Random-matrix theory of Majorana fermions and topological superconductors

Abstract

I. Introduction (What is new in RMT, Superconducting quasiparticles, Experimental platforms) II. Topological superconductivity (Kitaev chain, Majorana operators, Majorana zero-modes, Phase transition beyond mean-field) III. Fundamental symmetries (Particle-hole symmetry, Majorana representation, Time-reversal and chiral symmetry) IV. Hamiltonian ensembles (The ten-fold way, Midgap spectral peak, Energy level repulsion) V. Scattering matrix ensembles (Fundamental symmetries, Chaotic scattering, Circular ensembles, Topological quantum numbers) VI. Electrical conduction (Majorana nanowire, Counting Majorana zero-modes, Conductance distribution, Weak antilocalization, Andreev resonances, Shot noise of Majorana edge modes) VII. Thermal conduction (Topological phase transitions, Super-universality, Heat transport by Majorana edge modes, Thermopower and time-delay matrix, Andreev billiard with chiral symmetry) VIII. Josephson junctions (Fermion parity switches, 4π-periodic Josephson effect, Discrete vortices) IX. Conclusion

V1: 18 pages, 16 figures; pre-submission version, for feedback; V2: 33 pages, 31 figures; greatly expanded in response to feedback, thank you!; V3: minor corrections, version to be published in Reviews of Modern Physics

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• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Introduction to topological superconductivity and Majorana fermions
• Topological Defects and Gapless Modes in Insulators and Superconductors
• The Quantum Spin Hall Effect: Theory and Experiment
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• Majorana mode in vortex core of Bi2Te3/NbSe2 topological insulator-superconductor heterostructure
• Non-Abelian quantum order in spin-orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems
• Induced Superconductivity in the Quantum Spin Hall Edge
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• Non-Abelian Topological Orders and Majorana Fermions in Spin-Singlet Superconductors
• Quantized Transport in Graphene p-n Junctions in Magnetic Field
• Majorana bound states from exceptional points in non-topological superconductors
• Edge-mode Superconductivity in a Two Dimensional Topological Insulator
• Kitaev chains with long-range pairing
• Anomalous Andreev bound state in non-centrosymmetric superconductors
• Topological invariants and interacting one-dimensional fermionic systems
• Wire deconstructionism of two-dimensional topological phases
• Single fermion manipulation via superconducting phase differences in multiterminal Josephson junctions
• Is Sr2RuO4 a Chiral P-Wave Superconductor?
• Tunneling of anyonic Majorana excitations in topological superconductors
• Localization in disordered superconducting wires with broken spin-rotation symmetry
• Many-body characterization of topological superconductivity: The Richardson-Gaudin-Kitaev chain
• A proof of the Kramers degeneracy of transmission eigenvalues from antisymmetry of the scattering matrix
• Annihilation of colliding Bogoliubov quasiparticles reveals their Majorana nature
• Andreev billiards
• Spin connection and boundary states in a topological insulator
• Dephasing-enabled triplet Andreev conductance
• X-shaped and Y-shaped Andreev resonance profiles in a superconducting quantum dot
• Bimodal conductance distribution of Kitaev edge modes in topological superconductors
• Time-delay matrix, midgap spectral peak, and thermopower of an Andreev billiard
• A scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors
• Geodesic scattering by surface deformations of a topological insulator
• Density of states at disorder-induced phase transitions in a multichannel Majorana wire
• Effect of chiral symmetry on chaotic scattering from Majorana zero modes
• Generalization of the Poisson kernel to the superconducting random-matrix ensembles

Cited by in corpus (189)

• Topological phases of non-Hermitian systems
• Topological Origin of Non-Hermitian Skin Effects
• From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Topological phases with parafermions: theory and blueprints
• High-Temperature Majorana Corner States
• Two-dimensional platform for networks of Majorana bound states
• Superconducting Topological Surface States in Non-centrosymmetric Bulk Superconductor PbTaSe2
• Boundary Green functions of topological insulators and superconductors
• Topological tight-binding models from non-trivial square roots
• Universality classes of non-Hermitian random matrices
• Nonunitary Scaling Theory of Non-Hermitian Localization
• Defect states emerging from a non-Hermitian flat band of photonic zero modes
• Approximating the Sachdev-Ye-Kitaev model with Majorana wires
• Majorana nanowires for topological quantum computation
