Spectral properties, topological patches, and effective phase diagrams of finite disordered Majorana nanowires

Abstract

We consider theoretically the physics of bulk topological superconductivity accompanied by boundary non-Abelian Majorana zero modes in semiconductor-superconductor (SM-SC) hybrid systems consisting of finite wires in the presence of correlated disorder arising from random charged impurities. We find the system to manifest a highly complex behavior due to the subtle interplay between finite wire length and finite disorder, leading to copious low-energy in-gap states throughout the wire and considerably complicating the interpretation of tunneling spectroscopic transport measurements used extensively to search for Majorana modes. The presence of disorder-induced low-energy states may lead to the non-existence of end Majorana zero modes even when tunneling spectroscopy manifests zero bias conductance peaks in local tunneling and signatures of bulk gap closing/reopening in the nonlocal transport. In short wires within the intermediate disorder regime, apparent topology may manifest in small ranges ("patches") of parameter values, which may or may not survive the long wire limit depending on various details. Because of the dominance of disorder-induced in-gap states, the system may even occasionally have an appropriate topological invariant without manifesting isolated end Majorana zero modes. We discuss our findings in the context of a recent breakthrough experiment from Microsoft reporting the simultaneous observations of zero bias conductance peaks in local tunneling and gap opening in nonlocal transport within small patches of parameter space. Based on our analysis, we believe that the disorder strength to SC gap ratio must decrease further for the definitive realization of non-Abelian Majorana zero modes in SM-SC devices.

arXiv comment34 pages, 42 figures

References in corpus (46)

• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Kwant: a software package for quantum transport
• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• Zero-bias peaks in spin-orbit coupled superconducting wires with and without Majorana end-states
• Majorana Fermions in Semiconductor Nanowires
• Fractional ac Josephson effect in p- and d-wave superconductors
• A Majorana smoking gun for the superconductor-semiconductor hybrid topological system
• Observing Majorana Bound States in p-wave Superconductors Using Noise Measurements in Tunneling Experiments
• Quantized conductance at the Majorana phase transition in a disordered superconducting wire
• Zero-voltage conductance peak from weak antilocalization in a Majorana nanowire
• Midgap edge states and pairing symmetry of quasi-one-dimensional organic superconductors
• Class D spectral peak in Majorana quantum wires
• Search for Majorana fermions in multiband semiconducting nanowires
• The recursive Green's function method for graphene
• Reproducing topological properties with quasi-Majorana states
• Physical mechanisms for zero-bias conductance peaks in Majorana nanowires
• InAs-Al Hybrid Devices Passing the Topological Gap Protocol
• Scattering formula for the topological quantum number of a disordered multi-mode wire
• Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples
• Topological superconducting phases in disordered quantum wires with strong spin-orbit coupling
• Robustness of Majorana fermions in 2D topological superconductors
• Disorder-induced zero-bias peaks in Majorana nanowires
• Interplay of disorder and interaction in Majorana quantum wires
• Soft Superconducting Gap in Semiconductor Majorana Nanowires
• Andreev rectifier: a nonlocal conductance signature of topological phase transitions
• Effects of gate-induced electric fields on semiconductor Majorana nanowires
• Experimental and materials considerations for the topological superconducting state in electron and hole doped semiconductors: searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures
• Hybridization at superconductor-semiconductor interfaces
• Estimating disorder and its adverse effects in semiconductor Majorana nanowires
• Effects of electron scattering on the topological properties of nanowires: Majorana fermions from disorder and superlattices
• Density of states of disordered topological superconductor-semiconductor hybrid nanowires
• Effective theory approach to the Schrodinger-Poisson problem in semiconductor Majorana devices
• Three-terminal nonlocal conductance in Majorana nanowires: Distinguishing topological and trivial in realistic systems with disorder and inhomogeneous potential
• Generic quantized zero-bias conductance peaks in superconductor-semiconductor hybrid structures
• Robust low-energy Andreev bound states in semiconductor-superconductor heterostructures: Importance of partial separation of component Majorana bound states
• How to infer non-Abelian statistics and topological invariants from tunneling conductance properties of realistic Majorana nanowires
• Proximity effect and Majorana bound states in clean semiconductor nanowires coupled to disordered superconductors
• Proximity-induced low-energy renormalization in hybrid semiconductor-superconductor Majorana structures
• In search of Majorana
• Reentrant topological phase transitions in a disordered spinless superconducting wire
• Probing a topological quantum critical point in semiconductor-superconductor heterostructures
• Density of states, transport, and topology in disordered Majorana nanowires
• Quality factor for zero-bias conductance peaks in Majorana nanowire
• Random matrix theory for the robustness, quantization, and end-to-end correlation of zero-bias conductance peaks in a class D ensemble

Cited by in corpus (25)

• Majorana zero modes in gate-defined germanium hole nanowires
• Density of states, transport, and topology in disordered Majorana nanowires
• Rabi and Ramsey oscillations of a Majorana qubit in a quantum dot-superconductor array
• Effect of impurities and disorder on the braiding dynamics of Majorana zero modes
• Differential current noise as an identifier of Andreev bound states that induce nearly quantized conductance plateaus
• Disordered Majorana nanowires: Studying disorder without any disorder
• Machine Learning the Disorder Landscape of Majorana Nanowires
• Josephson effect and critical currents in trivial and topological full-shell hybrid nanowires
• Germanium-based hybrid semiconductor-superconductor topological quantum computing platforms: Disorder effects
• Vision transformer based Deep Learning of Topological indicators in Majorana Nanowires
• Stabilizing topological superconductivity in disordered spin-orbit coupled semiconductor-superconductor heterostructures
• Disorder effects in planar semiconductor-superconductor structures: Majorana wires versus Josephson junctions
• Topological gap protocol based machine learning optimization of Majorana hybrid wires
• Quantized Andreev conductance in semiconductor nanowires
• Capacitance-based Fermion parity read-out and predicted Rabi oscillations in a Majorana nanowire
• Bound state-continuum resonance transition in a shallow quantum well
• Majorana zero modes in semiconductor-superconductor hybrid structures: Defining topology in short and disordered nanowires through Majorana splitting
• Identifying biases of the Majorana scattering invariant
• Planar Josephson junction devices with narrow superconducting strips: Topological properties and optimization
• Mitigating disorder and optimizing topological indicators with vision-transformer-based neural networks in Majorana nanowires
• Current cross-correlation spectroscopy of Majorana bound states
• Excess photon-assisted noise of Majorana and Andreev bound states
• Rashba spin-orbit coupling and artificially engineered topological superconductors
• Ballistic transport in 1D Rashba systems in the context of Majorana nanowires
• Signatures of Majorana bound states in scanning gate microscopy of hybrid nanowires