Result: On the Extended Nature of Edge States of Quantum Hall Hamiltonians: On the extended nature of edge states of quantum Hall Hamiltonians
Title:
On the Extended Nature of Edge States of Quantum Hall Hamiltonians: On the extended nature of edge states of quantum Hall Hamiltonians
Authors:
Source:
Annales Henri Poincaré. 1:405-442
Publication Status:
Preprint
Publisher Information:
Springer Science and Business Media LLC, 2000.
Publication Year:
2000
Subject Terms:
two-dimensional electron gas, Condensed Matter - Mesoscale and Nanoscale Physics, FOS: Physical sciences, Mathematical Physics (math-ph), 01 natural sciences, absolute continuity of the energy spectrum, Mourre theory of positive commutators, General mathematical topics and methods in quantum theory, Many-body theory, quantum Hall effect, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), 0103 physical sciences, Landau levels, Mathematical Physics, Selfadjoint operator theory in quantum theory, including spectral analysis
Document Type:
Academic journal
Article<br />Other literature type
File Description:
application/xml
Language:
English
ISSN:
1424-0637
DOI:
10.1007/s000230050001
DOI:
10.48550/arxiv.math-ph/9903014
Access URL:
http://arxiv.org/abs/math-ph/9903014
https://zbmath.org/1540542
https://doi.org/10.1007/s000230050001
https://arxiv.org/abs/math-ph/9903014
https://link.springer.com/article/10.1007/s000230050001
https://ui.adsabs.harvard.edu/abs/2000AnHP....1..405F/abstract
https://link.springer.com/content/pdf/10.1007/s000230050001.pdf
https://zbmath.org/1540542
https://doi.org/10.1007/s000230050001
https://arxiv.org/abs/math-ph/9903014
https://link.springer.com/article/10.1007/s000230050001
https://ui.adsabs.harvard.edu/abs/2000AnHP....1..405F/abstract
https://link.springer.com/content/pdf/10.1007/s000230050001.pdf
Rights:
Springer TDM
arXiv Non-Exclusive Distribution
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....0f06a4d5f1e4dadb9d3f3a15e6cd9ba7
Database:
OpenAIRE
Further Information
Properties of eigenstates of one-particle Quantum Hall Hamiltonians localized near the boundary of a two-dimensional electron gas - so-called edge states - are studied. For finite samples it is shown that edge states with energy in an appropriate range between Landau levels remain extended along the boundary in the presence of a small amount of disorder, in the sense that they carry a non-zero chiral edge current. For a two-dimensional electron gas confined to a half-plane, the Mourre theory of positive commutators is applied to prove absolute continuity of the energy spectrum well in between Landau levels, corresponding to edge states.
45 pages, 7 figures, reference added