Testing the formation of Majorana states using the Majorana Polarization

Abstract

We study the formation of Majorana states in superconductors using the Majorana polarization, which can locally evaluate the Majorana character of a given state. We introduce the definition of the Majorana polarization vector and the corresponding criterion to identify a Majorana state, and we apply it to some simple cases such as a one-dimensional wire with spin-orbit coupling, subject to a Zeeman magnetic field, and proximitized by a superconductor, as well as to an NS junction made with such a wire. We also apply this criterion to two-dimensional finite-size strips and squares subject to the same physical conditions. Our analysis demonstrates the necessity of using the Majorana polarization local order parameter to characterize the Majorana states, particularly in finite-size systems.

16 pages, 11 figures, review article published in Comptes Rendus Physique

References in corpus (7)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films
• Mutation of Andreev into Majorana bound states in long NS and SNS junctions

Cited by in corpus (9)

• Identifying trivial and Majorana zero-energy modes using the Majorana polarization
• Hallmarks of non-trivial topology in Josephson junctions based on oxide nanochannels
• Edge states, Majorana fermions and topological order in superconducting wires with generalized boundary conditions
• Resilience of topological superconductivity under particle current
• Mixed higher-order topology and nodal and nodeless flat band topological phases in a superconducting multiorbital model
• Assessing bound states in a one-dimensional topological superconductor: Majorana versus Tamm
• Majorana polarization in disordered heterostructures
• Quantifying robustness and locality of Majorana bound states in interacting systems
• Majorana bound states in the presence of the half-smeared potential