Random matrix theory for the robustness, quantization, and end-to-end correlation of zero-bias conductance peaks in a class D ensemble

Abstract

We develop a general theory to study strong random quenched disorder effects in systems of experimental relevance in the search for Majorana zero modes (MZM) in topological superconductors. Using the random matrix theory in a class D ensemble, we simulate the transport properties of random quantum dots by attaching leads, and calculating the differential conductance in the $S$ matrix formalism. To add the concept of the length to the random system so that disordered Majorana nanowires can be simulated by the random matrix theory, we generalize the model of a single quantum dot to a chain of quantum dots by analogy with the superconductor-semiconductor (SC-SM) nanowire Majorana platform. We first define a new concept, the robustness of zero-bias conductance peaks (ZBCPs), in terms of an effective random Hamiltonian considering the self-energy of leads. We then study the joint distribution for the robustness and ZBCPs, and find a strong correlation that the ZBCP with stronger robustness is also prone to carry a larger conductance peak near $2e^2/h$. This trend is more prominent in shorter chains than in longer chains. This is consistent with experimentally observed ZBCPs associated with disorder-induced trivial Andreev bound states (the so-called ugly ZBCPs). Finally, we study the end-to-end correlation of the disorder-induced ZBCPs from two leads by calculating the normalized mutual information, which estimates the degrees of the correlation arising from the trivial ZBCPs. Our work provides an estimate of several important metrics used in SC-SM experiments to determine the nature of ZBCPs, including the robustness, quantization, and end-to-end correlation of the trivial ZBCPs. Therefore, in order to claim any evidence for MZMs, one must establish the observed ZBCPs to have considerable statistical significance well beyond what we find in this work to exist for the trivial peaks.

