Topology of Andreev bound states with flat dispersion

Abstract

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

Topological Insulator Materials

“…62,162,164) Also, whereas it was thought to be necessary for topological materials to have a fully-gapped energy spectrum for a topological invariant to be well defined, 4) it is becoming possible to conceive a nontrivial topology for gapless systems. 146,156,[251][252][253][254][255] It is an interesting time of topological expansion. Naturally, experimental discoveries of concrete materials that are nontrivial with respect to new topologies will continue to be crucially important.…”

Possible pairing symmetries in SrPtAs with a local lack of inversion center

“…As mentioned, the nodal structure results in Andreev bound states at a certain surface, 12 which is related to the topology of the bulk state. 13,14 The E g state is possible in some particular cases like DOS enhanced situation owing to the vHS of the saddle points in the hexagonal BZ. This state breaks time-reversal symmetry whose signal could be detected by µSR measurement for spontaneous magnetization around impurities and also the Kerr rotation experiment, for examples.…”

Crossed Surface Flat Bands of Weyl Semimetal Superconductors

“…Surface Andreev bound states.-Surface Andreev bound states (SABSs) [42][43][44][45] are a powerful probe of topological superconductivity because they directly reflect bulk topological structures [46][47][48]. To identify the nodal topological superconductivity in doped WSMs, we now examine the SABSs.…”