Stability of Majorana bound states in the presence of spin-flip scattering

Abstract

A popular evidence of the existence of Majorana bound states(MBS) is a quantized zero-bias conductance peak(ZBCP) which is robust to scattering by impurities, a consequence of its topological protection. In this work we examine the stability of this MBS induced ZBCP in a metal-superconductor junction in the vicinity of a spin flipper. We analytically calculate the differential charge conductance for metal-spin flipper-superconductor junction with two distinct superconductors: (a) spin less $p$-wave superconductor(pSc) and (b) spin-orbit-coupled s-wave superconducting wire in presence of a Zeeman field(SOCSW). We see that the quantized ZBCP remains stable in presence of spin-flip(SF) scattering for metal-pSc junction, while it loses its stability when pSc is replaced by SOCSW. Further, the scattering matrix(S-Matrix) of the metal-pSc junction satisfies BDI symmetry class regardless of SF scattering. For BDI symmetry class, both Hamiltonian as well as S-Matrix satisfy particle-hole(PH), time reversal(TR) and chiral symmetries. However, in case of metal-SOCSW junction the Hamiltonian as well as S-Matrix belongs to symmetry class D in absence of SF scattering. In symmetry class D both Hamiltonian and S-Matrix satisfy PH symmetry, but do not satisfy TR and chiral symmetry relations. In presence of SF scattering, the S-Matrix for metal-SOCSW junction belongs to symmetry class A for which S-Matrix does not satisfy either PH or TR or chiral symmetry relations. The reason for ZBCP at a metal-pSc junction is perfect Andreev reflection regardless of SF scattering, while for metal-SOCSW junction it is the exact cancellation between normal and Andreev reflection probabilities at zero bias and not perfect Andreev reflection, in absence of SF scattering. However, in presence of SF scattering, there is no exact cancellation at zero bias which leads to loss of quantized ZBCP for a metal-SOCSW junction.