arXiv subjects
Publications and source records attributed to N. B. Kopnin.
We show that vortex nucleation in superfluid $^3$He by rapid thermal quench in the presence of superflow is dominated by a transverse instability of the moving normal-superfluid interface. Exact expressions for the instability threshold as a function of supercurrent density and the front velocity are found. The results are verified by numerical solution of the Ginzburg-Landau equation.
We calculate the dynamic vortex mass for clean Fermi superfluids including both s- and d-wave superconductors as a response to a vortex acceleration. Assuming a finite quasiparticle mean free time, the vortex mass appears to be a tensor. The diagonal component dominates in the limit of long mean free time while the off-diagonal mass takes over in the moderately clean regime.
We reply to the criticism raised by Ao in his Comment (cond-mat/9801180). Being unable to properly treat the Hall conductivity in a mixed state of superconductors, Ao is looking for possible mistakes in microscopic and phenomenological calculations, as well as in the corresponding experiments. The errors in his treatment of the problem (cond-mat/9704247) are analized. We indicate where the approach advocated by him fails to properly account for the interaction with impurities and other sources of relaxation.
Effects of fermionic zero modes (bound states in a vortex core) on the rotational dynamics of vortices with sponaneously broken axisymmetry are considered. The results are compared with the Helsinki experiments where the vortex cores were driven to a fast rotation and torsional oscillations by an NMR r.f. field (Kondo et al, Phys. Rev. Lett. 67, 81 (1991)). We predict a resonance NMR absorption on localized states at the external frequency comparable with the interelevel distance, which is similar to the cyclotron Landau damping. The resonances can experimentally resolve the localized levels in vortex cores. For a pure rotation of the core, the effect depends on the relative signs of the vortex winding number and of the core rotation; thus it is sensitive to the direction of rotation of the container. The similarity with the fermionic zero modes on the fundamental strings, which simulate the thermodynamics of black holes, is discussed.
The condition for the appearance of event horizon is considered in such pair-correlated systems (superfluids and superconductors) where the fermionic quasiparticles obey the "relativistic" equations. In these systems, the Landau critical velocity of superflow corresponds to the speed of light. In conventional systems, such as s-wave superconductors, the superflow remains stable even above the Landau treshold. We showed that in the "relativistic" systems however the quantum vacuum becomes unstable and the superflow collapses after the "speed of light" is reached, so that horizon cannot appear. Thus an equilibrium dissipationless superfluid flow state and the horizon are incompatible due to quantum effects. This negative result is consistent with the quantum Hawking radiation from the horizon, which would lead to the dissipation of the flow.
We predict a resonant microwave absorption on collective vortex modes in a superclean d-wave superconductor. Energies of the collective modes are multiples of the distance between the exact quantum levels of bound states in the vortex core at lower temperatures and involve delocalized states for higher temperatures. We calculate the vortex mass in a d-wave superconductor as a response to a slow acceleration of the vortex. The universal flux-flow regime predicted by N. Kopnin and G. Volovik [Phys. Rev. Lett. 79, 1377 (1997)] is discussed in more detail.
We demonstrate that superclean d-wave superconductors display a novel type of vortex dynamics: At low temperatures, both dissipative and transverse components of the flux-flow conductivity are found to approach universal values even in the limit of infinite relaxation time. A finite dissipation in the superclean limit is explained in terms of the Landau damping on zero-frequency vortex modes which appear due to minigap nodes in the bound-state spectrum in the vortex core. In the moderately clean regime the scaling law at low T and low field is obtained.
In a recent Letter Simon and Lee suggested a scaling law for thermodynamic and kinetic properties of superconductors with lines of gap nodes. However their crossover parameter between the bulk dominated regime and the vortex dominated regime is different from that found in our paper (N.B. Kopnin and G.E. Volovik, JETP Lett., {\bf 64}, 690 (1996); see also cond-mat/9702093). We discuss the origin of the disagreement.
In d-wave superconductors, the electronic density of states (DOS) induced by a vortex exhibits 1/|E| divergency at low energies. It is the result of gap nodes in the excitations spectrum outside the vortex core. The heat capacity in two regimes, (T/T_c)^2 >> B/B_{c2} and (T/T_c)^2 << B/B_{c2}, is discussed.
Nondissipative force acting on a vortex in Fermi superfluids and superconductors is calculated from the spectral flow of fermion zero modes in the vortex core. The spectral flow effect casts a new light on the problem of mutual friction in superfluids. We demonstrate that, for vortices in an isotropic system, the reactive mutual friction parameter D'(T) is negative in the collisionless regime and it is positive in the hydrodynamic regime. This agrees with 3He-B measurements [1] ( T.D.C. Bevan, et al, Phys. Rev. Lett., 74, 750 (1995)), which thus give the experimental verification of the spectral flow effect in the vortex dynamics. General expression for all 3 nondissipative forces (Magnus, Iordanskii and spectral flow) is presented in the whole temperature range.