Majorana fermions in vortex lattices

Abstract

We consider Majorana fermions tunneling among an array of vortices in a 2D chiral p-wave superconductor or equivalent material. The amplitude for Majorana fermions to tunnel between a pair of vortices is found to necessarily depend on the background superconducting phase profile; it is found to be proportional to the sine of half the difference between the phases at the two vortices. Using this result we study tight-binding models of Majorana fermions in vortices arranged in triangular or square lattices. In both cases we find that the aforementioned phase-tunneling relationship leads to the creation of superlattices where the Majorana fermions form macroscopically degenerate localizable flat bands at zero energy, in addition to other dispersive bands. This finding suggests that tunneling processes in these vortex arrays do not change the energies of a finite fraction of Majorana fermions, contrary to previous expectation. The presence of flat Majorana bands, and hence less-than-expected decoherence in these vortex arrays, bodes well for the prospects of topological quantum computation with large numbers of Majorana states.

Final published version

References in corpus (10)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
• Approaching Zero-Temperature Metallic States in Mesoscopic Superconductor-Normal-Superconductor Arrays
• Tunneling of anyonic Majorana excitations in topological superconductors
• SU(2)-invariant spin liquids on the triangular lattice with spinful Majorana excitations
• Disorder-induced Majorana metal in interacting non-Abelian anyon systems
• Majorana fermions of a two-dimensional Px+iPy superconductor
• Majorana fermions on a disordered triangular lattice

Cited by in corpus (32)

• Zero-energy vortex bound state in the superconducting topological surface state of Fe(Se,Te)
• Symmetry Protected Topological Superfluids and Superconductors --- From the Basics to ${}^3$He ---
• Scalable Majorana vortex modes in iron-based superconductors
• Strongly interacting Majorana fermions
• STM as a single Majorana detector of Kitaev's chiral spin liquid
• Electronic structure of topological superconductors in the presence of a vortex lattice
• Perturbed vortex lattices and the stability of nucleated topological phases
• Majorana-Hubbard model on the square lattice
• Two-dimensional topological superconductivity with antiferromagnetic insulators
• Majorana bands, Berry curvature, and thermal Hall conductivity in the vortex state of a chiral p-wave superconductor
• Emergent vortex Majorana zero mode in iron-based superconductors
• Topological superconductivity in Quantum Hall-superconductor hybrid systems
• Phase diagrams of Majorana-Hubbard ladders
• Vortex Lattice Structure and Topological Superconductivity in the Quantum Hall Regime
• Phase diagram of superconductivity in the integer quantum Hall regime
• Majorana lattices from the quantized Hall limit of a proximitized spin-orbit coupled electron gas
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Majorana stripe order on the surface of a three-dimensional topological insulator
• Searching for Majorana quasiparticles at vortex cores in iron-based superconductors
• Quantum engineering of Majorana quasiparticles in one-dimensional optical lattices
• Identifying Majorana vortex modes via non-local transport
• Topological Mid-gap States of px+ipy Topological Superconductor with Vortex superlattice
• Preparation of topological modes by Lyapunov control
• Implementing Majorana fermions in a cold-atom honeycomb lattice with textured pairings
• Tomasch Oscillations as Above-Gap Signature of Topological Superconductivity
• Field-Programmable Topological Array: Framework and Case-Studies
• Non-Abelian Majorana fermions in topological $s$-wave Fermi superfluids
• Identifying Majorana Zero Modes in Vortex Lattices Using Fano Factor Tomography
• Generic Weyl phase in the vortex state of quasi-two-dimensional chiral superconductors
• Vortex-state-mediated Josephson effect
• Theory of collective topologically-protected Majorana fermion excitations of networks of localized Majorana modes
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands