Spin liquids from Majorana Zero Modes in a Cooper Box

Abstract

We propose a path for constructing diverse interacting spin systems from topological nanowires in Cooper Boxes. The wires are grouped into a three-wire building block called an 'hexon', consisting of six Majorana zero modes. In the presence of a strong charging energy, the hexon becomes a Cooper box equivalent to two spin-$1/2$ degrees of freedom. By considering arrays of hexons and controlling the distances between the various wires, one can tune the Hamiltonian governing the low-energy spins, thus providing a route for controllably constructing interacting spin systems in one- and two-dimensions. We explicitly present realizations of the one-dimensional spin-$1/2$ XXZ chain, as well as the transverse field Ising model. We propose an experiment capable of revealing the nature of critical points in such effective spin systems by applying a local gate voltage and measuring the induced charge at a distance. To demonstrate the applicability of this approach to two-dimensions, we provide a scheme for realizing the topologically ordered Yao-Kivelson spin-liquid model, which has a collective Majorana edge mode, similar to the B-phase of Kitaev's honeycomb model.

References in corpus (35)

• Anyons in an exactly solved model and beyond
• 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
• 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
• Observation of the fractional ac Josephson effect: the signature of Majorana particles
• Exponential Protection of Zero Modes in Majorana Islands
• Realizing Majorana zero modes in superconductor-semiconductor heterostructures
• 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
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Observation of half-integer thermal Hall conductance
• An exact chiral spin liquid with non-Abelian anyons
• Topological Kondo effect with Majorana fermions
• Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator
• Towards realistic implementations of a Majorana surface code
• Roadmap to Majorana surface codes
• New quantum phases in a one-dimensional Josephson array
• Multi-Terminal Coulomb-Majorana Junction
• Majorana-Klein hybridization in topological superconductor junctions
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• Multi-channel Kondo impurity dynamics in a Majorana device
• Topological Superconducting Phases of Weakly Coupled Quantum Wires
• Arbitrary Dimensional Majorana Dualities and Network Architectures for Topological Matter
• Transport properties of the Coulomb-Majorana junction
• Majorana Fermion Representation For An Antiferromagnetic Spin-1/2 Chain
• Kondo physics from quasiparticle poisoning in Majorana devices
• Fractional chiral superconductors
• Majorana Spin Liquids, Topology and Superconductivity in Ladders
• Physical Architecture for a Universal Topological Quantum Computer based on a Network of Majorana Nanowires
• Ubiquitous non-local entanglement with Majorana bound states
• Engineering Quantum Spin Liquids and Many-Body Majorana States with a Driven Superconducting Box Circuit

Cited by in corpus (19)

• Materials design of Kitaev spin liquids beyond the Jackeli-Khaliullin mechanism
• Majorana nanowires for topological quantum computation
• Hunting for Majoranas
• Higher order topological superconductors as generators of quantum codes
• Interacting Majorana Fermions
• Majorana Quantum Lego, a Route Towards Fracton Matter
• Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium
• $\text{Draiding}$ majoranas to dynamically engineer Hamiltonians
• Non-Abelian chiral spin liquid on a simple non-Archimedean lattice
• Simulating topological tensor networks with Majorana qubits
• Supersymmetry in the Insulating Phase of a Chain of Majorana Cooper Pair Boxes
• Non-Abelian defects in Fracton phase of matter
• Time-reversal-invariant topological superconductivity
• Topological Kondo effect with spinful Majorana fermions
• Valence bond fluctuations in the Kitaev spin model
• Simulating spin systems with Majorana networks
• Simulating exotic phases of matter with bond-directed interactions with arrays of Majorana-Cooper pair boxes
• Assembling Kitaev honeycomb spin liquids from arrays of 1D symmetry protected topological phases
• Josephson junction arrays as a platform for topological phases of matter