Stability of flat zero-energy states at the dirty surface of a nodal superconductor

Abstract

We discuss the stability of highly degenerate zero-energy states tha 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.

arXiv comment12 pages, 7 figures

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• Disorder-robust phase crystal in high-temperature superconductors stabilized by strong correlations
• 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
• Anomalous proximity effect under Andreev and Majorana bound states
• Cartesian Nodal Lines and Magnetic Kramers Weyl Nodes in Spin-Split Antiferromagnets
• Impurity strength-temperature phase diagram with phase crystals and competing time-reversal symmetry breaking states in nodal $d$-wave superconductors