Degeneracy of Majorana bound states and fractional Josephson effect in a dirty SNS junction

Abstract

We theoretically study the stability of more than one Majorana Fermion appearing in a $p$-wave superconductor/dirty normal metal/$p$-wave superconductor junction in two-dimension by using chiral symmetry of Hamiltonian. At the phase difference across the junction $\phi$ being $\pi$, we will show that all of the Majorana bound states in the normal metal belong to the same chirality. Due to this pure chiral feature, the Majorana bound states retain their high degree of degeneracy at the zero energy even in the presence of random potential. As a consequence, the resonant transmission of a Cooper pair via the degenerate MBSs carries the Josephson current at $\phi =\pi -0^{+}$, which explains the fractional current-phase relationship discussed in a number of previous papers.

11 pages, 2 figures

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Cited by in corpus (9)

• Quantization of Conductance Minimum and Index Theorem
• Anomalous Proximity Effect of Planer Topological Josephson Junctions
• Stability of flat zero-energy states at the dirty surface of a nodal superconductor
• Symmetry conditions of a nodal superconductor for generating robust flat-band Andreev bound states at its dirty surface
• Strong anomalous proximity effect from spin-singlet superconductors
• Effects of the phase coherence on the local density of states in superconducting proximity structures
• Odd-parity pairing correlations in a d-wave superconductor
• Superconductor/normal-metal/superconductor junction of topological superconductors revisited: Fractional Josephson current, fermion parity, and oscillating wavefunctions
• Multi-locational Majorana Zero Modes