Anomalous Proximity Effect and Theoretical Design for its Realization

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 the 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 field due to the effective $p$-wave pairing symmetry. The pure chiral nature in the wave function enables the penetration of the zero-energy states into the dirty normal metal with keeping their high degree of degeneracy. By applying a theorem, we prove the the perfect Andreev reflection into the dirty normal metal at the zero-energy. This paper gives a microscopic understanding of the anomalous proximity effect.