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The quantum Hall effect (or integer quantum Hall effect) is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductance σ undergoes quantum Hall transitions to take on the quantized values σ = I channel V Hall = ν e 2 h , where I channel is the channel current, V Hall is the Hall voltage , e is the elementary charge and h is Planck's constant. The prefactor: ν is known as the " filling factor " , and can take on either integer (ν = 1, 2, 3, ...) or fractional (ν = 1/3, 2/5, 3/7, 2/3, 3/5, 1/5, 2/9, 3/13, 5/2, 12/5, ...) values. The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction, respectively. The striking feature of the integer quantum Hall effect is the persistence of the quantization (i.e. the Hall plateau) as the electron density is varied. Since the electron density remains constant when the Fermi level is in a clean spectral gap, this situation corresponds to one where the Fermi level is an energy with a finite density of states, though these states are localized (see Anderson localiza-tion). The fractional quantum Hall effect is more complicated, as its existence relies fundamentally on electron–electron interactions. Although the microscopic origins of the fractional quantum Hall effect are unknown, there are several phenomenological approaches that provide accurate approximations. For example, the effect can be thought of as an integer quantum Hall effect, not of electrons but of charge-flux composites known as composite fermions. In 1988, it was proposed that there was quantum Hall effect without Landau levels. [1] This quantum Hall effect is referred to as the quantum anomalous Hall (QAH) effect. There is also a new concept of the quantum spin Hall effect which is an analogue of the quantum Hall effect, where spin currents flow instead of charge currents. [2]
The Quantum Mechanical Hall Effect
Springer Series in Solid-State Sciences, 1987
The quantum dynamics of a two-dimensiona l electron gas at very low temperatures in applied electric and magnetic fields is investigated using a tightbinding model. The ratio of the current to the Hall potential is calculated and it i s found that the Hall conduc t ance is not proportiona l to the particle density. Thi a contradicta results ob t ained uaing the Kubo theory for the same model.
Quantum Anomalous Hall Effect Induce
A new device has been fabricated that can demonstrate the quantum anomalous Hall effect, in which tiny, discrete voltage steps are generated by an external magnetic field. This work may enable extremely low-power electronics, as well as future quantum computers. [28] Nontrivial band topology can combine with magnetic order in a magnetic topological insulator to produce exotic states of matter such as quantum anomalous Hall (QAH) insulators and axion insulators. [27] A FLEET study of ultracold atomic gases-a billionth the temperature of outer spacehas unlocked new, fundamental quantum effects. [26]
Physical principles underlying the quantum Hall effect
Comptes Rendus Physique, 2011
In this contribution, we present an introduction to the physical principles underlying the quantum Hall effect. The field theoretic approach to the integral and fractional effect is sketched, with some emphasis on the mechanism of electromagnetic gauge anomaly cancellation by chiral degrees of freedom living on the edge of the sample. Applications of this formalism to the design and theoretical interpretation of interference experiments are outlined.
Anomalous Hall Effect Observation
"Our results could lead to the exploration of topological Berry phases and dissipationless quantum transport in crystals of abundant elements and with a compensated antiparallel magnetic order," Feng and his colleagues wrote. [44] A large, unconventional anomalous Hall resistance in a new magnetic semiconductor in the absence of large-scale magnetic ordering has been demonstrated by Tokyo Tech materials scientists, validating a recent theoretical prediction. [43]
The Quantum Hall Effect in Graphene
Modern Physics Letters B, 2012
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.
The quantum Hall effect in graphene samples and the relativistic Dirac effective action
Journal of Physics A: Mathematical and Theoretical, 2007
We study the Euclidean effective action per unit area and the charge density for a Dirac field in a two-dimensional spatial region, in the presence of a uniform magnetic field perpendicular to the 2D-plane, at finite temperature and density. In the limit of zero temperature we reproduce, after performing an adequate Lorentz boost, the Hall conductivity measured for different kinds of graphene samples, depending upon the phase choice in the fermionic determinant.
Theory of the quantum Hall effect in graphene
We study the quantum Hall effect (QHE) in graphene based on the current injection model. In our model, the presence of disorder, the edge-state picture, extended states and localized states, which are believed to be indispensable ingredients in describing the QHE, do not play an important role. Instead the boundary conditions during the injection into the graphene sheet, which are enforced by the presence of the Ohmic contacts, determine the current-voltage characteristics.
Theory of anomalous quantum Hall effects in graphene
Physical Review B, 2008
Recent successes in manufacturing of atomically thin graphite samples [1] (graphene) have stimulated intense experimental and theoretical activity . The key feature of graphene is the massless Dirac type of low-energy electron excitations. This gives rise to a number of unusual physical properties of this system distinguishing it from conventional two-dimensional metals. One of the most remarkable properties of graphene is the anomalous quantum Hall effect . It is extremely sensitive to the structure of the system; in particular, it clearly distinguishes single-and double-layer samples. In spite of the impressive experimental progress, the theory of quantum Hall effect in graphene has not been established. This theory is a subject of the present paper. We demonstrate that the Landau level structure by itself is not sufficient to determine the form of the quantum Hall effect. The Hall quantization is due to Anderson localization which, in graphene, is very peculiar and depends strongly on the character of disorder . It is only a special symmetry of disorder that may give rise to anomalous quantum Hall effects in graphene. We analyze the symmetries of disordered singleand double-layer graphene in magnetic field and identify the conditions for anomalous Hall quantization.