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Edge states, transmission matrices, and the Hall resistance
Abstract
We consider the Landauer formula, relating conductances to transmission matrices, for a two-dimensional system in a magnetic field. We argue that the magnetoresistance, R, and the Hall resistance, ${\mathrm{R}}_{\mathrm{H}}$, satisfy the sum rule (R+${\mathit{R}}_{\mathrm{H}}$${)}^{\mathrm{\ensuremath{-}}1}$=(${\mathit{e}}^{2}$/h)Tr(${\mathit{t}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$t) where t is the transmission matrix. For zero field our expressions reduce to the usual multichannel Landauer formulas. In the absence of dissipation, R approaches zero, t approaches a unit matrix, and quantized values are obtained for the Hall resistance.
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Cites
Halperin, B. I. (1982) · Physical Review B · doi:10.1103/physrevb.25.2185 · Cited by 2,547
Cited by
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Büttiker, M. (1988) · Physical Review B · doi:10.1103/physrevb.38.9375 · Cited by 1,555
Spatial variation of currents and fields due to localized scatterers in metallic conduction
Landauer, R. (1988) · IBM Journal of Research and Development · doi:10.1147/rd.323.0306 · Cited by 1,042
What is measured when you measure a resistance?—The Landauer formula revisited
Stone, A. D., & Szafer, A. (1988) · IBM Journal of Research and Development · doi:10.1147/rd.323.0384 · Cited by 454
Wave-packet approach to noise in multichannel mesoscopic systems
Martin, T., & Landauer, R. (1992) · Physical Review B · doi:10.1103/physrevb.45.1742 · Cited by 416
Introduction to Mesoscopic Electron Transport
Kouwenhoven, L. P., Schön, G., & Sohn, L. L. (1997) · Mesoscopic Electron Transport · doi:10.1007/978-94-015-8839-3_1 · Cited by 399
Metadata
- Authors
- Streda, P., Kucera, J., & MacDonald, A. H.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1987-10-26
- Volume
- 59
- Issue
- 17
- Pages
- 1973-1975
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2072296880
- Cited by
- 248
- References
- 1
- FWCI
- 17.75
- Type
- journal article
- Language
- en
- Open access
- closed
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