Imaging anyons with scanning tunneling microscopy

Abstract

Anyons are exotic quasi-particles with fractional charge that can emerge as fundamental excitations of strongly interacting topological quantum phases of matter. Unlike ordinary fermions and bosons, they may obey non-abelian statistics--a property that would help realize fault tolerant quantum computation. Non-abelian anyons have long been predicted to occur in the fractional quantum Hall (FQH) phases that form in two-dimensional electron gases (2DEG) in the presence of a large magnetic field, su ch as the $\nu =\frac{5}{2}$ FQH state. However, direct experimental evidence of anyons and tests that can distinguish between abelian and non-abelian quantum ground states with such excitations have remained elusive. Here we propose a new experimental approach to directly visualize the structure of interacting electronic states of FQH states with the scanning tunneling microscope (STM). Our theoretical calculations show how spectroscopy mapping with the STM near individual impurity defects can be used to image fractional statistics in FQH states, identifying unique signatures in such measurements that can distinguish different proposed ground states. The presence of locally trapped anyons should leave distinct signatures in STM spectroscopic maps, and enables a new approach to directly detect - and perhaps ultimately manipulate - these exotic quasi-particles.

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Cited by in corpus (29)

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• Creating, probing, and manipulating fractionally charged excitations of fractional Chern insulators in optical lattices
• Time-of-Flight Measurements as a Possible Method to Observe Anyonic Statistics
• Topological chiral spin liquids and competing states in triangular lattice SU($N$) Mott insulators
• Tracing non-Abelian anyons via impurity particles
• Quantum Hall Valley Nematics
• Fractional angular momentum and anyon statistics of impurities in Laughlin liquids
• STM in the fractional quantum Hall effect: Spectroscopy of composite-fermion bound states
• Theory of Competing Charge Density Wave, Kekule and Antiferromagnetic ordered Fractional Quantum Hall states in Graphene aligned with Boron Nitride
• Optical control over bulk excitations in fractional quantum Hall systems
• Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians
• Local density of states and particle entanglement in topological quantum fluids
• Fingerprints of Composite Fermion Lambda Levels in Scanning Tunneling Microscopy
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional Lattices
• Gully quantum Hall ferromagnetism in biased trilayer graphene
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
• Local Probes for Quantum Hall Ferroelectrics and Nematics
• Anyon-trions in atomically thin semiconductor heterostructures
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids
• Sensing the binding and unbinding of anyons at impurities
• Natural orbitals and their occupation numbers for free anyons in the magnetic gauge
• Excitation and tunneling spectra of a fractional quantum Hall system in the thin cylinder limit
• Z${}_2$ topological orders in kagomé dipolar systems: Feedback from Rydberg quantum simulator
• An exactly solvable model for anyons with non-Abelian flux