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.

CORRELATION AND LOCALIZATION OF TWO-DIMENSIONAL ELECTRONS IN A STRONG MAGNETIC FIELD

1990 ◽  
Vol 04 (05) ◽  
pp. 301-310 ◽  
Author(s):  
D. C. TSUI
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Two Dimensional ◽  
Quantum Liquid ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Integral Quantum

This paper gives a brief review of some recent experiments on the localization-delocalization transition in the integral quantum Hall effect and the new quantum liquid ground states giving rise to the fractional quantum Hall effect.

Quantum Hall Effect in AlGaAs and Graphite Quantum Dots

2013 ◽  
Vol 667 ◽  
pp. 1-9 ◽  
Author(s):  
Keshav N. Shrivastava
Keyword(s):  
Magnetic Field ◽  
Quantum Wells ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Two Dimensional ◽  
Hall Resistivity ◽  
Angular Momenta ◽  
The Difference ◽  
Density Of Electrons

Abstract. The 30 nm wide quantum wells on a 4x4 mm2 piece of GaAs/AlGaAs are formed when the layers of GaAs are deposited on AlGaAs films. The two-dimensional density of electrons is 3x1011 cm-2 and the mobility is 32x106 cm2/Vs. In such a sample the Hall resistivity as a function of magnetic field is not a linear function. Hence a suitable theory to understand the Hall effect is formulated. We find that there are phase transitions as a function of temperature. There are lots of fractions of charge which are explained on the basis of spin and orbital angular momentum of the electron. The nano meter size films of graphite also show that the Hall resistivity is non-linear and shows steps as a function of magnetic field. We make an effort to understand the steps in the Hall effect resistivity of graphite with quantum wells formed on the surface. It is found that the fractions are in four categories, (i) the principal fractions which are determined by spin and orbital angular momenta, (ii) the resonances which occur at the difference between two values such as =1-2, (iii) two-particle states which occur at the sum of the two frequencies and (iv) there are clusters of electrons localized in some areas of the sample. The spin in the clusters is polarized so that it becomes NS which is not 1/2 but depends on the number N, of electrons in a cluster.

scholarly journals Two-Dimensional Gases of Generalized Statistics in A Uniform Magnetic Field

1997 ◽  
Vol 11 (11) ◽  
pp. 461-470 ◽  
Author(s):  
Choon-Lin Ho ◽  
Man-Jui Liao
Keyword(s):  
Magnetic Field ◽  
Low Temperature ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Low Temperatures ◽  
Uniform Magnetic Field ◽  
Quantum Hall ◽  
Charge Carriers ◽  
Two Dimensional ◽  
Ideal Gases

We study the low temperature properties of two-dimensional ideal gases of generalized statistics in a uniform magnetic field. The generalized statistics considered here are the parafermion statistics and the exclusion statistics. Similarity in the behaviors of the parafermion gas of finite order p and the gas with exclusion coefficient g=1/p at very low temperatures is noted. These two systems become exactly equivalent at T=0. Quantum Hall effect with these particles as charge carriers is briefly discussed.

scholarly journals An all-epitaxial nitride heterostructure with concurrent quantum Hall effect and superconductivity

2021 ◽  
Vol 7 (8) ◽  
pp. eabf1388
Author(s):  
Phillip Dang ◽  
Guru Khalsa ◽  
Celesta S. Chang ◽  
D. Scott Katzer ◽  
Neeraj Nepal ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Electron Gas ◽  
Quantum Hall ◽  
High Electron Mobility Transistor ◽  
High Electron ◽  
2D Electron Gas ◽  
Integer Quantum Hall Effect ◽  
Topological Quantum ◽  
Integer Quantum

Creating seamless heterostructures that exhibit the quantum Hall effect and superconductivity is highly desirable for future electronics based on topological quantum computing. However, the two topologically robust electronic phases are typically incompatible owing to conflicting magnetic field requirements. Combined advances in the epitaxial growth of a nitride superconductor with a high critical temperature and a subsequent nitride semiconductor heterostructure of metal polarity enable the observation of clean integer quantum Hall effect in the polarization-induced two-dimensional (2D) electron gas of the high-electron mobility transistor. Through individual magnetotransport measurements of the spatially separated GaN 2D electron gas and superconducting NbN layers, we find a small window of magnetic fields and temperatures in which the epitaxial layers retain their respective quantum Hall and superconducting properties. Its analysis indicates that in epitaxial nitride superconductor/semiconductor heterostructures, this window can be significantly expanded, creating an industrially viable platform for robust quantum devices that exploit topologically protected transport.

scholarly journals The quantum Hall effect in the absence of disorder

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Kyung-Su Kim ◽  
Steven A. Kivelson
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Finite Interval ◽  
Quantum Hall ◽  
Wigner Crystal ◽  
Quasi Particle ◽  
Hall Conductance ◽  
Finite Extent

AbstractIt is widely held that disorder is essential to the existence of a finite interval of magnetic field in which the Hall conductance is quantized, i.e., for the existence of “plateaus” in the quantum Hall effect. Here, we show that the existence of a quasi-particle Wigner crystal (QPWC) results in the persistence of plateaus of finite extent even in the limit of vanishing disorder. Several experimentally detectable features that characterize the behavior in the zero disorder limit are also explored.

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