scholarly journals THE QUANTUM HALL EFFECT IN GRAPHENE

2012 ◽  
Vol 26 (13) ◽  
pp. 1250084 ◽  
Author(s):  
PAOLO CEA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Magnetic Fields ◽  
Numerical Simulations ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Landau Levels ◽  
Dynamical Generation ◽  
Dirac Sea

We investigate the quantum Hall effect in graphene. We argue that in graphene in presence of an external magnetic field there is dynamical generation of mass by a rearrangement of the Dirac sea. We show that the mechanism breaks the lattice valley degeneracy only for the n = 0 Landau levels and leads to the new observed ν = ±1 quantum Hall plateaus. We suggest that our result can be tested by means of numerical simulations of planar Quantum Electro Dynamics with dynamical fermions in an external magnetic fields on the lattice.

DYNAMICAL GAPS AND QUANTUM HALL EFFECT IN GRAPHENE

2009 ◽  
Vol 23 (07) ◽  
pp. 891-902
Author(s):  
E. V. GORBAR ◽  
V. P. GUSYNIN ◽  
V. A. MIRANSKY
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Ground State ◽  
Quantum Hall ◽  
Low Energy ◽  
Strong Magnetic Fields ◽  
Gap Equation ◽  
Magnetic Catalysis

We analyze the gap equation for Dirac quasiparticles in graphene in a magnetic field using a low-energy effective model with a contact interaction. It is found that the order parameters connected with the quantum Hall (QH) ferromagnetism and the magnetic catalysis scenarios necessarily coexist. The ground-state solutions of the gap equation describe all the recently discovered novel QH plateaus in graphene in strong magnetic fields.

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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