scholarly journals Limits of Applicability of the Composite Fermion Model

Materials ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4267
Author(s):  
Janusz E. Jacak
Keyword(s):  
Landau Level ◽  
Landau Levels ◽  
Graphene Monolayer ◽  
Composite Fermions ◽  
Composite Fermion ◽  
Topological Methods ◽  
Fermion Model ◽  
Lowest Landau Level ◽  
Further Development

The popular model of composite fermions, proposed in order to rationalize FQHE, were insufficient in view of recent experimental observations in graphene monolayer and bilayer, in higher Landau levels in GaAs and in so-called enigmatic FQHE states in the lowest Landau level of GaAs. The specific FQHE hierarchy in double Hall systems of GaAs 2DES and graphene also cannot be explained in the framework of composite fermions. We identify the limits of the usability of the composite fermion model by means of topological methods, which elucidate the phenomenological assumptions in composite fermion structure and admit further development of FQHE understanding. We demonstrate how to generalize these ideas in order to explain experimentally observed FQHE phenomena, going beyond the explanation ability of the conventional composite fermion model.

scholarly journals Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level

1997 ◽  
Vol 11 (22) ◽  
pp. 2621-2660 ◽  
Author(s):  
J. K. Jain ◽  
R. K. Kamilla
Keyword(s):  
Landau Level ◽  
Ground State ◽  
Quantum Hall ◽  
Monte Carlo Study ◽  
Composite Fermions ◽  
Composite Fermion ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Lowest Landau Level ◽  
Standard Manner

Single particle basis functions for composite fermions are obtained from which many-composite fermion states confined to the lowest electronic Landau level can be constructed in the standard manner, i.e. by building Slater determinants. This representation enables a Monte Carlo study of systems containing a large number of composite fermions, yielding new quantitative and qualitative information. The ground state energy and the gaps to charged and neutral excitations are computed for a number of fractional quantum Hall effect (FQHE) states, earlier off-limits to a quantitative investigation. The ground state energies are estimated to be accurate to ~0.1% and the gaps at the level of a few percent. It is also shown that at Landau level fillings smaller than or equal to 1/9 the FQHE is unstable to a spontaneous creation of excitons of composite fermions. In addition, this approach provides new conceptual insight into the structure of the composite fermion wave functions, resolving in the affirmative the question of whether it is possible to motivate the composite fermion theory entirely within the lowest Landau level, without appealing to higher Landau levels.

scholarly journals COMPOSITE FERMIONS CLOSE TO THE ONE-HALF FILLING OF THE LOWEST LANDAU LEVEL REVISITED

2005 ◽  
Vol 19 (04) ◽  
pp. 775-782
Author(s):  
BEHNAM FARID
Keyword(s):  
Landau Level ◽  
Microscopic Theory ◽  
Mean Free Path ◽  
Experimental Results ◽  
Two Dimensional ◽  
Composite Fermions ◽  
Lowest Landau Level ◽  
Longitudinal Conductivity ◽  
Half Filling ◽  
The One

By strictly adhering to the microscopic theory of composite fermions (CFs) for the Landau-level filling fractions ν e =p/(2p+1), we reproduce, with remarkable accuracy, the surface-acoustic-wave (SAW)-based experimental results by Willett and co-workers concerning two-dimensional electron systems with ν e close to ½. Our results imply that the electron band mass m b , as distinct from the CF mass m⋆, must undergo a substantial increase under the conditions corresponding to ν e ≈ ½. In view of the relatively low aerial electronic densities n e to which the underlying SAW experiments correspond, our finding conforms with the experimental results by Shashkin et al. [Phys. Rev. B 66, 073303 (2002)], concerning two-dimensional electrons in silicon, that signal sharp increase in m b for n e decreasing below approximately 2×1011 cm -2. We further establish that a finite mean-free path ℓ0 is essential for the observed linearity of the longitudinal conductivity σxx(q) as deduced from the SAW velocity shifts.

