Topological superconductors with periodically modulated magnetic fields: Andreev vs Majorana bound states, and emergent supersymmetry

Majorana bound states can be realized in one-dimensional proximized superconductors in the presence of spatially-modulated magnetic fields. We will show that, if the field amplitude is not uniform, these systems can exhibit also topologically nontrivial Andreev bound states[1], which correspond to a topological invariant, the particle-hole Chern number, defined in a synthetic two-dimensional space in analogy to the spin Chern number of quantum spin Hall systems. Majorana and nontrivial Andreev states have similar spectroscopic signatures but are topologically inequivalent. Moreover, we will then show that emergent supersymmetry (SUSY) can be induced by spatially-modulated fields. The possible realization of SUSY in mesoscopic systems may lead to useful insights and unexpected analogies between high-energy and condensed matter physics.
[1] Marra, Nitta, PRB 100, 220502 (2019)