Localization problem of a two-dimensional lattice in a random magnetic field

1993 ◽  
Vol 47 (15) ◽  
pp. 9561-9565 ◽  
Author(s):  
Y. Avishai ◽  
Y. Hatsugai ◽  
M. Kohmoto
Keyword(s):  
Magnetic Field ◽  
Two Dimensional ◽  
Localization Problem ◽  
Dimensional Lattice ◽  
Random Magnetic Field

Two-dimensional electron in a random magnetic field

1994 ◽  
Vol 49 (5) ◽  
pp. 3340-3346 ◽  
Author(s):  
Armelle Barelli ◽  
Robert Fleckinger ◽  
Timothy Ziman
Keyword(s):  
Magnetic Field ◽  
Two Dimensional ◽  
Dimensional Electron ◽  
Random Magnetic Field

scholarly journals Fractionally Charged Anyon Generated by Topological Path Fusion in Magnetic Flux Lattice

2020 ◽  
Author(s):  
Tieyan Si
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Collective Excitation ◽  
Quantum Hall ◽  
Experimental System ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Topological Quantum ◽  
Fusion Theory

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.

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