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)
Si, T. Fractionally Charged Anyons Generated by Topological Path Fusion of Propagating Electron in Magnetic Flux Lattice. Nuclear Physics B, 2021, 969, 115446. https://doi.org/10.1016/j.nuclphysb.2021.115446.
Si, T. Fractionally Charged Anyons Generated by Topological Path Fusion of Propagating Electron in Magnetic Flux Lattice. Nuclear Physics B, 2021, 969, 115446. https://doi.org/10.1016/j.nuclphysb.2021.115446.
Si, T. Fractionally Charged Anyons Generated by Topological Path Fusion of Propagating Electron in Magnetic Flux Lattice. Nuclear Physics B, 2021, 969, 115446. https://doi.org/10.1016/j.nuclphysb.2021.115446.
Si, T. Fractionally Charged Anyons Generated by Topological Path Fusion of Propagating Electron in Magnetic Flux Lattice. Nuclear Physics B, 2021, 969, 115446. https://doi.org/10.1016/j.nuclphysb.2021.115446.
Abstract
Anyon usually exists as collective excitation of two dimensional electron gas subjected to strong magnetic field, carrying fractional charges and exotic statistical character beyond fermion and boson. Fractional quantum Hall effect (FQHE) is the only experimental system showing solid evidence of anyon and a serial of fractional charges so far. Searching for new serial of fractional charges in FQHE or other physical system is still a challenge for both theoretical and experimental study. Here a topological fusion theory of propagating paths winding around a pair of fluxes is proposed to explore the physical origin of fractional charges. This topological path fusion theory not only generated all of the existed serial of fractional charges in FQHE and found the exact correspondence between FQHE and integral quantum Hall effect (IQHE), but also predicted new serial of fractional charges in FQHE. Further more, serial irrational charges like $2/(3+\sqrt{2})$ in one dimensional lattice of magnetic fluxes as well as that in two dimensional lattice of magnetic fluxes, such as $(1+\sqrt{2})$, are predicted. Even in three dimensional network of magnetic fluxes, a serial of fractionally charged anyon is predicted by this topological path fusion theory, which has exactly correspondence with the knot lattice model of anyon. In fact, in a multi-connected space time without magnetic field, this topological path fusion theory still holds, revealing an universal existence of fractional charge and mass in quantum material with strong confinement of particles (such as photonic crystal with porous nano-structures) and paving a new way for topological quantum computation.
Keywords
Topological order; Fractional charge; Fractional quantum Hall effect; Magnetic flux lattice
Subject
Physical Sciences, Quantum Science and Technology
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
