Majorana Zero-Energy Mode and Fractal Structure in Fibonacci-Kitaev Chain

Abstract

We theoretically study a Kitaev chain with a quasiperiodic potential, where the quasiperiodicity is introduced by a Fibonacci sequence. Based on an analysis of the Majorana zero-energy mode, we find the critical $p$-wave superconducting pairing potential separating a topological phase and a non-topological phase. The topological phase diagram with respect to Fibonacci potentials follow a self-similar fractal structure characterized by the box-counting dimension, which is an example of the interplay of fractal and topology like the Hofstadter's butterfly in quantum Hall insulators.

arXiv comment5 pages, 4 figures

References in corpus (10)

• Unpaired Majorana fermions in quantum wires
• Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
• Anderson localization in Bose-Einstein condensates
• Majorana Fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials
• Majorana Fermions in superconducting wires: effects of long-range hopping, broken time-reversal symmetry and potential landscapes
• Topological phases, Majorana modes and quench dynamics in a spin ladder system
• Strongly interacting Majorana modes in an array of Josephson junctions
• Topological Classification of Gapped Spin Chains :Quantized Berry Phase as a Local Order Parameter
• Chern and Majorana Modes of Quasiperiodic Systems
• From the Hofstadter to the Fibonacci butterfly

Cited by in corpus (19)

• Antiferromagnetic order in the Hubbard Model on the Penrose Lattice
• Topological states in quasicrystals
• Physical properties of weak-coupling quasiperiodic superconductors
• Topological superconductivity in quasicrystals
• Mean-field study of the Bose-Hubbard model in Penrose lattice
• Resilience of Majorana Fermions in the face of Disorder
• Topological superconductivity in Fibonacci quasicrystals
• String and conventional order parameters in the solvable modulated quantum chain
• Coexistence of Strong and Weak Majorana Zero Modes in Anisotropic XY Spin Chain with Second-Neighbor Interaction
• Pattern-dependent proximity effect and Majorana edge mode in one-dimensional quasicrystals
• Quasiperiodic pairing in graphene quasicrystals
• Higher-dimensional Hofstadter butterfly on Penrose lattice
• Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing
• Confined states and topological phases in two-dimensional quasicrystalline $\pi$-flux model
• Boundary obstructed topological superconductor in buckled honeycomb lattice under perpendicular electric field
• Unconventional superfluidity of superconductivity on Penrose lattice
• Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials
• Localization and Topology in Noncentrosymmetric Superconductors with Disorder
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal