THE CHIRAL BOSON THEORY AND EDGE STATES IN THE QUANTUM HALL EFFECT

1993 ◽  
Vol 08 (14) ◽  
pp. 1297-1303 ◽  
Author(s):  
YUN SOO MYUNG
Keyword(s):  
Hall Effect ◽  
Landau Level ◽  
Quantum Hall Effect ◽  
Condensed Matter ◽  
Quantum Hall ◽  
Electron System ◽  
Wave Functions ◽  
Edge States ◽  
Lowest Landau Level ◽  
Boson Theory

We construct the wave functions for the edge states of a droplet of quantum Hall effect by performing the Gupta-Bleuler quantization of a chiral boson. These wave functions describe the chiral edge states of a many-electron system in the lowest Landau level. This demonstrates a crucial connection between the particle and condensed matter physics.

Magnetocapacitance Investigation of Quantum Hall Effect and Edge States

1997 ◽  
Vol 11 (22) ◽  
pp. 2593-2619 ◽  
Author(s):  
Sadao Takaoka ◽  
Kenichi Oto ◽  
Kazuo Murase
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Electron System ◽  
Edge Length ◽  
Capacitance Measurement ◽  
Edge States ◽  
Bulk Conductivity ◽  
Cyclotron Radius ◽  
Bulk State

The quantum Hall effect for the GaAs/AlGaAs heterostrcture is investigated by an ac capacitance measurement between the two-dimensional electron system (2DES) and the gate on GaAs/AlGaAs. The capacitance minima at the quantum Hall plateaus are mainly determined not by the 2DES area under the gate but by the edge length of 2DES. There exists the high conductive region due to the edge states along the 2DES boundary, when the bulk conductivity σxx is small enough at low temperatures and high magnetic fields. From the temperature and frequency dependence of the capacitance minima, it is found that the measured capacitance consists of the contribution from the edge states and that of the bulk state, which is treated as a distributed circuit of a resistive plate with the conductivity σxx. The evaluated width of edge states from the capacitance is much larger than the magnetic length and the cyclotron radius expected from the one-electron picture. This wide width of edge states can be explained by the compressible-incompressible strip model, in which the screening effect is taken into account. Further the bulk conductivity of less than 10-12 S (S=1/Ω) is measured by the capacitance of the Corbino geometry sample, where the edge states are absent and the capacitance is determined by only σxx in this geometry. The localization of the bulk state is investigated by the obtained σxx.

VERTEX OPERATORS IN THE QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (03) ◽  
pp. 509-527 ◽  
Author(s):  
MICHAEL STONE
Keyword(s):  
Hall Effect ◽  
Landau Level ◽  
Quantum Hall Effect ◽  
Group Action ◽  
Quantum Hall ◽  
Vertex Operators ◽  
Edge States ◽  
Many Body ◽  
Level I ◽  
The Many

The edge states of the quantum Hall effect carry representations of chiral current algebras and their associated groups. In the simplest case of a single filled Landau level, I demonstrate explicitly how the group action affects the many-body states, and why the Kac-Peterson cocycle appears in the group multiplication law. I show how these representations may be used to construct vertex operators which create localised edge excitations, and indicate how they are related to the bulk quasi-particles.

scholarly journals Tunable dispersion of the edge states in the integer quantum Hall effect

2017 ◽  
Vol 3 (4) ◽  
Author(s):  
Maik Malki ◽  
Götz Uhrig
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Condensed Matter ◽  
Quantum Hall ◽  
External Control ◽  
Fermi Velocity ◽  
Control Parameters ◽  
Edge States ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum

Topological aspects represent currently a boosting area in condensed matter physics. Yet there are very few suggestions for technical applications of topological phenomena. Still, the most important is the calibration of resistance standards by means of the integer quantum Hall effect. We propose modifications of samples displaying the integer quantum Hall effect which render the tunability of the Fermi velocity possible by external control parameters such as gate voltages. In this way, so far unexplored possibilities arise to realize devices such as tunable delay lines and interferometers.

scholarly journals Unconventional Hall response in the quantum limit of HfTe5

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
S. Galeski ◽  
X. Zhao ◽  
R. Wawrzyńczak ◽  
T. Meng ◽  
T. Förster ◽  
...  
Keyword(s):  
Hall Effect ◽  
Landau Level ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Three Dimensional ◽  
Quantum Limit ◽  
Strong Electron ◽  
Electron Band ◽  
Lowest Landau Level ◽  
Interacting Electrons

AbstractInteracting electrons confined to their lowest Landau level in a high magnetic field can form a variety of correlated states, some of which manifest themselves in a Hall effect. Although such states have been predicted to occur in three-dimensional semimetals, a corresponding Hall response has not yet been experimentally observed. Here, we report the observation of an unconventional Hall response in the quantum limit of the bulk semimetal HfTe5, adjacent to the three-dimensional quantum Hall effect of a single electron band at low magnetic fields. The additional plateau-like feature in the Hall conductivity of the lowest Landau level is accompanied by a Shubnikov-de Haas minimum in the longitudinal electrical resistivity and its magnitude relates as 3/5 to the height of the last plateau of the three-dimensional quantum Hall effect. Our findings are consistent with strong electron-electron interactions, stabilizing an unconventional variant of the Hall effect in a three-dimensional material in the quantum limit.

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