Majorana fermions in finite-size strips with in-plane magnetic fields

Abstract

We study the Majorana bound states arising in quasi-one-dimensional systems with Rashba spin-orbit coupling in the presence of an in-plane Zeeman magnetic field. Using two different methods, first, the numerical diagonalization of the tight-binding Hamiltonian, and second, finding the singular points of the Hamiltonian (see Refs. [1-4]), we obtain the topological phase diagram for these systems as a function of the chemical potential and the magnetic field, and we demonstrate the consistency of these two methods. By introducing disorder into these systems we confirm that the states with even number of Majorana pairs are not topologically protected. Finally, we show that a formal calculation of the ${\mathbb{Z}}_2$ topological invariants recovers correctly the parity of the number of Majorana bound states pairs, and it is thus fully consistent with the phase diagrams of the disordered systems.

8,5 pages, 8 figures (+2,5 pages, 1 figure in Appendixes)

References in corpus (17)

• 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
• Exponential Protection of Zero Modes in Majorana Islands
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• Chiral Majorana edge state in a quantum anomalous Hall insulator-superconductor structure
• Multichannel Generalization of Kitaev's Majorana End States and a Practical Route to Realize Them in Thin Films
• Majorana Fermions in Nodal Superconductors: Gapless Topological Phase
• Detecting Majoranas in 1D wires by charge sensing
• Flat Majorana bands in 2-d lattices with inhomogeneous magnetic fields: topology and stability
• Coexisting edge states and gapless bulk in topological states of matter
• Majorana flat bands, chiral Majorana edge states, and unidirectional Majorana edge states in noncentrosymmetric superconductors
• Majorana states and magnetic orbital motion in planar hybrid nanowires

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• Identifying trivial and Majorana zero-energy modes using the Majorana polarization
• Dimerization-induced topological superconductivity in a Rashba nanowire
• Symmetry-breaking signatures of multiple Majorana zero modes in one-dimensional spin-triplet superconductors
• Analytical and semianalytical tools to determine the topological character of Shiba chains
• Topology from Triviality
• Majorana Zero Modes in Nanowires with Combined Triangular and Hexagonal Geometry
• Instability of Majorana states in Shiba chains due to leakage into a topological substrate
• Circular dichroism of chiral Majoranas
• Spatial coupling of quantum-anomalous-Hall and chiral-Majorana modes
• Majorana modes in graphene strips: polarization, wavefunctions, disorder, and Andreev states