Incompressible Quantum Fluids of Ideal Anyons in a Strong Magnetic Field

1991 ◽  
Vol 05 (10) ◽  
pp. 1725-1729
Author(s):  
F. C. Zhang ◽  
M. Ma
Keyword(s):  
Magnetic Field ◽  
Strong Magnetic Field ◽  
Ground State ◽  
Similarity Transformation ◽  
Quantum Hall ◽  
Quantum Fluids ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum

Ideal anyons with statistics ν in a strong magnetic field are studied by means of a similarity transformation. The ground state exhibits "integer" quantum Hall effect at filling factor 1/ν with quasiparticle excitations of charge q/ν and statistics -1/ν. Certain electron FQH states can be considered as realization of this, for example, the sequence 2/5, 3/7, … hierarchy of the 1/3 state. This may explain the observed quasiparticle-quasihole asymmetry in the fractional quantum Hall hierarchy.

THE CONNECTION BETWEEN INTEGER QUANTUM HALL EFFECT AND FRACTIONAL QUANTUM HALL EFFECT

2007 ◽  
Vol 21 (02n03) ◽  
pp. 109-113
Author(s):  
JE HUAN KOO ◽  
GUANGSUP CHO
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Matter Wave ◽  
Hall Resistance ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum

We investigate the integer quantum Hall effect (IQHE) and the fractional quantum Hall effect (FQHE). We derive the quantized Hall resistance of IQHE in the presence of the high magnetic field using the scheme of standing waves by de Broglie matter wave of electron gas confined within a two-dimensional square-type quantum well. Without any modification of electrons and holes, it is shown that FQHE is only a decoupling mode of the Hall resistance by two-band-type of electrons and holes, which are governed by IQHE respectively.

COLLECTIVE PHENOMENA IN THE QUANTUM HALL EFFECT

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2253-2273
Author(s):  
R. FERRARI
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Collective Phenomena ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum ◽  
Magnetic Translation

The main phenomenological features of Integer Quantum Hall Effect (IQHE) and Fractional Quantum Hall Effect (FQHE) are reviewed. A theory is proposed based on a new basis for the single particle states, given by a representation of the Magnetic Translation Group (MTG).

scholarly journals Theoretical, Unified Derivation of Both the Integer Quantum Hall Effect and Fractional Quantum Hall Effect

2021 ◽  
Author(s):  
Shinichi Ishiguri
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Integer Quantum Hall Effect ◽  
Charge Quantization ◽  
Integer Quantum ◽  
Dimensional Wave

In this paper, using the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the balance between the Lorentz force and electrical force, we succeed in deriving the fractional quantum Hall effect and the integer quantum Hall effect; we find that the latter exists as a special case of the former. Moreover, using the derived expression describing the fractional quantum Hall effect, a relationship between the plateau in the resistivity of the sample and the applied magnetic field is obtained. The findings of this model agree well with experimental measurements. Because the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the force balance have concrete physical meanings in this work, we could provide a clear picture of the origin of both the integer quantum Hall effect and the fractional quantum Hall effect.

SOME FRACTIONS ARE MORE SPECIAL THAN OTHERS: NEWS FROM THE FRACTIONAL QUANTUM HALL ZONE

2002 ◽  
Vol 16 (20n22) ◽  
pp. 2940-2945 ◽  
Author(s):  
W. PAN ◽  
H. L. STORMER ◽  
D. C. TSUI ◽  
L. N. PFEIFFER ◽  
K. W. BALDWIN ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Ground State ◽  
Field Data ◽  
Quantum Hall ◽  
Fractional Quantum ◽  
Magnetic Field Data ◽  
Fractional Quantum Hall ◽  
Spin Polarized

We report observation of new fractions: 4/11, 5/13, and 6/17 between ν=2/5 and ν=1/3, 4/3 and 5/17 between ν=1/3 and ν=2/7, and 4/19 between ν=2/9 and ν=1/5. The ν=4/11 state was studied in detail. The tilting magnetic field data show that its ground state is spin-polarized.

BRAID GROUP REPRESENTATION AND FRACTIONAL QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (19) ◽  
pp. 1293-1299 ◽  
Author(s):  
CHRISTOPHER TING ◽  
C. H. LAI
Keyword(s):  
Magnetic Field ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Group Representation ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Integral Approach ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Coulomb Term

We discuss Laughlin's ground state and its derivation in the path integral approach. When the external magnetic field is very strong, we regard all electron-electron interactions such as the Coulomb term as weak perturbations. It seems that from the non-trivial topology of the configuration space alone, it is possible to arrive at a Hamiltonian for which Laughlin wavefunctions are exact ground states.

scholarly journals Fractional Quantum Hall States at Zero Magnetic Field

2011 ◽  
Vol 106 (23) ◽  
Author(s):  
Titus Neupert ◽  
Luiz Santos ◽  
Claudio Chamon ◽  
Christopher Mudry
Keyword(s):  
Magnetic Field ◽  
Quantum Hall ◽  
Zero Magnetic Field ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall States ◽  
Hall States

SPIN STRUCTURES IN INHOMOGENEOUS FRACTIONAL QUANTUM HALL SYSTEMS

2004 ◽  
Vol 18 (27n29) ◽  
pp. 3871-3874 ◽  
Author(s):  
KAREL VÝBORNÝ ◽  
DANIELA PFANNKUCHE
Keyword(s):  
Ground State ◽  
Quantum Hall ◽  
Exact Diagonalization ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Spin Structures ◽  
Quantum Hall Systems ◽  
Magnetic Inhomogeneities ◽  
Spin Singlet ◽  
Spin Polarized

Transitions between spin polarized and spin singlet incompressible ground state of quantum Hall systems at filling factor 2/3 are studied by means of exact diagonalization with eight electrons. We observe a stable exactly half–polarized state becoming the absolute ground state around the transition point. This might be a candidate for the anomaly observed during the transition in optical experiments. The state reacts strongly to magnetic inhomogeneities but it prefers stripe–like spin structures to formation of domains.

scholarly journals A non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effect

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Ajit Coimbatore Balram
Keyword(s):  
Wave Function ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Topological Structure ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of 5/25/2. We consider the FQHE at another even denominator fraction, namely \nu=2+3/8ν=2+3/8, where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the ``\bar{3}\bar{2}^{2}1^{4}3‾2‾214" parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at \nu=2+3/8ν=2+3/8. We make predictions for experimentally measurable properties of the \bar{3}\bar{2}^{2}1^{4}3‾2‾214 state that can reveal its underlying topological structure.

Sign in / Sign up

Export Citation Format

Share Document