scholarly journals Edge states in graphene quantum dots: Fractional quantum Hall effect analogies and differences at zero magnetic field

2009 ◽  
Vol 79 (7) ◽  
Author(s):  
Igor Romanovsky ◽  
Constantine Yannouleas ◽  
Uzi Landman
Keyword(s):  
Magnetic Field ◽  
Quantum Dots ◽  
Quantum Hall Effect ◽  
Graphene Quantum Dots ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Zero Magnetic Field ◽  
Edge States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

Topological Aspects of Quantum Hall Fluid and Berry Phase

1998 ◽  
Vol 12 (26) ◽  
pp. 2649-2707 ◽  
Author(s):  
Banasri Basu ◽  
P. Bandyopadhyay
Keyword(s):  
Quantum Hall Effect ◽  
Berry Phase ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Chiral Anomaly ◽  
Edge States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall Systems ◽  
Characteristic Features

We have analyzed here the recent development towards our understanding of the Integral and Fractional Quantum Hall effect. It has been pointed out that the chiral anomaly and Berry phase approach embraces in a unified way the whole spectrum of quantum Hall systems with their various characteristic features. This formalism also helps us to understand the edge states observed in Hall fluids. It is argued that Hall fluids with even denominator filling factor leads to the non-Abelian Berry phase.

scholarly journals WANNIER FUNCTIONS AND FRACTIONAL QUANTUM HALL EFFECT

1995 ◽  
Vol 09 (25) ◽  
pp. 3333-3344 ◽  
Author(s):  
R. FERRARI
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Wannier Functions ◽  
Hartree Fock ◽  
Fock State

We introduce and study the Wannier functions for an electron moving in a plane under the influence of a perpendicular uniform and constant magnetic field. The relevance for the Fractional Quantum Hall Effect is discussed; in particular, it shown that an interesting Hartree–Fock state can be constructed in terms of Wannier functions.

FRACTIONAL QUANTUM HALL EFFECT: CONSTRUCTION OF THE HARTREE–FOCK STATE BY USING TRANSLATIONAL COVARIANCE

1994 ◽  
Vol 08 (05) ◽  
pp. 529-579 ◽  
Author(s):  
R. FERRARI
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Landau Level ◽  
Quantum Hall Effect ◽  
Filling Factor ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Hartree Fock

The formalism introduced in a previous paper is used for discussing the Coulomb interaction of many electrons moving in two space-dimensions in the presence of a strong magnetic field. The matrix element of the Coulomb interaction is evaluated in the new basis, whose states are invariant under discrete translations (up to a gauge transformation). This paper is devoted to the case of low filling factor, thus we limit ourselves to the lowest Landau level and to spins all oriented along the magnetic field. For the case of filling factor νf = 1/u we give an Ansatz on the state of many electrons which provides a good approximated solution of the Hartree–Fock equation. For general filling factor νf = u′/u a trial state is given which converges very rapidly to a solution of the self-consistent equation. We generalize the Hartree–Fock equation by considering some correlation: all quantum states are allowed for the u′ electrons with the same translation quantum numbers. Numerical results are given for the mean energy and the energy bands, for some values of the filling factor (νf = 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5). Our results agree numerically with the Charge Density Wave approach. The boundary conditions are shown to be very important: only large systems (degeneracy of Landau level over 200) are not affected by the boundaries. Therefore results obtained on small scale systems are somewhat unreliable. The relevance of the results for the Fractional Quantum Hall Effect is briefly discussed.

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