Variable Lande splitting factor and Composite Fermion

2019 ◽  
Vol 34 (36) ◽  
pp. 1950302
Author(s):  
S. Pal ◽  
A. Bhattacharya ◽  
R. Ghosh ◽  
B. Chakrabarti
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Additional Contribution ◽  
Composite Fermions ◽  
Composite Fermion ◽  
Fermion Model ◽  
Effective Masses ◽  
Qcd Vacuum ◽  
Splitting Factor ◽  
Spin Contribution

The effective Lande splitting factor [Formula: see text] for heavy pentaquarks has been investigated, where the pentaquarks are described as Composite Fermions (CFs). The effective Lande splitting factor for heavy pentaquarks [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text] has been extracted. It has been suggested that due to color magnetic field, diquarks behave like CFs and effective masses of the pentaquarks [Formula: see text] have been estimated in diquark–diquark–antiquark scheme with the input of effective diquark masses calculated in the framework of Composite Fermion model (CFM). With [Formula: see text] as the additional contribution to the energy expression, the variation of [Formula: see text] with angular momentum [Formula: see text] has been studied. The vacuum value of [Formula: see text] has been extracted, which can be attributed to the splitting due to spin contribution of CFs and choromo-electromagnetic character of the QCD vacuum.

scholarly journals Composite fermion liquid to Wigner solid transition in the lowest Landau level of zinc oxide

2018 ◽  
Vol 9 (1) ◽  
Author(s):  
D. Maryenko ◽  
A. McCollam ◽  
J. Falson ◽  
Y. Kozuka ◽  
J. Bruin ◽  
...  
Keyword(s):  
Zinc Oxide ◽  
Landau Level ◽  
Composite Fermion ◽  
Wigner Solid ◽  
Lowest Landau Level

scholarly journals GEOMETRIC TRANSFORMATIONS AND NCCS THEORY IN THE LOWEST LANDAU LEVEL

2002 ◽  
Vol 16 (25) ◽  
pp. 3725-3736 ◽  
Author(s):  
M. ELIASHVILI ◽  
G. TSITSISHVILI
Keyword(s):  
Landau Level ◽  
Quantum Hall ◽  
Simons Theory ◽  
Composite Fermions ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Geometric Transformations ◽  
Lowest Landau Level ◽  
Chern Simons ◽  
Area Preserving

Chern-Simons type gauge field is generated by the means of singular area preserving transformations in the lowest Landau level of electrons forming fractional quantum Hall state. Dynamics is governed by the system of constraints which correspond to the Gauss law in the non-commutative Chern-Simons gauge theory and to the lowest Landau level condition in the picture of composite fermions. Physically reasonable solution to this constraints corresponds to the Laughlin state. It is argued that the model leads to the non-commutative Chern-Simons theory of the QHE and composite fermions.

PERIODIC AHARONOV–BOHM SOLENOIDS IN A CONSTANT MAGNETIC FIELD

2006 ◽  
Vol 18 (08) ◽  
pp. 913-934 ◽  
Author(s):  
TAKUYA MINE ◽  
YUJI NOMURA
Keyword(s):  
Magnetic Field ◽  
Landau Level ◽  
Density Of States ◽  
Homogeneous Magnetic Field ◽  
Landau Levels ◽  
Sufficient Condition ◽  
Absolutely Continuous ◽  
Lowest Landau Level ◽  
Aharonov Bohm ◽  
The Magnetic Field

We consider the magnetic Schrödinger operator on R2. The magnetic field is the sum of a homogeneous magnetic field and periodically varying pointlike magnetic fields on a lattice. We shall give a sufficient condition for each Landau level to be an infinitely degenerated eigenvalue. This condition is also necessary for the lowest Landau level. In the threshold case, we see that the spectrum near the lowest Landau level is purely absolutely continuous. Moreover, we shall give an estimate for the density of states for Landau levels and their gaps. The proof is based on the method of Geyler and Šťovíček, the magnetic Bloch theory, and canonical commutation relations.

scholarly journals Landau levels in QCD in an external magnetic field

2018 ◽  
Vol 175 ◽  
pp. 07014 ◽  
Author(s):  
Falk Bruckmann ◽  
Gergely Endrődi ◽  
Matteo Giordano ◽  
Sándor D. Katz ◽  
Tamás G. Kovács ◽  
...  
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Landau Level ◽  
Low Energy ◽  
Landau Levels ◽  
Dimensional Case ◽  
Strong Interactions ◽  
Two Dimensional ◽  
Energy Models ◽  
Lowest Landau Level

We will discuss the issue of Landau levels of quarks in lattice QCD in an external magnetic field. We will show that in the two-dimensional case the lowest Landau level can be identified unambiguously even if the strong interactions are turned on. Starting from this observation, we will then show how one can define a “plowest Landau level” in the four-dimensional case, and discuss how much of the observed effects of a magnetic field can be explained in terms of it. Our results can be used to test the validity of low-energy models of QCD that make use of the lowest-Landau-level approximation.

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