scholarly journals Counterflowing edge current and its equilibration in quantum Hall devices with sharp edge potential: Roles of incompressible strips and contact configuration

2019 ◽  
Vol 99 (12) ◽  
Author(s):  
T. Akiho ◽  
H. Irie ◽  
K. Onomitsu ◽  
K. Muraki
Keyword(s):  
Quantum Hall ◽  
Sharp Edge ◽  
Contact Configuration ◽  
Edge Current

EDGE CURRENT CHANNELS AND CHERN NUMBERS IN THE INTEGER QUANTUM HALL EFFECT

2002 ◽  
Vol 14 (01) ◽  
pp. 87-119 ◽  
Author(s):  
J. KELLENDONK ◽  
T. RICHTER ◽  
H. SCHULZ-BALDES
Keyword(s):  
Exact Sequence ◽  
Half Plane ◽  
Quantum Hall Effect ◽  
Duality Theorem ◽  
Quantum Hall ◽  
Edge Channel ◽  
Integer Quantum Hall Effect ◽  
Edge Current ◽  
Chern Numbers ◽  
Integer Quantum

A quantization theorem for the edge currents is proven for discrete magnetic half-plane operators. Hence the edge channel number is a valid concept also in presence of a disordered potential. Under a gap condition on the corresponding planar model, this quantum number is shown to be equal to the quantized Hall conductivity as given by the Kubo–Chern formula. For the proof of this equality, we consider an exact sequence of C*-algebras (the Toeplitz extension) linking the half-plane and the planar problem, and use a duality theorem for the pairings of K-groups with cyclic cohomology.

Breakdown of the quantum Hall effect as a function of the filling factor and the contact configuration

1992 ◽  
Vol 4 (15) ◽  
pp. 4003-4015 ◽  
Author(s):  
G Nachtwei ◽  
C Breitlow ◽  
A Jaeger ◽  
J Breitlow-Hertzfeldt
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Filling Factor ◽  
Quantum Hall ◽  
Contact Configuration

Edge States of Quantum Hall Fluid and Berry Phase

1997 ◽  
Vol 11 (22) ◽  
pp. 2707-2726 ◽  
Author(s):  
B. Basu ◽  
P. Bandyopadhyay
Keyword(s):  
Berry Phase ◽  
Quantum Hall ◽  
Edge States ◽  
Anomaly Cancellation ◽  
Edge Current

The edge states of Abelian and non-Abelian Hall Fluids have been studied in a unified way from topological aspects. It is shown that the edge current is related to the fact that the effective Berry phase of quasiparticles at the edge should be vanishing which leads to the anomaly cancellation.

Edge Penetration Effects in the Low-Loss Electron Image in the SEM

1988 ◽  
Vol 46 ◽  
pp. 202-203
Author(s):  
Oliver C. Wells
Keyword(s):  
Electron Microscope ◽  
Scanning Electron Microscope ◽  
Beam Energy ◽  
Secondary Electron ◽  
Sharp Edge ◽  
Beam Diameter ◽  
Low Loss ◽  
Additional Information ◽  
Electron Image ◽  
Scanning Electron

The low-loss electron (LLE) image in the scanning electron microscope (SEM) is useful for the study of uncoated photoresist and some other poorly conducting specimens because it is less sensitive to specimen charging than is the secondary electron (SE) image. A second advantage can arise from a significant reduction in the width of the “penetration fringe” close to a sharp edge. Although both of these problems can also be solved by operating with a beam energy of about 1 keV, the LLE image has the advantage that it permits the use of a higher beam energy and therefore (for a given SEM) a smaller beam diameter. It is an additional attraction of the LLE image that it can be obtained simultaneously with the SE image, and this gives additional information in many cases. This paper shows the reduction in penetration effects given by the use of the LLE image.

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