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Abstract The proposal of fault-tolerant quantum computations, which promise to dramatically improve the operation of quantum computers and to accelerate the development of the compact hardware for them, is based on topological quantum field theories, which rely on the existence in Nature of physical systems described by a Lagrangian containing a non-Abelian (NA) topological term. These are solid-state systems having two-dimensional electrons, which are coupled to magnetic-flux-quanta vortexes, forming complex particles, known as anyons. Topological quantum computing (TQC) operations thus represent a physical realization of the mathematical operations involving NA representations of a braid group B n , generated by a set of n localized anyons, which can be braided and fused using a “tweezer” and controlled by a detector. For most of the potential TQC material systems known so far, which are 2D-electron–gas semiconductor structure at high magnetic field and a variety of hybrid superconductor/topological-material heterostructures, the realization of anyon localization versus tweezing and detecting meets serious obstacles, chief among which are the necessity of using current control, i.e., mobile particles, of the TQC operations and high density electron puddles (containing thousands of electrons) to generate a single vortex. Here we demonstrate a novel system, in which these obstacles can be overcome, and in which vortexes are generated by a single electron. This is a ~ 150 nm size many electron InP/GaInP 2 self-organized quantum dot, in which molecules, consisting of a few localized anyons, are naturally formed and exist at zero external magnetic field. We used high-spatial-resolution scanning magneto-photoluminescence spectroscopy measurements of a set of the dots having five and six electrons, together with many-body quantum mechanical calculations to demonstrate spontaneous formation of the anyon magneto-electron particles ( e ν ) having fractional charge ν = n / k, where n = 1–4 and k = 3–15 are the number of electrons and vortexes, respectively, arranged in molecular structures having a built-in (internal) magnetic field of 6–12 T. Using direct imaging of the molecular configurations we observed fusion and braiding of e ν - anyons under photo-excitation and revealed the possibility of using charge sensing for their control. Our investigations show that InP/GaInP 2 anyon-molecule QDs, which have intrinsic transformations of localized e ν - anyons compatible with TQC operations and capable of being probed by charge sensing, are very promising for the realization of TQC.
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Density wave halo around anyons in fractional quantum anomalous Hall states
The recent observation of fractional quantum anomalous Hall (FQAH) states in tunable moiré materials encourages study of several new phenomena that may be uniquely accessible in these platforms. Here, we show that an isolated localized anyon of the FQAH state will nucleate a “halo” of charge-density-wave (CDW) order around it. We demonstrate this effect using a recently proposed quantum Ginzburg-Landau theory that describes the interplay between the topological order of the FQAH state and the broken-symmetry order of a CDW. The spatial extent of the CDW order will, in general, be larger than the length scale at which the fractional charge of the anyon is localized. The strength and the decay length of the CDW order around anyons induced by doping or the magnetic field differ qualitatively from those nucleated by a random potential. Our results leverage a precise mathematical analogy to earlier studies of the superfluid-CDW competition of a system of lattice bosons which has been used to interpret the observed CDW halos around vortices in high-Tc superconductors. We show that measurement of these patches of CDW order can give an indirect route to measuring the fractional charge of the anyon. Such a measurement may be possible by scanning tunneling microscopy in moiré systems.
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- Award ID(s):
- 2206305
- PAR ID:
- 10535802
- Publisher / Repository:
- Physical Review B
- Date Published:
- Journal Name:
- Physical Review B
- Volume:
- 110
- Issue:
- 8
- ISSN:
- 2469-9950
- Page Range / eLocation ID:
- 085120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1103/PhysRevB.110.085120
