quasiparticles on the vortex, both in the Bose and the Fermi liquid, originates from the Aharonov--Bohm effect. However, in the Fermi liquid one should take into account peculiarities of the Aharonov--Bohm effect for BCS quasiparticles described by two-component spinor wave functions. There is no connection between the transverse force (either from free bulk quasiparticles or from vortex-core bound quasiparticles) and the spectral flow in the vortex core in superfluid Fermi liquid, in contrast to widely known claims. In fact, there is no steady spectral flow in the core of the moving vortex, and the analogy with the Andreev bound states in the SNS junction, where the spectral flow is really possible, is not valid in this respect. The role of the backflow on the vortex mass is clarified. The backflow is an inevitable consequence of a mismatch between the currents inside and outside the vortex core and restores the conservation of the particle number (charge) violated by this mismatch. In the Fermi liquid the backflow compensates the current through the core bound states, which is a source of the vortex mass (the Kopnin mass). This results in renormalization of the Kopnin vortex mass by a numerical factor.Comment: 20 pages, 4 figures, the version accepted for publication in Phys. Rev.

Spin and mass superfluidity in ferromagnetic spin-1 Bose-Einstein condensate

The paper investigates the coexistence and interplay of spin and mass superfluidity in a ferromagnetic spin-1 Bose-Einstein condensate. Superfluidity is possible only in the presence of uniaxial anisotropy (linear and quadratic Zeeman effect). This follows from the topology of the order-parameter space (vacuum manifold). According to the Landau criterion, the critical phase gradients, both for mass and spin supercurrents, vanish at the phase transition from the easy-plane to the easy-axis anisotropy. However, mass superfluidity is still possible at the phase transition. This is because the Landau criterion signals instability only with respect to nonsingular vortices with special ratio between circulations of mass and spin currents. Phase slips produced by these vortices are not sufficient for complete decay of supercurrents. Full decay of supercurrents requires phase slips with vortices of another topological class and larger energy. These phase slips are suppressed by energetic barriers up to the upper critical velocity (gradient) exceeding the Landau critical velocity. The upper critical velocity does not vanish nor has any anomaly in the critical point at the phase transition from the easy-plane to the easy-axis anisotropy.Comment: 13 pages, 6 figures, revised version published in Phys. Rev.

Charge transport and shot noise in ballistic graphene sheet

The current and the shot noise in a graphene sheet were analyzed in the ballistic regime for arbitrary voltage drops between leads and the sheet in the limit of infinite aspect ratio of the sheet width to its length, when quantization of transversal wave vectors is not essential. The cases of coherent and incoherent ballistic transport were compared. At high voltages the difference with coherent transport is not essential. But at low voltages conductance and Fano-factor dependences for incoherent transport become non-monotonous so that the conductance has a minimum and the Fano factor has a maximum at non-zero voltage bias.Comment: 6 pages, 2 figure

Transverse force on a vortex in lattice models of superfluids

The paper derives the transverse forces (the Magnus and the Lorentz forces) in the lattice models of superfluids in the continuous approximation. The continuous approximation restores translational invariance absent in the original lattice model, but the theory is not Galilean invariant. As a result, calculation of the two transverse forces on the vortex, Magnus force and Lorentz force, requires the analysis of two balances, for the true momentum of particles in the lattice (Magnus force) and for the quasimomentum (Lorentz force) known from the Bloch theory of particles in the periodic potential. While the developed theory yields the same Lorentz force, which was well known before, a new general expression for the Magnus force was obtained. The theory demonstrates how a small Magnus force emerges in the Josephson-junction array if the particle-hole symmetry is broken. The continuous approximation for the Bose--Hubbard model close to the superfluid-insulator transition was developed, which was used for calculation of the Magnus force. The theory shows that there is an area in the phase diagram for the Bose--Hubbard model, where the Magnus force has an inverse sign with respect to that which is expected from the sign of velocity circulation.Comment: 8 pages, 1 figur

