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A theory of dispersionless Andreev bound states on surfaces of time-reversalinvariant unconventional superconductors is presented. The generalizedcriterion for the dispersionless Andreev bound state is derived from thebulk-edge correspondence, and the chiral spin structure of the dispersionlessAndreev bound states is argued from which the Andreev bound state isstabilized. Then we summarize the criterion in a form of index theorems. Theindex theorems are proved in a general framework to certify the bulk-edgecorrespondence. As concrete examples, we discuss (i) dxy-wave superconductor(ii) px-wave superconductor, and (iii) noncentrosymmetric superconductors. Inthe last example, we find a peculiar time-reversal invariant Majorana fermion.The time-reversal invariant Majorana fermion shows an unusual response to theZeeman magnetic field, which can be used to identify it experimentally.

Topology of Andreev Bound States with Flat Dispersion