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.

arXiv comment16 pages, 11 figures, review article published in Comptes Rendus Physique

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• Identifying trivial and Majorana zero-energy modes using the Majorana polarization
• Hallmarks of non-trivial topology in Josephson junctions based on oxide nanochannels
• Effects of geometric frustration in Kitaev chains
• Effective model for Majorana modes in graphene
• Spin-orbital polarization of Majorana edge states in oxides nanowires
• Quantum engineering of Majorana quasiparticles in one-dimensional optical lattices
• Dispersive 1D Majorana modes with emergent supersymmetry in 1D proximitized superconductors via spatially-modulated potentials and magnetic fields
• 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