Semi-classical study of the Quantum Hall conductivity
Frederic Faure, Bernard Parisse
Abstract
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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