Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
1997-02-12
Phys. Rev. B 56, 6823 (1997).
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
20 pages, 5 figures
Scientific paper
10.1103/PhysRevB.56.6823
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 $\sigma_{xx}$. 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.
Dobin Alexander Yu.
Fogler Michael M.
Perel' V. I.
Shklovskii Boris I.
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