### arXiv:1907.05416 [cond-mat.supr-con]AbstractReferencesReviewsResources

#### Coexistence of Majorana and topologically nontrivial Andreev bound states in 1D superconductors

Published 2019-07-11Version 1

The unambiguous detection of Majorana bound states in nanowires and in magnetic atom chains is hindered by the possible presence of near-zero-energy Andreev bound states which have similar experimental signatures. These near-zero energy states are expected to be topologically trivial. Here, we report the theoretical prediction of topologically nontrivial Andreev bound states in one-dimensional superconductors with spatially varying magnetic fields. These states correspond to a novel topological invariant defined in a synthetic two-dimensional space, the particle-hole Chern number, which is an analogue of the spin Chern number in quantum spin Hall systems. Topologically nontrivial Andreev bound states and Majorana bound states have distinct features and are topologically nonequivalent. Yet they can coexist in the same system, have similar spectral signatures, and materialize with the concomitant opening of the particle-hole gap. Consequently, the simultaneous observation of a zero-bias peak and the closing and reopening of the gap cannot be considered an exclusive fingerprint of Majorana bound states. In contrast to Majorana states, which appear simultaneously at both edges and at zero energy, nontrivial Andreev states may appear with different energies at the opposite edges of the system.

**Comments:**6 pages, 3 figures