• Low-energy theory of transport in Majorana wire junctions
• Three-terminal nonlocal conductance in Majorana nanowires: Distinguishing topological and trivial in realistic systems with disorder and inhomogeneous potential
• Wigner time delay and related concepts -- Application to transport in coherent conductors
• Symmetry-protected zero-mode laser with a tunable spatial profile
• Majorana wavefunction oscillations, fermion parity switches, and disorder in Kitaev chains
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Theory of Majorana zero modes in unconventional superconductors
• Non-Hermitian Floquet topological superconductors with multiple Majorana edge modes
• Interference of chiral Andreev edge states
• Weyl nodes in Andreev spectra of multiterminal Josephson junctions: Chern numbers, conductances and supercurrents
• Extreme Decoherence and Quantum Chaos
• Quantized and unquantized zero-bias tunneling conductance peaks in Majorana nanowires: Conductance below and above $2e^2/h$
• Electromagnetic response of quantum Hall systems in dimensions five and six and beyond
• Approaching a topological phase transition in Majorana nanowires
• Skyrmion-induced bound states in a superconductor
• Bulk disorder in the superconductor affects proximity-induced topological superconductivity
• Spectral transitions and universal steady states in random Kraus maps and circuits
• Transition from Quantum Chaos to Localization in Spin Chains
• Current Correlations in a Majorana Beam Splitter
• Majorana spintronics
• Bulk and edge-state arcs in non-hermitian coupled-resonator arrays
• Direct measurement of topological numbers with spins in diamond
• Disorder effects on Majorana zero modes: Kitaev chain versus semiconductor nanowire
• Topological supercurrents interaction and fluctuations in the multiterminal Josephson effect
• Many-body quantum chaos in stroboscopically-driven cold atoms
• Universal Majorana thermoelectric noise
• Persistent current and zero-energy Majorana modes in a p-wave disordered superconducting ring
• Existence of zero-energy impurity states in different classes of topological insulators and superconductors and their relation to topological phase transitions
• Quench dynamics in superconducting nanojunctions: metastability and dynamical Yang-Lee zeros
• Subband occupation in semiconductor-superconductor nanowires
• Topological dynamics and excitations in lasers and condensates with saturable gain or loss
• Robustness of Majorana bound states in the short junction limit
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Compatibility of transport effects in non-Hermitian nonreciprocal systems
• Andreev bound states formation and quasiparticle trapping in quench dynamics revealed by time-dependent counting statistics
• Real spectra in non-Hermitian topological insulators
• Recent progress on Majorana in semiconductor-superconductor heterostructures--Engineering and detection
• Majorana/Andreev crossover and the fate of the topological phase transition in inhomogeneous nanowires
• Braiding-based quantum control of a Majorana qubit built from quantum dots
• Photoinduced $\frac{1}{2}\frac{e^2}{h}$ and $\frac{3}{2}\frac{e^2}{h}$ conductance plateaus in topological insulator-superconductor heterostructures
• Supersymmetric polarization anomaly in photonic discrete-time quantum walks
• Dynamic Majorana resonances and universal symmetry of nonequilibrium thermoelectric quantum noise
• Quench dynamics of fermion-parity switches in a Josephson junction
• Majorana finite frequency nonequilibrium quantum noise
• Crossover between trivial zero modes in Majorana nanowires
• Josephson current signatures of the Majorana flat bands on the surface of time-reversal-invariant Weyl and Dirac semimetals
• Distinguishing between Topological and Quasi Majorana Zero Modes with a Dissipative Resonant Level
• Nonequilibrium Majorana fluctuations
• Supercurrent-enabled Andreev reflection in a chiral quantum Hall edge state
• Kondo physics from quasiparticle poisoning in Majorana devices
• Majorana bound states in hybrid 2D Josephson junctions with ferromagnetic insulators
• Phase-tunable Majorana bound states in a topological N-SNS junction
• Identification of topological superconductivity in magnetic impurity systems using bulk spin-polarization
• Distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles
• Andreev reflection in s-type superconductor proximized 3D topological insulator
• A classification of magnetic frustration and metamaterials from topology
• Chiral symmetry in non-Hermitian systems: product rule and Clifford algebra
• A microwave realization of the chiral orthogonal, unitary, and symplectic ensembles
• Recursion scheme for the largest $\beta$-Wishart-Laguerre eigenvalue and Landauer conductance in quantum transport
• Bulk Bogoliubov Fermi arcs in non-Hermitian superconducting systems
