Fermion zero modes on vortices in chiral superconductors

The energy levels of the fermions bound to the vortex core are considered for the general case of chiral superconductors. There are two classes of chiral superconductivity: in the superconducting state of class I the axisymmetric singly quantized vortex has the same energy spectrum of bound states as in s-wave superconductor: E=(n+1/2)\omega_0 with integral n. In the class II the corresponding spectrum is E=n\omega_0 and thus contains the state with exactly zero energy. The effect of a single impurity on the spectrum of bound state is also considered. For the class I the spectrum acquires the double period \Delta E=2\omega_0 and consists of two equidistant sets of levels in accordance with A.I. Larkin and Yu.N. Ovchinnikov, Phys. Rev. B57 (1998) 5457. The spectrum is not influenced by a single impurity if the same approximation is applied for vortices in the class II superconducting states.