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Suppression of chaotic dynamics and localization of two-dimensional electrons by a weak magnetic field
- Source :
- Physical Review B. 56:6823-6838
- Publication Year :
- 1997
- Publisher :
- American Physical Society (APS), 1997.
-
Abstract
- We study a two-dimensional motion of a charged particle in a weak random potential and a perpendicular magnetic field. The correlation length of the potential is assumed to be much larger than the de Broglie wavelength. Under such conditions, the motion on not too large length scales is described by classical equations of motion. We show that the phase-space averaged diffusion coefficient is given by Drude-Lorentz formula only at magnetic fields $B$ smaller than certain value $B_c$. At larger fields, the chaotic motion is suppressed and the diffusion coefficient becomes exponentially small. In addition, we calculate the quantum-mechanical localization length as a function of $B$ in the minima of $��_{xx}$. At $B < B_c$ it is exponentially large but decreases with increasing $B$. At $B > B_c$, the localization length drops precipitously, and ceases to be exponentially large at a field $B_\ast$, which is only slightly above $B_c$. Implications for the crossover from the Shubnikov-de Haas oscillations to the quantum Hall effect are discussed.<br />20 pages, 5 figures
- Subjects :
- Physics
Condensed Matter - Mesoscale and Nanoscale Physics
Field (physics)
Condensed matter physics
FOS: Physical sciences
Equations of motion
02 engineering and technology
Electron
Quantum Hall effect
Nonlinear Sciences - Chaotic Dynamics
021001 nanoscience & nanotechnology
01 natural sciences
Charged particle
Magnetic field
Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
0103 physical sciences
Matter wave
Chaotic Dynamics (nlin.CD)
Diffusion (business)
010306 general physics
0210 nano-technology
Subjects
Details
- ISSN :
- 10953795 and 01631829
- Volume :
- 56
- Database :
- OpenAIRE
- Journal :
- Physical Review B
- Accession number :
- edsair.doi.dedup.....74793e184806ed3f8023768cd61d7024