scholarly journals Current Percolation in Medium with Boundaries under Quantum Hall Effect Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
M. U. Malakeeva ◽  
V. E. Arkhincheev
Keyword(s):  
Finite Number ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Hall Current ◽  
Quantum Hall ◽  
Singular Points ◽  
Hall Conductivity

The current percolation has been considered in the medium with boundaries under quantum Hall effect conditions. It has been shown that in that case the effective Hall conductivity has a nonzero value due to percolation of the Hall current through the finite number of singular points (in our model these are corners at the phase joints).

Chiral bosonic field theories and the quantum Hall effect

2001 ◽  
Vol 79 (9) ◽  
pp. 1121-1131 ◽  
Author(s):  
P Bracken
Keyword(s):  
Hall Effect ◽  
Gauge Transformation ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Equation Of Motion ◽  
Hall Conductivity ◽  
Field Theories ◽  
Bosonic Field ◽  
Chern Simons

The gauge-transformation properties of the actions of certain scalar and Chern–Simons theories are investigated, including contributions from the boundary. By imposing chirality constraints on the fields, these types of theories can be used to describe the quantum Hall effect. It is shown that the corresponding equation of motion for the associated current for the theory generates an anomaly, which can be related directly to the Hall conductivity. PACS Nos.: 73.43, 03.70, 11.10, 11.30R

WILSON LOOPS AND NON-ABELIAN STATISTICS IN THE QUANTUM HALL EFFECT

1992 ◽  
Vol 06 (17) ◽  
pp. 2875-2891
Author(s):  
MICHAEL STONE
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Conductivity Tensor ◽  
Hall Conductivity ◽  
Wilson Loops ◽  
Many Body ◽  
Quantum Numbers ◽  
The Many ◽  
Chern Simons

There is a topological connection between the boundary excitations of a quantum Hall fluid and the quantum numbers of its vortex-like bulk quasi-particles. I use this connection to examine the group properties of vortex excitations in a generalized quantum Hall fluid, and show how the vortex trajectories become Wilson lines interacting via Chern-Simons fields. As a result, I argue that non-abelian statistics, if they exist, should be independent of the detailed properties of the many-body wavefunction and will depend only on the bulk Hall conductivity tensor.

scholarly journals Floquet Energies and Quantum Hall Effect in a Periodic Potential

1998 ◽  
Vol 12 (11) ◽  
pp. 1105-1123 ◽  
Author(s):  
Ruggero Ferrari
Keyword(s):  
Schrödinger Equation ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Schrodinger Equation ◽  
Periodic Potential ◽  
Quantum Hall ◽  
Hall Conductivity ◽  
Moving Frame ◽  
Periodicity Cell ◽  
Integer Multiple

The Quantum Hall Effect for free electrons in external periodic potential is discussed without using the linear response approximation. We find that the Hall conductivity is related in a simple way to Floquet energies (associated to the Schrödinger equation in the co-moving frame). By this relation one can analyze the dependence of the Hall conductivity from the electric field. Subbands can be introduced by the time average of the expectation value of the Hamiltonian on the Floquet states. Moreover we prove previous results in form of sum rules as, for instance: the topological character of the Hall conductivity (being an integer multiple of e2/h), the Diofantine equation which constrains the Hall conductivity by the rational number which measure the flux of the magnetic field through the periodicity cell. The Schrödinger equation fixes in a natural way the phase of the wave function over the reduced Brillouin zone: thus the topological invariant providing the Hall conductivity can be evaluated numerically without ambiguity.

Hall Conductivity at Microwave and Submillimeter Frequencies in the Quantum Hall Effect Regime

1987 ◽  
Vol T19A ◽  
pp. 79-86 ◽  
Author(s):  
F Kuchar ◽  
R Meisels ◽  
K Y Lim ◽  
P Pichler ◽  
G Weimann ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Hall Conductivity

CONSTRAINTS ON NONCOMMUTATIVE HALL EFFECT REVISITED

2008 ◽  
Vol 23 (26) ◽  
pp. 4361-4370 ◽  
Author(s):  
CRESUS F. L. GODINHO
Keyword(s):  
Gauge Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Hall Conductivity ◽  
Second Step ◽  
Direct Relation ◽  
General Constraints ◽  
Chern Simons

We consider a semiclassical formulation of the quantum Hall effect by means of an Chern–Simons gauge theory constructed for a Schrödinger field. We build up constraints managing the Faddeev–Jackiw algorithm and show a direct relation of the constraints with Hall conductivity. In the second step, we consider the noncommutative extension to the action computing the new and more general constraints and, as a right consequence, an interesting correction for the conductivity expression is found. Finally, we speculate possible interpretations of this new result and its consequences.

scholarly journals Quantum Hall Conductivity in the Presence of Interactions

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 200
Author(s):  
Xi Wu ◽  
Mikhail Zubkov
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Interaction Strength ◽  
Fractional Quantum Hall Effect ◽  
Landau Levels ◽  
Hall Conductivity ◽  
Filling Fraction ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that, irrespective of the interaction strength, the Hall conductivity is given by the filling fraction of Landau levels averaged over the ground state of the system. This conclusion remains valid for both the integer and fractional quantum Hall effect.

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