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Fermions in the vortex core as edge states

Fermions in the vortex core as edge states. Abstract The splitting of the spectrum of the electronic bound states in the vortex core with broken parity and axisymmetry is dicussed using (i) the phenomenological approach, and (ii) the simple model, in which the vortex core is represented by the vortex sheet of the radius R much larger than the coherence length ξ. In this model the bound states are concentrated in the vortex sheet and represent the chiral edge states similar to that in Quantum Hall Effect. The fermions are 1D particles with the " relativistic " spectrum moving in the direction determined by the sign of the winding number. This motion is governed by the effective gauge and gravity fields simulated by the order parameter texture. For the vortex with winding number n = 1 the effective " electric " charge of the fermion changes sign after the fermion trajectory encloses the vortex axis. This phenomenon is similar to that in the Alice cosmic string. The energy levels are obtained by quasiclassical quantization of the fermion motion on closed classical trajectories along the sheet. We found that the energy levels remain equidistant even in the presence of the broken symmetry fields. This conradicts to the Feigel'man and Skvortsov [1] suggestion that the 1 spectrum becomes chaotic in the presence of impurities. For the vor-tex with winding number n = 1 we found that the symmetry violation leads to the splitting of the spectrum into two sub-branches. The levels on each sub-branch are equidistant, but the sub-branches are symmetrically shifted from each other. This is similar to what was found by Larkin and Ovchinnikov in a recent preprint cond-mat/9708202 [2] for the case when the symmetry is violated by impurities.