Majorana nanowires, Kitaev chains, and spin models

Abstract

Motivated by the fact that the idealized Kitaev chain toy model and the experimental semiconductor-superconductor Majorana nanowire can both host the Majorana zero modes, we theoretically investigate the question to what extent the two models are equivalent or similar, using the perspective of the corresponding dual spin models for both. We start with the duality between the Kitaev chain and the transverse-field XY spin model through the Jordan-Wigner transformation with the goal of establishing the connection between the Kitaev chain and the nanowire. By applying the Jordan-Wigner transformation to the nanowire, we find that the corresponding bosonic spin model is a generalized spin cluster model, containing 3-spin and 4-spin terms, with staggered couplings. By projecting out the upper band of the bare semiconductor with higher energy, we obtain an effective low-energy spinless system from the spinful nanowire system deep in the topological regime. Finally, we establish the connection between the Kitaev chain and Majorana nanowire by showing that the spinless Kitaev chain can be viewed as the first-order approximation of the spinful Majorana nanowire deep in the topological regime.

arXiv comment10 pages, 0 figures

References in corpus (27)

• 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
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Helical liquids and Majorana bound states in quantum wires
• New directions in the pursuit of Majorana fermions in solid state systems
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Persistent entanglement in arrays of interacting particles
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Periodic table for topological insulators and superconductors
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Majorana Zero Modes and Topological Quantum Computation
• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• Majorana Fermions in Semiconductor Nanowires
• $p_x+i{p}_y$ superfluid from s-wave interactions of fermionic cold atoms
• Topological invariants for spin-orbit coupled superconductor nanowires
• Search for Majorana fermions in multiband semiconducting nanowires
• How to realize a robust practical Majorana chain in a quantum dot-superconductor linear array
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Majorana Fermions in superconducting wires: effects of long-range hopping, broken time-reversal symmetry and potential landscapes
• Majorana zero modes in a quantum Ising chain with longer-ranged interactions
• Extended Kitaev chain with longer-range hopping and pairing
• The 1D Ising model and topological order in the Kitaev chain
• Disorder effects on Majorana zero modes: Kitaev chain versus semiconductor nanowire
• Ising quantum criticality in Majorana nanowires

Cited by in corpus (8)

• Enhancing the excitation gap of a quantum-dot-based Kitaev chain
• Kitaev chain in an alternating quantum dot-Andreev bound state array
• Majorana zero modes in semiconductor-superconductor hybrid structures: Defining topology in short and disordered nanowires through Majorana splitting
• Bound energy, entanglement and identifying critical points in 1D long-range Kitaev model
• Dynamics of Majorana zero modes across hybrid Kitaev chain
• Structure and scaling of Kitaev chain across a quantum critical point in real space
• Adiabatic preparation of a number-conserving atomic Majorana phase
• Rashba spin-orbit coupling and artificially engineered topological superconductors