• Quantum phases of disordered three-dimensional Majorana-Weyl fermions
• Topologically protected charge transfer along the edge of a chiral $\text{p}$-wave superconductor
• Electrical detection of the Majorana fusion rule for chiral edge vortices in a topological superconductor
• Thermal superconducting quantum interference proximity transistor
• Non-Abelian monopoles in the multiterminal Josephson effect
• Quantum Spin Hall Effect in Twisted Bilayer Graphene
• Efficient Statistical Model for Predicting Electromagnetic Wave Distribution in Coupled Enclosures
• Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials
• Field theory of non-Hermitian disordered systems
• Non-Hermitian zero-energy pinning of Andreev and Majorana bound states in superconductor-semiconductor systems
• Sinai Diffusion at Quasi-1D Topological Phase Transitions
• Topological phase transitions in the 1D multichannel Dirac equation with random mass and a random matrix model
• Robust zero modes in non-Hermitian systems without global symmetries
• Chaos due to symmetry-breaking in deformed Poisson ensemble
• Quantized conductance with non-zero shot noise as a signature of Andreev edge state
• Nonequilibrium electrical, thermal and spin transport in open quantum systems of topological superconductors, semiconductors and metals
• Zero-bias anomaly in nano-scale hole-doped Mott insulators on a triangular silicon surface
• Dual Majorana universality in thermally induced nonequilibrium
• Majorana bound states in magnetic impurity chains: effects of $d$-wave pairing
• Wave scattering properties of multiple weakly-coupled complex systems
• Superconducting proximity effect in $d$-wave cuprate/ graphene heterostructures
• Fluxoid-induced pairing suppression and near-zero modes in quantum dots coupled to full-shell nanowires
• Magnetic-impurity resonance states for different pairing symmetries in twisted bilayer graphene
• Edge currents as a probe of the strongly spin-polarized topological noncentrosymmetric superconductors
• Magnetization governed magnetoresistance anisotropy in topological semimetal CeBi
• Superposition and higher-order spacing ratios in random matrix theory with application to complex systems
• Non-Hermitian minimal Kitaev chains
• Majorana orthogonal transformation and Majorana zero modes in free fermionic systems
• Phase space methods for Majorana fermions
• Majorana quanta, string scattering, curved spacetimes and the Riemann Hypothesis
• Hermitian chiral boundary states in non-Hermitian topological insulators
• First principles study of topological phase in chains of $3d$ transition metals
• Fundamental constraints on the observability of non-Hermitian effects in passive systems
• Pfaffian formula for fermion parity fluctuations in a superconductor and application to Majorana fusion detection
• Odd-frequency superconductivity induced in topological insulators with and without hexagonal warping
• Sea of Majorana fermions from pseudo-scalar superconducting order in three dimensional Dirac materials
• The invisible Majorana bound state at the helical edge
• Transport in deformed centrosymmetric networks
• Spectral statistics of multi-parametric Gaussian ensembles with chiral symmetry
• Topological superconductivity and anti-Shiba states in disordered chains of magnetic adatoms
• Wiedemann-Franz-type relation between shot noise and thermal conduction of Majorana surface states in a three-dimensional topological superconductor
• Statistical Majorana Bound State Spectroscopy
• Boundary-dependent dynamical instability of bosonic Green's function: Dissipative Bogoliubov-de Gennes Hamiltonian and its application to non-Hermitian skin effect
• Concomitant opening of a topological bulk-gap with an emerging Majorana edge-state
• Transport properties of an interacting Majorana chain
• Extended Majorana zero modes in a topological superconducting-normal T-junction
• Nonequilibrium Andreev bound states population in short superconducting junctions coupled to a resonator
• Universal hard-edge statistics of non-Hermitian random matrices
• Unusual upper critical fields of the topological nodal-line semimetal candidate Sn${}_x$NbSe${}_{2-\delta }$
• The tenfold way redux: Fermionic systems with $N$-body interactions
• Hybridization mechanism of the dual proximity effect in superconductor-topological insulator interfaces
• Linear localization of zero modes in weakly coupled non-Hermitian reservoirs
• Winding Number Statistics of a Parametric Chiral Unitary Random Matrix Ensemble
• Symmetry analysis of transport properties in helical superconductor junctions
• Approximate treatment of noncommutative curvature in quartic matrix model
• Interplay between Coulomb blockade and Josephson effect in a topological superconductor-quantum dot device
