Distinguishing trivial and topological zero energy states in long nanowire junctions

Abstract

The emergence of zero energy states in non-topological superconductors represents an inevitable problem that obscures the proper identification of zero energy Majorana bound states (MBSs) and prevents their use as topologically protected qubits. In this work we investigate long superconductornormal-superconductor junctions where trivial zero energy states, robust over a large range of parameters, appear as a result of helicity and confinement in the normal region. We demonstrate that both equilibrium supercurrents and critical currents are sensitive to variations in the length of the superconductor regions in the topological phase hosting MBSs, but, remarkably, no such length dependence exists when robust, but trivial, zero energy states are present. This strikingly different response originates from the non-local nature of the MBSs and we, therefore, propose it as a simple protocol for distinguishing between trivial and topological zero energy states.

Assessing bound states in a one-dimensional topological superconductor: Majorana versus Tamm

“…However, a clear evidence of the quantization of the zero bias peak, which is one of the predicted signatures ascribed to the presence of Majorana zero modes, or other unambiguous fingerprints of their formation are still lacking to date. Indeed, an additional challenge in the field is posed by the fact that Majorana zero modes behave, in many terms, similarly to more conventional Andreev bound states, which do not exhibit non-abelian statistics, and are thus less useful in quantum computation [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50]. Indeed, on one hand it is still possible to distinguish between trivial Andreev bound states that emerge at finite chemical potential in clean systems and Majorana bound states due to the fact that the phase containing Majorana fermions and the one with the trivial bound states are separated by a region with extended states only [51].…”

Confinement-induced zero-bias peaks in conventional superconductor hybrids

“…In great part because several works have reported ZBCPs due to quasi zero-energy states (qZESs) at finite magnetic fields but well below the topological phase and, hence, not tied to topology . In this regard, recent theoretical efforts have suggested interesting detection protocols of MBSs [53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72], but the emergence of trivial qZESs still seems puzzling in conductance measurements.…”

“…[74] for more details. Previously, the appearance of trivial qZESs has been confirmed in junctions with spin-orbit coupling and magnetism [34,70]. However, these junctions require that the middle region is within the helical regime, and it was not clearly determined if the qZESs originate due to confinement or helicity.…”