Abstract
The semi-classical study of the integer quantum Hall conductivity is investigated for electrons in a biperiodic potential V(x,y). The Hall conductivity is due to the tunnelling effect and we concentrate our study on potentials having three wells in a periodic cell. We show that a nonzero topological conductivity requires special conditions for the positions and shapes of the wells. The results are derived by changing the potential, using the topological nature of Chern indices. Our numerical calculations show that these semi-classical results are still valid for small value of B.
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