Visualising Majorana bound states in 1D and 2D using the generalized Majorana polarization

Abstract

We study the solutions of generic Hamiltonians exhibiting particle-hole mixing. We show that there exists a universal quantity that can describe locally the Majorana nature of a given state. This pseudo-spin like two-component quantity is in fact a generalization of the Majorana polarization (MP) measure introduced in Sticlet et al. 2012, which was applicable only for some models with specific spin and symmetry properties. We apply this to an open two-dimensional Kitaev system, as well as to a one-dimensional topological wire. We show that the MP characterization is a necessary and sufficient criterion to test whether a state is a Majorana or not, and use it to numerically determine the topological phase diagram.

8 pages, 7 figures

References in corpus (33)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Helical liquids and Majorana bound states in quantum wires
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures
• Probing Neutral Majorana Fermion Edge Modes with Charge Transport
• Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling
• Majorana Fermions in Semiconductor Nanowires
• Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films
• Non-Abelian Topological Orders and Majorana Fermions in Spin-Singlet Superconductors
• Spin and Majorana polarization in topological superconducting wires
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Majorana states in helical Shiba chains and ladders
• Majorana End-States in Multi-band Microstructures with Rashba Spin-Orbit Coupling
• Robustness of Majorana Fermion induced Fractional Josephson Effect
• Majorana edge modes in the Kitaev model
• Topological Superconducting Phases of Weakly Coupled Quantum Wires
• Majorana Fermions and Multiple Topological Phase Transition in Kitaev Ladder Topological Superconductors
• Dimensional crossover in spin-orbit-coupled semiconductor nanowires with induced superconducting pairing
• Flat Majorana bands in 2-d lattices with inhomogeneous magnetic fields: topology and stability
• Majorana Fermions in Honeycomb Lattices
• The fate and heir of Majorana zero modes in a quantum wire array
• Topological qubits in graphenelike systems
• Effects of finite superconducting coherence lengths and of phase gradients in topological SN and SNS junctions and rings

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• Probing Majorana localization in minimal Kitaev chains through a quantum dot
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• Strong Coulomb interactions in the problem of Majorana modes in a wire of the nontrivial topological class BDI
• Minimal Kitaev-transmon qubit based on double quantum dots
• Skyrmion Control of Majorana States in Planar Josephson Junctions
• Topological superconductivity and Majorana states in low-dimensional systems
• On the bulk boundary correspondence and the existence of Majorana bound states on the edges of 2D topological superconductors
• Long-range Kitaev Chains via Planar Josephson Junctions
• How to measure the Majorana polarization of a topological planar Josephson junction
• Identifying trivial and Majorana zero-energy modes using the Majorana polarization
• Obtaining Majorana and other boundary modes from the metamorphosis of impurity-induced states: exact solutions via T-matrix
• Testing the formation of Majorana states using the Majorana Polarization
• Formation of Majorana fermions in finite-size graphene strips
• Dimerization-induced topological superconductivity in a Rashba nanowire
• Quantum-dot-based Kitaev chains: Majorana quality measures and scaling with increasing chain length
• Majorana fermions in finite-size strips with in-plane magnetic fields
• Effects of geometric frustration in Kitaev chains
• Topological superconductivity in Fibonacci quasicrystals
• Signature of a topological phase transition in long SN junctions in the spin-polarized density of states
• Machine-learned tuning of artificial Kitaev chains from tunneling-spectroscopy measurements
• Majorana modes in quantum dots coupled via a floating superconducting island
• Majorana sweet spots in 3-site Kitaev chains
• Tailoring phase transition from topological superconductor to trivial superconductor induced by magnetic textures of a spin-chain on a $p$-wave superconductor
• Enhanced Majorana bound states in magnetic chains on superconducting topological insulator edges
• Spin-orbital polarization of Majorana edge states in oxides nanowires
• Topological spin-singlet superconductors with underlying sublattice structure
• Transverse profile and 3D spin canting of a Majorana state in carbon nanotubes
• Fisher zeroes and dynamical quantum phase transitions for two- and three-dimensional models
• Edge states, Majorana fermions and topological order in superconducting wires with generalized boundary conditions
• Unconventional topological transitions in a self-organized magnetic ladder
• Topological indicators for systems with open boundaries: Application to the Kitaev wire
• Analytical and semianalytical tools to determine the topological character of Shiba chains
• High critical temperature nodal superconductors as building block for time-reversal invariant topological superconductivity
• Topology from Triviality
• Anomalous proximity effect under Andreev and Majorana bound states
• Assessing bound states in a one-dimensional topological superconductor: Majorana versus Tamm
• Instability of Majorana states in Shiba chains due to leakage into a topological substrate
• Characterizing local Majorana properties using Andreev states
• Majorana polarization in disordered heterostructures
• Quantum critical points in tunneling junction of topological superconductor and topological insulator
• Extended edge modes and disorder preservation of a symmetry-protected topological phase out of equilibrium
• Dynamics of Majorana zero modes across hybrid Kitaev chain
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• Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors
• Analytical classification of Majorana zero-mode spatial profiles in extended Kitaev chains: probability maxima can shift inward
• Creating and detecting poor man's Majorana bound states in interacting quantum dots
• Optimal Majoranas in Mesoscopic Kitaev Chains
• A Dynamical Bulk-Boundary Correspondence in Two Dimensional Topological Matter