Semi-classical study of the origin of quantized Hall conductance in periodic potentials

The semi-classical study of the integer quantum Hall conductivity is invest igated for electrons in a biperiodic potential V(x,y). The Hall conductivit y is due to the tunnelling effect and we concentrate our study on potential s having three wells in a periodic cell. We show that a nonzero topological conductivity requires special conditions for the positions and shapes of t he wells. The results are derived by changing the potential, using the topo logical nature of Chern indices. Our numerical calculations show that these semi-classical results are still valid for small value of B. (C) 2000 Amer ican Institute of Physics. [S0022-2488(00)00101-8].