Working Paper Article Version 2 This version is not peer-reviewed

Fractionally Charged Anyons Generated by Topological Path Fusion of Propagating Electron in Magnetic Flux Lattice

Version 1 : Received: 22 July 2020 / Approved: 23 July 2020 / Online: 23 July 2020 (12:43:33 CEST)
Version 2 : Received: 4 June 2021 / Approved: 4 June 2021 / Online: 4 June 2021 (11:21:38 CEST)
(This article belongs to the Research Topic Quantum Computing)

A peer-reviewed article of this Preprint also exists.

Journal reference: Nuclear Physics B 2021, 969, 115446
DOI: 10.1016/j.nuclphysb.2021.115446


Anyon is collective excitation of two dimensional electron gas subjected to strong magnetic field, carrying fractional charges and exotic statistical character beyond fermion and boson. So far, anyons with serial fractional charges only exist in fractional quantum Hall effect. It is still a challenge to find new serial of fractional charges in other physical system and develop an unified mathematical physics theory based on the same root. Here a topological path fusion theory of propagating electrons in magnetic flux lattice is proposed to explore the physical origin of fractional charges based on a generalization of Feynman's path integral theory and Thurston's train track theory. This mathematical physics theory generated the existed serial of fractional charges in fractional quantum Hall effect and predicted new serial of fractional charges. A serial of irrational charges are predicted in one dimensional lattice of magnetic fluxes. Fractionally charged anyons are also generated in two dimensional and three dimensional lattice of train tracks of electric currents, revealing an exact correspondence between knot lattice model and train track model. A new explanation for the modular symmetry of complex Hall conductance and composite fermion in fractional quantum Hall effect is also derived from this topological path fusion theory. Experimental observation of anyon in three dimensions can be realized by constructing three dimensional interlocking magnetic fluxes or mapping magnetic fluxes into forbidden zones in multi-connected space filled by solid state material. A photonic crystal with porous nano-structures is a promising system for detecting fractional charges and paves a new way for topological quantum computation.


Topological order; Fractional charge; Fractional quantum Hall effect; Magnetic flux lattice



Comments (1)

Comment 1
Received: 4 June 2021
Commenter: Tieyan Si
Commenter's Conflict of Interests: Author
Comment: The whole manuscript is revised. Figures are updated. References are added. Published in Nuclear Physics B, 969, (2021), 115446.
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