Magnetotransport in a Two-Dimensional Electron Gas Subject to a Weak Superlattice Potential
We present experimental and theoretical results on commensurability oscillations of the magnetoresistivity in high-mobility two-dimensional electron systems subject to a weak superlattice potential. Experimentally, the band conductivity of a sample with a hologra-phically produced square-grid potential is shown to be considerably smaller than that of the same sample with a similar linear grating potential of the same lattice constant. This is explained by a magnetotransport theory with due consideration of collision broadening effects and the peculiar subband splitting of Landau levels resulting in a Hofstadter-type energy spectrum.
KeywordsBand Conductivity Landau Level Flat Band Perpendicular Magnetic Field Grid Modulation
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- R.R Gerhardts, in Science and Engineering of One-and Zero-Dimensional Semiconductors, ed. by S.P. Beaumont and C.M. Sotomajor Torres (Plenum Press, New York, 1990), p. 231.Google Scholar
- M.Y. Azbel’, Sov. Phys. JETP 19, 634 (1964).Google Scholar
- M. Ya. Azbel’, [Zh. Eksp. Teor. Fiz. 46, 929 (1964)].Google Scholar
- For a recent review see: D.J. Thouless, in The Quantum Hall Effect, edited by R.E. Prange and S.M. Girvin (Springer-Verlag, New York, 1987).Google Scholar
- N.A. Usov Sov. Phys. JETP 67 2565 1988Google Scholar
- N.A. Usov, [Zh. Eksp. Teor. Fiz. 94, 305 (1988)].Google Scholar
- The sample is considered as a part of an infinitely extended system. The plane waves are normalized on a length L y, the øn on the total x-axis. To count states correctly, x 0 is considered within a length L x taken as a suitable (B-dependent) multiple of the period a. Finally, the limit L x, L y → ∞ is taken.Google Scholar
- For computational convenience, the plots are calculated using the approximation A n α(E) = (2πГ2)−½ exp[−(E − E n aα)2/2Г2]Google Scholar
- If one replaces, in the spirit of Eq.(ll), the factor […]2 in Eq.(14) by 2l 2Г0 D n(E), one gets the n-independent scattering rate Гn = 2Г0, and σsc xx reduces to Eq.(9) of Ref.21, where Г0 is written as (N 1U2 0/2πl 2)/Г One thus misses the leading order contribution to the oscillations of ρyy, retaining higher order contributions with small amplitudes of the order.Google Scholar
- P. Streda and A.H MacDonald, Phys. Rev. B 41, 11 892 (1990).Google Scholar