Symmetry conditions of a nodal superconductor for generating robust flat-band Andreev bound states at its dirty surface

Abstract

We discuss the symmetry property of a nodal superconductor that hosts robust flat-band zero-energy states at its surface under potential disorder. Such robust zero-energy states are known to induce the anomalous proximity effect in a dirty normal metal attached to a superconductor. A recent study has shown that a topological index ${\mathcal{N}}_{\mathrm{ZES}}$ describes the number of zero-energy states at the dirty surface of a $p$-wave superconductor. We generalize the theory to clarify the conditions required for a superconductor that enables ${\mathcal{N}}_{\mathrm{ZES}}\ne 0$. Our results show that ${\mathcal{N}}_{\mathrm{ZES}}\ne 0$ is realized in a topological material that belongs to either the BDI or CII class. We also present two realistic Hamiltonians that result in ${\mathcal{N}}_{\mathrm{ZES}}\ne 0$.

9 pages, 3 figures

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Cited by in corpus (7)

• Tuning Topological Superconductivity in Phase-Controlled Josephson Junctions with Rashba and Dresselhaus Spin-Orbit Coupling
• Majorana corner flat bands in two-dimensional second-order topological superconductors
• Theory of proximity effect in two-dimensional unconventional superconductor with Rashba spin-orbit interaction
• Strong anomalous proximity effect from spin-singlet superconductors
• Odd-parity pairing correlations in a d-wave superconductor
• Anomalous proximity effect under Andreev and Majorana bound states
• Statistic physics in bound state in 3D fermi gas system