Quantifying the non-Abelian property of Andreev bound states in inhomogeneous Majorana nanowires

Abstract

Non-Abelian braiding is a key property of Majorana zero modes (MZMs) that can be utilized for topological quantum computation. However, the presence of trivial Andreev bound states (ABSs) in topological superconductors can hinder the non-Abelian braiding of MZMs. We systematically investigate the braiding properties of ABSs induced by various inhomogeneous potentials in nanowires and quantify the main obstacles to non-Abelian braiding. We find that if a trivial ABSs is present at zero energy with a tiny energy fluctuation, their non-Abelian braiding property can be sustained for a longer braiding time cost, since the undesired dynamic phase is suppressed. Under certain conditions, the non-Abelian braiding of ABSs can even surpass that of MZMs in realistic systems, suggesting that ABSs might also be suitable for topological quantum computation.

arXiv comment13 pages, 9 figures

References in corpus (65)

• 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
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Non-Abelian statistics and topological quantum information processing in 1D wire networks
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Majorana fermions in a tunable semiconductor device
• Exponential Protection of Zero Modes in Majorana Islands
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• Manipulation of Majorana fermion, Andreev reflection and Josephson current on topological insulators
• Andreev bound states versus Majorana bound states in quantum dot-nanowire-superconductor hybrid structures: Trivial versus topological zero-bias conductance peaks
• Evidence of topological superconductivity in planar Josephson junctions
• Near-zero-energy end states in topologically trivial spin-orbit coupled superconducting nanowires with a smooth confinement
• Transport spectroscopy of NS nanowire junctions with Majorana fermions
• Ballistic Majorana nanowire devices
• Coulomb-assisted braiding of Majorana fermions in a Josephson junction array
• Topological Superconductivity in a Phase-Controlled Josephson Junction
• Non-Abelian Topological Orders and Majorana Fermions in Spin-Singlet Superconductors
• High-resolution studies of the Majorana atomic chain platform
• Reproducing topological properties with quasi-Majorana states
• Physical mechanisms for zero-bias conductance peaks in Majorana nanowires
• Measuring Majorana non-locality and spin structure with a quantum dot
• Two terminal charge tunneling: Disentangling Majorana zero modes from partially separated Andreev bound states in semiconductor-superconductor heterostructures
• Majorana bound states in non-homogeneous semiconductor nanowires
• InAs-Al Hybrid Devices Passing the Topological Gap Protocol
• Topological charge pumping in a one-dimensional optical lattice
• Quantized zero bias conductance plateau in semiconductor-superconductor heterostructures without non-Abelian Majorana zero modes
• SNS junctions in nanowires with spin-orbit coupling: role of confinement and helicity on the sub-gap spectrum
• Next steps of quantum transport in Majorana nanowire devices
• Zero-energy Andreev bound states from quantum dots in proximitized Rashba nanowires
• Andreev rectifier: a nonlocal conductance signature of topological phase transitions
• Supercurrent detection of topologically trivial zero-energy states in nanowire junctions
• Decaying spectral oscillations in a Majorana wire with finite coherence length
• Distinguishing topological Majorana bound states from trivial Andreev bound states: Proposed tests through differential tunneling conductance spectroscopy
• Conductance-matrix symmetries of a three-terminal hybrid device
• On controlling the bound states in quantum-dot hybrid-nanowire
• Topological Order and Non-Abelian Statistics in Noncentrosymmetric s-Wave Superconductors
• Nonlocal conductance spectroscopy of Andreev bound states: Symmetry relations and BCS charges
• Quantifying wave-function overlaps in inhomogeneous Majorana nanowires
• Conductance Spectroscopy of Spin-triplet Superconductors
• Theory of Majorana zero modes in unconventional superconductors
• Robust low-energy Andreev bound states in semiconductor-superconductor heterostructures: Importance of partial separation of component Majorana bound states
• Electron temperature and tunnel coupling dependence of zero-bias and almost-zero-bias conductance peaks in Majorana nanowires
• Weak measurement protocols for Majorana bound state identification
• Fractional Josephson Effect with and without Majorana Zero Modes
• Plateau regions for zero-bias peaks within 5% of the quantized conductance value $2e^2/h$
• Approaching a topological phase transition in Majorana nanowires
• Trivial Andreev band mimicking topological bulk gap reopening in the non-local conductance of long Rashba nanowires
• Dephasing and leakage dynamics of noisy Majorana-based qubits: Topological versus Andreev
• Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires
• Crossover between trivial zero modes in Majorana nanowires
• Effects of disorder on Coulomb-assisted braiding of Majorana zero modes
• Differentiating Majorana from Andreev Bound States in a Superconducting Circuit
• Quantum spin liquids and the metal-insulator transition in doped semiconductors
• Many-body Majorana braiding without an exponential Hilbert space
• Majorana Zero-Modes in a Two-Dimensional $p$-Wave Superconductor
• Effect of impurities and disorder on the braiding dynamics of Majorana zero modes
• Majorana orthogonal transformation and Majorana zero modes in free fermionic systems
• Probing electron-hole weights of an Andreev bound state by transient currents
• Disorder effects on the so-called Andreev band in Majorana nanowires
• Properties and application of the SO(3) Majorana representation of spin: equivalence with the Jordan-Wigner transformation and exact $Z_2$ gauge theories for spin models
• Reply to "Comment on 'Trivial Andreev Band Mimicking Topological Bulk Gap Reopening in the Nonlocal Conductance of Long Rashba Nanowires'"
• Mirror-protected Majorana zero modes in $f$-wave multilayer graphene superconductors