Semi-classical study of the Quantum Hall conductivity

Details Semi-classical study of the Quantum Hall conductivity Semi-classical study of the Quantum Hall conductivity

1998-05-07

arxiv.org/abs/cond-mat/9805086v1

Journal of Mathematical Physics, vol 41, p62-75 (2000)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

23 pages, 13 figures

Scientific paper

10.1063/1.533122

The semi-classical study of the integer Quantum Hall conductivity is investigated for electrons in a bi-periodic potential $V(x,y)$. The Hall conductivity is due to the tunnelling effect and we concentrate our study to potentials having three wells in a periodic cell. A non-zero topological conductivity requires special conditions for the positions, and shapes of the wells. The results are derived analytically and well confirmed by numerical calculations.

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