We discuss the stability of zero-energy states appearing in a dirty normal metal attached to a superconducting thin film with Dresselhaus [110] spin-orbit coupling under an in-plane Zeeman field. The Dresselhaus superconductor preserves an additional chiral symmetry and traps more than one zero-energy state at its edges. All the zero-energy states at an edge belong to the same chirality in large Zeeman fields due to the effective p-wave pairing symmetry. The pure chiral nature of the wave function enables the zero-energy states to penetrate the dirty normal metal while retaining their high degree of degeneracy. We prove the perfect Andreev reflection into the dirty normal metal at zero energy.
We discuss the minimum value of the zero-bias differential conductance G min in a junction consisting of a normal metal and a nodal superconductor preserving time-reversal symmetry. Using the quasiclassical Green function method, we show that G min is quantized at (4e 2 /h)N ZES in the limit of strong impurity scatterings in the normal metal at the zero temperature. The integer N ZES represents the number of perfect transmission channels through the junction. An analysis of the chiral symmetry of the Hamiltonian indicates that N ZES corresponds to the Atiyah-Singer index in mathematics.
We discuss the stability of highly degenerate zero-energy states that appear at the surface of a nodal superconductor preserving time-reversal symmetry. The existence of such surface states is a direct consequence of the nontrivial topological numbers defined in the restricted Brillouin zones in the clean limit. In experiments, however, potential disorder is inevitable near the surface of a real superconductor, which may lift the high degeneracy at zero energy. We show that an index defined in terms of the chiral eigenvalues of the zero-energy states can be used to measure the degree of degeneracy at zero energy in the presence of potential disorder. We also discuss the relationship between the index and the topological numbers.
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 ϕ being π, 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 ϕ = π − 0 + , which explains the fractional current-phase relationship discussed in a number of previous papers.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.