Majorana states in prismatic core-shell nanowires

Abstract

We consider core-shell nanowires with conductive shell and insulating core, and with polygonal cross section. We investigate the implications of this geometry on Majorana states expected in the presence of proximity-induced superconductivity and an external magnetic field. A typical prismatic nanowire has a hexagonal profile, but square and triangular shapes can also be obtained. The low-energy states are localized at the corners of the cross section, i.e. along the prism edges, and are separated by a gap from higher energy states localized on the sides. The corner localization depends on the details of the shell geometry, i.e. thickness, diameter, and sharpness of the corners. We study systematically the low-energy spectrum of prismatic shells using numerical methods and derive the topological phase diagram as a function of magnetic field and chemical potential for triangular, square, and hexagonal geometries. A strong corner localization enhances the stability of Majorana modes to various perturbations, including the orbital effect of the magnetic field, whereas a weaker localization favorizes orbital effects and reduces the critical magnetic field. The prismatic geometry allows the Majorana zero-energy modes to be accompanied by low-energy states, which we call pseudo Majorana, and which converge to real Majoranas in the limit of small shell thickness. We include the Rashba spin-orbit coupling in a phenomenological manner, assuming a radial electric field across the shell.

14 pages, 16 figures, accepted for publication in Phys. Rev. B

References in corpus (16)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• 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
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Epitaxy of Semiconductor-Superconductor nanowires
• Hard gap in epitaxial semiconductor-superconductor nanowires
• Majorana Fermions: The race continues
• Conductance through a helical state in an InSb nanowire
• Majorana Fermions in Ge/Si Hole Nanowires
• Electron localization and optical absorption of polygonal quantum rings
• Majorana modes and complex band structure of quantum wires

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• Distinguishing Majorana Zero Modes from Impurity States through Time-Resolved Transport
• Robust topological phase in proximitized core-shell nanowires coupled to multiple superconductors
• Enhanced Rashba spin-orbit coupling in core-shell nanowires by the interfacial effect
• Conductance features of core-shell nanowires determined by the internal geometry
• Coulomb Blockade from the Shell of an InP-InAs Core-Shell Nanowire with a Triangular Cross Section
• Magneto-conductance of topological junctions based on two-dimensional electron gases reveals Majorana phases
• Transverse profile and 3D spin canting of a Majorana state in carbon nanotubes
• Corner and side localization of electrons in irregular hexagonal semiconductor shells
• Low-symmetry nanowire cross-sections for enhanced Dresselhaus spin-orbit interaction
• Majorana Zero Modes in Nanowires with Combined Triangular and Hexagonal Geometry
• Flux-periodic oscillations in proximitized core-shell nanowires
• Electromagnetic field emitted by core-shell semiconductor nanowires driven by an alternating current
• Effect of Impurities on Charge and Heat Transport in Tubular Nanowires
• Electron-hole coherence in core-shell nanowires with partial proximity induced superconductivity