Tunneling into 1D and quasi-1D conductors and Luttinger-liquid behavior

The paper addresses the problem whether and how it is possible to detect the Luttinger-liquid behavior from the $IV$ curves for tunneling to 1D or quasi-1D conductors. The power-law non-ohmic $IV$ curve, which is usually considered as a manifestation of the Luttinger-liquid behavior, can be also deduced from the theory of the Coulomb blockaded junction between 3D conductors affected by the environment effect. In both approaches the power-law exponents are determined by the ratio of the impedance of an effective electric circuit to the quantum resistance. Though two approaches predict different power-law exponents (because of a different choice of effective circuits), the difference becomes negligible for a large number of conductance channels.Comment: 13 pages, submitted to Proceedings of Symposium on Ultra Low Energy Physics, Helsinki, January 200

Effect of Klein tunneling on conductance and shot noise in ballistic graphene

The conductance and the Fano factor in a graphene sheet in the ballistic regime are calculated. The electrostatic potential in the sheet is modeled by a trapezoid barrier, which allows to use the exact solution of the Dirac equation in a uniform electric field in the slope areas (the two lateral sides of the trapezoid). A special attention is devoted to asymmetry with respect to the sign of the gate voltage, which is connected with the difference between the Klein tunneling and the over-barrier reflection. The comparison of the developed theory with the experiment supports the conclusion that the Klein tunneling was revealed experimentally.Comment: 12 pages, 6 figures, typos correcte

Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T=0 superfluid turbulence

The article considers implications of tilt symmetry (symmetry with respect to tilting of the coordinate axis with respect to which vortex motion is studied) in the non-linear dynamics of Kelvin waves. The conclusion is that although the spectrum of Kelvin wave is not tilt-invariant, this does not compromise tilt invariance of the Kelvin-wave cascade vividly argued now in the theory of superfluid turbulence. The article investigates the effect of strong kelvon interaction on the power-law exponent for the Kelvin-wave cascade and suggests a simple picture of the crossover from the classical Kolmogorov cascade to the quantum Kelvin-wave cascade, which does not encounter with mismatch of the energy distributions at the crossover and does not require a broad intermediate interval for realization of the crossover.Comment: 7 pages, 1 figur

Reply to Comment on "Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T=0 superfluid turbulence" [arXiv:1208.4593]

I discuss the Comment by L'vov and Nazarenko (arXiv:1208.4593) aiming at refutation of my perviously published criticism of their mechanism of the Kelvin-wave cascade. It is important that in their Comment L'vov and Nazarenko admitted that the Hamiltonian, from which they derived their mechanism, is not tilt-invariant. This provides full ammunition to their critics, who believe that their mechanism is in conflict with tilt symmetry of the Kelvin-wave dynamics in an isotropic space.Comment: 2 page

Superfluid spin transport in ferro- and antiferromagnets

This paper focuses on spin superfluid transport, observation of which was recently reported in antiferromagnet Cr$_2$O$_3$ [Yuan et al., Sci. Adv. 4, eaat1098 (2018)]. This paper analyzes the role of dissipation in transformation of spin current injected with incoherent magnons to a superfluid spin current near the interface where spin is injected. The Gilbert damping parameter in the Landau-Lifshitz-Gilbert theory does not describe dissipation properly, and the dissipation parameters are calculated from the Boltzmann equation for magnons scattered by defects. The two-fluid theory is developed similar to the two-fluid theory for superfluids. This theory shows that the influence of temperature variation in bulk on the superfluid spin transport (bulk Seebeck effect) is weak at low temperatures. The scenario that the results of Yuan et al. are connected with the Seebeck effect at the interface between the spin detector and the sample is also discussed. The Landau criterion for an antiferromagnet put in a magnetic field is derived from the spectrum of collective spin modes. The Landau instability starts in the gapped mode earlier than in the Goldstone gapless mode, in contrast to easy-plane ferromagnets where the Goldstone mode becomes unstable. The structure of the magnetic vortex in the geometry of the experiment is determined. The vortex core has the skyrmion structure with finite magnetization component normal to the magnetic field. This magnetization creates stray magnetic fields around the exit point of the vortex line from the sample, which can be used for experimental detection of vortices.Comment: 15 pages, 3 figures, the version after corrections of some equation

Superfluid spin transport in magnetically ordered solids

The paper reviews the theory of the long-distance spin superfluid transport in solid ferro- and antiferromagnets based on the analysis of the topology, the Landau criterion, and phase slips. Experiments reporting evidence of the existence of spin superfluidity are also overviewed.Comment: Review article, 29 pages, 10 figure