Fermions in the vortex core in chiral superconductors

Abstract

Using the semiclassical approach to the energy levels of the fermions bound to the vortex core, we found the difference between the states in nonchiral and chiral superconductors, determined by the Berry phase. The bound states of fermions in the singly quantized vortex in the layered superconductor with the symmetry of superfluid 3He-A is E=nω_0 (as distinct from E=(n+1/2)ω_0 in s-wave superconductor) and thus contains the state with exactly zero energy. This is in accordance with the result obtained in microscopic theory by Kopnin and Salomaa. Using this approach for calculations of the effect of impurities on the spectrum of bound state we reproduced the Larkin-Ovchinnikov result for single impurity in s-wave vortex: the spectrum has the double period ΔE=2ω_0 and consists of two equdistant sets of levels. The same approach however shows that the single impurity does not change the spectrum E=nω_0 in the p-wave vortex .