Reply to Comment "Invalidity of classes of approximate Hall effect calculations."

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.Comment: reply to Comment by Ao (cond-mat/9801180) on our paper in PRL, 79, 1377 (1997), revtex file, 1 page, no figure

Resonant absorption at the vortex-core states in d-wave superconductors

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.Comment: RevTex file, 10 page

Dynamic vortex mass in clean Fermi superfluids and superconductors

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.Comment: 4 pages, no figures, typeset using RevTe

Rotating vortex core: An instrument for detecting the core excitations

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.Comment: RevTex file, 7 pages, 1 Figure, extended and clarified after referee Reports, to appear in Phys. Rev.

Comment on "Transverse Force on a Quantized Vortex in a Superfluid"

The result of Thouless, Ao and Niu (TAN), that the mutual friction parameter $d_\perp =0$, contradicts to the experiments made in rotating 3He-B by Manchester group. The Manchester group observed that $d_\perp <0$ at low temperature and approaches 1 at high temperature. The reason of the contradiction is that TAN did not take into account the Iordanskii force on the vortex and the spectral flow force, which comes from the anomaly related to the low-energy bound states of fermions in cores of quantized vortices. The Iordanskii force is responsible for the negative $d_\perp <0$ at low temperature, while due to the spectral flow $d_\perp$ approaches 1 at high temperature. Relation of the spectral flow anomaly with the paradoxes of the linear and angular momenta in gapless superfluids is discussed.Comment: revtex, 2 pages, submitted to Physical Review Letters as "Comment" to the paper D.J. Thouless, P. Ao and Q. Niu, Phys. Rev. Lett. 76, 3758 (1996

Magnetic resonance within vortex cores in the B phase of superfluid 3^3He

We investigate a magnetic susceptibility of vortices in the B phase of multicomponent triplet superfluid $^3$He focusing on a contribution of bound fermionic states localized within vortex cores. Several order parameter configurations relevant to different types of quantized vortices in $^3$He B are considered. It is shown quite generally that an ac magnetic susceptibility has a sharp peak at the frequency corresponding to the energy of interlevel spacing in the spectrum of bound fermions. We suggest that measuring of a magnetic resonance within vortex cores can provide a direct probe of a discrete spectrum of bound vortex core excitations