Fermion zero modes on vortices in chiral superconductors

The energy levels of fermions bound to the vortex core are considered for the general case of chiral superconductors. There are two classes of chiral superconductivity: in the class I superconducting state the axisymmetric singly quantized vortex has the same energy spectrum of bound states as in an s -wave superconductor: E =(n+1/2)ω 0 , with integral n . In class II the corresponding spectrum is E = n ω 0 and thus contains a state with exactly zero energy. The effect of a single impurity on the spectrum of bound states is also considered. For class I the spectrum acquires the doubled period Δ E =2ω 0 and consists of two equidistant sets of levels, in accordance with A. I. Larkin and Yu. N. Ovchinnikov, Phys. Rev. B 57 , 5457 (1998). For the class II states the spectrum is not influenced by a single impurity if the same approximation is applied.