arXiv comment17 pages, 8 figures

References in corpus (95)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• Random-Matrix Theory of Quantum Transport
• Random Matrix Theories in Quantum Physics: Common Concepts
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Exponential Protection of Zero Modes in Majorana Islands
• Majorana bound states in a coupled quantum-dot hybrid-nanowire system
• 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
• Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures
• Quantized Majorana conductance
• 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
• Scaling of Majorana Zero-Bias Conductance Peaks
• Andreev bound states versus Majorana bound states in quantum dot-nanowire-superconductor hybrid structures: Trivial versus topological zero-bias conductance peaks
• Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling
• Near-zero-energy end states in topologically trivial spin-orbit coupled superconducting nanowires with a smooth confinement
• Towards a realistic transport modeling in a superconducting nanowire with Majorana fermions
• Ballistic Majorana nanowire devices
• A Majorana smoking gun for the superconductor-semiconductor hybrid topological system
• Quantized conductance at the Majorana phase transition in a disordered superconducting wire
• Class D spectral peak in Majorana quantum wires
• Search for Majorana fermions in multiband semiconducting nanowires
• How to realize a robust practical Majorana chain in a quantum dot-superconductor linear array
• Quantum point contact as a probe of a topological superconductor
• Ballistic superconductivity in semiconductor nanowires
• Physical mechanisms for zero-bias conductance peaks in Majorana nanowires
• 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
• 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
• Experimental Phase Diagram of a One-Dimensional Topological Superconductor
• 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
• Quantized zero bias conductance plateau in semiconductor-superconductor heterostructures without non-Abelian Majorana zero modes
• Topological superconductivity in full shell proximitized nanowires
• Flux-induced topological superconductivity in full-shell nanowires
• Flux-induced Majorana modes in full-shell nanowires
• Scattering theory of topological insulators and superconductors
• Probability distribution of Majorana end-state energies in disordered wires
• Topological superconducting phases in disordered quantum wires with strong spin-orbit coupling
• Robustness of Majorana fermions in 2D topological superconductors
• Non-Majorana states yield nearly quantized conductance in superconductor-semiconductor nanowire devices
• Zero-energy Andreev bound states from quantum dots in proximitized Rashba nanowires
• Disorder-induced zero-bias peaks in Majorana nanowires
• Ubiquitous non-Majorana Zero-Bias Conductance Peaks in Nanowire Devices
• Nontopological zero-bias peaks in full-shell nanowires induced by flux tunable Andreev states
• Andreev rectifier: a nonlocal conductance signature of topological phase transitions
• Adaptive tuning of Majorana fermions in a quantum dot chain
• Zero bias conductance peak in Majorana wires made of semiconductor-superconductor hybrid structures
• Conductance Quantization at zero magnetic field in InSb nanowires
• 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
• Conductance-matrix symmetries of a three-terminal hybrid device
• Conductance through a helical state in an InSb nanowire
• Density of states of disordered topological superconductor-semiconductor hybrid nanowires
• Electric field tunable superconductor-semiconductor coupling in Majorana nanowires
• Effective g-factor in Majorana Wires
• Three-terminal nonlocal conductance in Majorana nanowires: Distinguishing topological and trivial in realistic systems with disorder and inhomogeneous potential
• Topologically trivial zero bias conductance peak in semiconductor Majorana wires from boundary effects
• Shiba impurity bound states as a probe of topological superconductivity and Fermion parity changing quantum phase transitions
• Spin-Orbit Protection of Induced Superconductivity in Majorana Nanowires
• Majorana wavefunction oscillations, fermion parity switches, and disorder in Kitaev chains
• 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
• Electron temperature and tunnel coupling dependence of zero-bias and almost-zero-bias conductance peaks in Majorana nanowires
• Topological properties of superconducting junctions
• How to infer non-Abelian statistics and topological invariants from tunneling conductance properties of realistic Majorana nanowires
• Quantized and unquantized zero-bias tunneling conductance peaks in Majorana nanowires: Conductance below and above $2e^2/h$
• Charge impurity effects in hybrid Majorana nanowires
• Conductance of a superconducting Coulomb blockaded Majorana nanowire
• Closing of the Induced Gap in a Hybrid Superconductor-Semiconductor Nanowire
• End-to-end correlated subgap states in hybrid nanowires
• Two types of topological transitions in finite Majorana wires
• Presence versus absence of end-to-end nonlocal conductance correlations in Majorana nanowires: Majorana bound states versus Andreev bound states
• Large zero bias peaks and dips in a four-terminal thin InAs-Al nanowire device
• Bulk disorder in the superconductor affects proximity-induced topological superconductivity
• Quasiclassical theory of disordered multi-channel Majorana quantum wires
• Non-locality of zero-bias anomalies in the topologically-trivial phase of Majorana wires
• Disorder effects on Majorana zero modes: Kitaev chain versus semiconductor nanowire
• Majorana bound states in a disordered quantum dot chain
• Nonlocal conductance spectroscopy of Andreev bound states in gate-defined InAs/Al nanowires
• Subband occupation in semiconductor-superconductor nanowires
• X-shaped and Y-shaped Andreev resonance profiles in a superconducting quantum dot
• Crossover between trivial zero modes in Majorana nanowires
• On-demand large-conductance in trivial zero-bias tunneling peaks in Majorana nanowires
• Parametric exploration of zero-energy modes in three-terminal InSb-Al nanowire devices
• Disorder-induced topological transitions in multichannel Majorana wires
• Time-delay matrix, midgap spectral peak, and thermopower of an Andreev billiard
• Quality factor for zero-bias conductance peaks in Majorana nanowire
• Theory of Coulomb blockaded transport in realistic Majorana nanowires
• Ising quantum criticality in Majorana nanowires

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• Plateau regions for zero-bias peaks within 5% of the quantized conductance value $2e^2/h$
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• Proximity effect in PbTe-Pb hybrid nanowire Josephson junctions
• Progress in superconductor-semiconductor topological Josephson junctions
• Density of states, transport, and topology in disordered Majorana nanowires
• Disorder effects in planar semiconductor-superconductor structures: Majorana wires versus Josephson junctions
• Majorana zero modes in semiconductor-superconductor hybrid structures: Defining topology in short and disordered nanowires through Majorana splitting
• Planar Josephson junction devices with narrow superconducting strips: Topological properties and optimization