Angular momenta of composite Fermion excitations and the band structure of fractional quantum Hall systems

1994 ◽  
Vol 92 (11) ◽  
pp. 865-868 ◽  
Author(s):  
X.M. Chen ◽  
J.J. Quinn
Keyword(s):  
Band Structure ◽  
Quantum Hall ◽  
Composite Fermion ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall Systems ◽  
Angular Momenta

EXPLANATION OF COMPOSITE FERMION STRUCTURE IN FRACTIONAL QUANTUM HALL SYSTEMS

2012 ◽  
Vol 26 (23) ◽  
pp. 1230011 ◽  
Author(s):  
JANUSZ JACAK ◽  
RYSZARD GONCZAREK ◽  
LUCJAN JACAK ◽  
IRENEUSZ JÓŹWIAK
Keyword(s):  
Quantum Hall ◽  
High Mobility ◽  
Flat Band ◽  
Composite Fermions ◽  
Composite Fermion ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Flux Tubes ◽  
Quantum Hall Systems ◽  
Developing Area

The topological explanation of the origin of Laughlin correlations in 2D charged systems under strong magnetic fields is formulated. Formal, self-consistent mathematical model of originally identified cyclotron braid subgroups is given in order to fully describe fundamentals of fractional quantum Hall effect, retrieve Laughlin correlations and point physical conditions which stand behind mysterious composite fermion structure. The new complete implementation of composite fermion basing on the first principles, without involving any artificial constructions (with flux-tubes or vortices) supply an explanation of previous models of composite fermions. Presented approach can lead to some corrections of numerical results in energy minimizations made within the traditional formulation of composite fermion model. Authors also identify the relations of FQHE in cyclotron braid terms within newly developing area of topological insulators and optical lattices. The prerequisites needed for formation of the fractional state are identified beyond the traditionally assumed factors, like the flat band condition and the interaction presence. The role of high mobility of carriers is highlighted in agreement with the experimental observations. Description, in terms of cyclotron braid subgroups, of the nature of yet unexplained novel experiments in Hall 2D systems including graphene is provided as well.

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.

Entanglement entropy of fractional quantum Hall systems with short range disorder

2015 ◽  
Vol 29 (12) ◽  
pp. 1550065 ◽  
Author(s):  
B. A. Friedman ◽  
G. C. Levine
Keyword(s):  
Short Range ◽  
Entanglement Entropy ◽  
Quantum Hall ◽  
Finite Size ◽  
Disorder Strength ◽  
Fractional Quantum ◽  
Finite Size Effects ◽  
Fractional Quantum Hall ◽  
Quantum Hall Systems ◽  
Liquid Transition

The critical value of the mobility for which the ν = 5/2 quantum Hall effect is destroyed by short range disorder is determined from an earlier calculation of the entanglement entropy. The value μ = 2.0 ×106 cm 2/ Vs agrees well with experiment. This agreement is particularly significant in that there are no adjustable parameters. Entanglement entropy versus disorder strength for ν = 1/2, ν = 9/2 and ν = 7/3 is calculated. For ν = 1/2 there is no evidence for a transition for the disorder strengths considered; for ν = 9/2 there appears to be a stripe-liquid transition. For ν = 7/3 there again appears to be a transition at similar value of the disorder strength as the ν = 5/2 transition but there are stronger finite size effects.

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