Disorder-induced topological superconductivity in a spherical quantum-Hall--superconductor hybrid

Abstract

Quantum-Hall--Superconductor hybrids have been predicted to exhibit various types of topological order, providing possible platforms for intrinsically fault-tolerant quantum computing. In this paper, we develop a formulation to construct this hybrid system on a sphere, a useful geometry for identifying topologically ordered states due to its compact and contractible nature. As a preliminary step using this framework, we investigate disorder effects on the Rashba-coupled quantum Hall system combined with the type-II superconductor. By diagonalizing the BdG Hamiltonian projected into a Rashba-coupled Landau level, we demonstrate the emergence of a topological superconducting phase resulting from disorders and proximity-induced pairing. Distinctive gapless modes appear in the real-space entanglement spectrum, which is consistent with topological superconductivity.

arXiv comment11 pages, 6 figures

References in corpus (73)

• The electronic properties of graphene
• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• 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
• Helical liquids and Majorana bound states in quantum wires
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• String-net condensation: A physical mechanism for topological phases
• Majorana fermions in a tunable semiconductor device
• Calculation of reduced density matrices from correlation functions
• Topological orders and Edge excitations in FQH states
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Quantum Hall Ferromagnetism in Graphene
• Electrically detected interferometry of Majorana fermions in a topological insulator
• Chiral Topological Superconductor From the Quantum Hall State
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Fractional statistics in anyon collisions
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Topological phases with parafermions: theory and blueprints
• Half-integer quantized anomalous thermal Hall effect in the Kitaev material $\alpha$-RuCl${}_3$
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Extreme magnetic field-boosted superconductivity
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Electron interactions in graphene in a strong magnetic field
• Robustness of the thermal Hall effect close to half-quantization in a field-induced spin liquid state
• Entanglement entropy and the Berry phase in solid states
• Fractional topological superconductors with fractionalized Majorana fermions
• Resonant Spin Hall Conductance in Two-Dimensional Electron Systems with Rashba Interaction in a Perpendicular Magnetic Field
• The Fractional Quantum Hall States of Dirac Electrons in Graphene
• Fractional Quantum Hall Effect in Graphene
• Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
• Real-Space Entanglement Spectrum of Quantum Hall States
• Even denominator fractional quantum Hall states in higher Landau levels of graphene
• Fractionalization, topological order, and quasiparticle statistics
• Fibonacci anyons and charge density order in the 12/5 and 13/5 plateaus
• Trace Index and Spectral Flow in the Entanglement Spectrum
• Superconducting analogue of the parafermion fractional quantum Hall states
• SU(4) composite fermions in graphene: New fractional quantum Hall states
• Andreev reflection in the fractional quantum Hall state
• Entanglement entropy of integer Quantum Hall states
• Magnetic Oscillations and Quasiparticle Band Structure in the Mixed State of Type-II Superconductors
• Variational study of the nu=1 quantum Hall ferromagnet in the presence of spin-orbit interaction
• Vortices in a Thin Film Superconductor with a Spherical Geometry
• Topological degeneracy of non-Abelian states for dummies
• Crystallization in the Fractional Quantum Hall Regime Induced by Landau-level Mixing
• Topological phases in two-dimensional arrays of parafermionic zero modes
• Spontaneous polarization of composite fermions in the $n=1$ Landau level of graphene
• Fibonacci Topological Superconductor
• Commensurate and Incommensurate States of Topological Quantum Matter
• Fractional chiral superconductors
• Reentrant superconductivity in a strong applied field within the tight-binding model
• Relativistic Landau Models and Generation of Fuzzy Spheres
• Anomalous Quantum Hall Effect on Sphere
• Investigation on the Ground States of a Model Thin-Film Superconductor on a Sphere
• Topological superconductivity in Quantum Hall-superconductor hybrid systems
• A non-Abelian twist to integer quantum Hall states
• Quantum Mechanics and Superconductivity in a Magnetic Field
• Quantum Hall Superconductivity from Moir{é} Landau Levels
• Vortex Lattice Structure and Topological Superconductivity in the Quantum Hall Regime
• Parafermions, induced edge states and domain walls in the fractional quantum Hall effect spin transitions
• Entanglement entropy and entanglement spectrum of triplet topological superconductors
• Phase diagram of superconductivity in the integer quantum Hall regime
• Majorana lattices from the quantized Hall limit of a proximitized spin-orbit coupled electron gas
• Landau level quantization for massless Dirac fermions in the spherical geometry: graphene fractional quantum Hall effect on the Haldane sphere
• Formulation of the Relativistic Quantum Hall Effect and "Parity Anomaly"
• Braid Group, Gauge Invariance and Topological Order
• General pairing theory for condensed and non-condensed pairs of a superconductor in a high magnetic field

Cited by in corpus (2)

• Chirality-selective proximity effect between chiral $p$-wave superconductors and quantum Hall insulators
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor