Majorana edge modes in isolated wires

Abstract

Topological superconductors are believed to host exotic quasiparticle excitations known as Majorana zero-modes (MZMs), with much of the evidence based on BCS mean-field theory. The direct application of mean-field arguments is tenuous in finite, isolated systems relevant in some experiments. Here, we develop a new correlation-based method for identifying MZMs in interacting, number-conserving systems. Using DMRG, we study fermion number-conserving models with long-range interactions, which under periodic boundary conditions exhibit robust topological and non-topological superconductivity, tuned by the strength of interaction [1]. We find evidence that, on the topological side, Majorana edge modes appear in open chains, manifesting as the vanishing of the energy splitting between odd- and even-parity ground states with increasing system size. Additionally, off-diagonal two-point correlation functions show nonlocal, parity-dependent edge effects. These correlations reveal the spatial structure of Majorana modes in the many-body wavefunction. We show that the correlation diagnostic applies broadly, including to short-range interacting models, where topological superconductivity is more fragile due to the absence of a bulk excitation gap.

12 pages, 16 figures

References in corpus (38)

• Fault-tolerant quantum computation by anyons
• 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
• New directions in the pursuit of Majorana fermions in solid state systems
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Topological phases of fermions in one dimension
• Superconductor-Nanowire Devices from Tunneling to the Multichannel Regime: Zero-Bias Oscillations and Magnetoconductance Crossover
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Evidence for Majorana bound state in an iron-based superconductor
• Majorana fermions in chains of magnetic atoms on a superconductor
• Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling
• Electron Teleportation via Majorana Bound States in a Mesoscopic Superconductor
• Topological Superconductivity in a Planar Josephson Junction
• Kitaev chains with long-range pairing
• InAs-Al Hybrid Devices Passing the Topological Gap Protocol
• Majorana Zero Modes in 1D Quantum Wires Without Long-Ranged Superconducting Order
• Braiding without Braiding: Teleportation-Based Quantum Information Processing with Majorana Zero Modes
• Majorana fermions in superconducting helical magnets
• Majorana bound states in magnetic skyrmions
• Topological invariants and interacting one-dimensional fermionic systems
• A number conserving theory for topologically protected degeneracy in one-dimensional fermions
• Majorana Edge States in Interacting Two-chain Ladders of Fermions
• Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain
• Localized Majorana-like modes in a number conserving setting: An exactly solvable model
• Topological phases with long-range interactions
• Topological states in a microscopic model of interacting fermions
• Superfluid stiffness of a KTaO3-based two-dimensional electron gas
• Heuristic bounds on superconductivity and how to exceed them
• Number conserving analysis of measurement-based braiding with Majorana zero modes
• Number-conserving interacting fermion models with exact topological superconducting ground states
• $\text{Draiding}$ majoranas to dynamically engineer Hamiltonians
• Optimizing the transport of Majorana zero modes in one-dimensional topological superconductors
• Learning fermionic correlations by evolving with random translationally invariant Hamiltonians
• Dynamical approach to improving Majorana qubits and distinguishing them from trivial bound states
• Shuttling Majorana zero modes in disordered and noisy topological superconductors