• Zero energy modes in a superconductor with ferromagnetic adatom chains and quantum phase transitions
• Bound fermion states in pinned vortices in the surface states of a superconducting topological insulator: The Majorana bound state
• Phonon-induced Majorana Qubit Relaxation in Tunnel-Coupled Two-Island Topological Superconductors
• Transport in a long-range Kitaev ladder: role of Majorana and subgap Andreev states
• Dynamical signatures of ground-state degeneracy to discriminate against Andreev levels in a Majorana fusion experiment
• Symmetry classification of typical quantum entanglement
• Exactly solvable spin chain models corresponding to BDI class of topological superconductors
• Origin of robust exceptional points: a restricted bulk zero mode
• Critical Current Anomaly at the Topological Quantum Phase Transition in a Majorana Josephson Junction
• Finite size effects. The averaged eigenvalue density of Wigner random sign real symmetric matrices
• Interaction effects in superconductor/quantum spin Hall devices: universal transport signatures and fractional Coulomb blockade
• Renormalization approach to the analysis and design of Hermitian and non-Hermitian interfaces
• Detrimental effects of disorder in two-dimensional time-reversal invariant topological superconductors
• Signatures of spectral crossovers in the short- and long-range spectral correlations of a disordered spin-chain with Kramers degeneracy
• Effect of a tunnel barrier on the scattering from a Majorana bound state in an Andreev billiard
• Topology and Spectrum in Measurement-Induced Phase Transitions
• Exotic quantum statistics and thermodynamics from a number-conserving theory of Majorana fermions
• Experimental Realization of Anti-Unitary Wave-Chaotic Photonic Topological Insulator Graphs Showing Kramers Degeneracy and Symplectic Ensemble Statistics
• Full tomography of topological Andreev bands in graphene Josephson junctions
• Non-Hermitian Josephson junctions with four Majorana zero modes
• Atomic Visualization of Bulk and Surface Superconductivity in Weyl Semimetal γ-PtBi2
• Spin-Exchange Induced Spillover on Poor Man's Majoranas in Minimal Kitaev Chains
• Fractionalization of Majorana-Ising-type quasiparticles
• Universal scaling of higher-order spacing ratios in Gaussian random matrices
• Spectral and Strength Statistics of Chiral Brownian Ensemble
• Sparse Random Block Matrices
• One-dimensional ${\mathbb{Z}}_4$ topological superconductor
• Stochastic and long-distance level spacing statistics in many-body localization
• Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos
• Microwave studies of the three chiral ensembles in chains of coupled dielectric resonators
• Spin and charge order in doped spin-orbit coupled Mott insulators
• Universal distributions from non-Hermitian Perturbation of Zero-Modes
• Persistent current in 2D topological superconductors
• Thermal properties of the superconductor-quantum Hall interfaces
• Stochastic and Quantum Dynamics of Repulsive Particles: from Random Matrix Theory to Trapped Fermions
• Universal Broadening of Zero Modes: A General Framework and Identification
• Preserving Topology while Breaking Chirality: From Chiral Orthogonal to Anti-symmetric Hermitian Ensemble
• Detecting Majorana modes through Josephson junction ring-quantum dot hybrid architectures
• Spin-mixing-tunneling network model for Anderson transitions in two-dimensional disordered spinful electrons
• Fractional Wannier Orbitals and Tight-Binding Gauge Fields for Kitaev Honeycomb Superlattices with Flat Majorana Bands
• Fock-space geometry and strong correlations in many-body localized systems
• Noninteracting tight-binding models for Fock parafermions
• Diode effect in microwave irradiated Josephson junctions with Yu-Shiba-Rusinov states
• Excess photon-assisted noise of Majorana and Andreev bound states
• Observing complementary Lucas sequences using non-Hermitian zero modes
• Hidden duality and accidental degeneracy in cycloacene and Möbius cycloacene
• Planar Hall supercurrent and δϕ-shift in the topological Josephson junction
• Solvable random matrix ensemble with a logarithmic weakly confining potential
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems
• Pinpointing Triple Point of Noncommutative Matrix Model with Curvature
• Mixed-pairing superconductivity in 5d Mott insulators with antisymmetric exchange
• Microwave limiters implemented by coupled dielectric resonators based on a topological defect mode and CT-symmetry breaking
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal
• Topological Properties and Characterizations
• Direct observation of zero modes in a non-Hermitian nanocavity array
• Two Dimensional Honeycomb Materials: random fields, dissipation and fluctuations
• New term in effective field theory at fixed topology
• Theoretical study on thermalization in isolated quantum systems