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Semi-classical study of the origin of quantized Hall conductance in periodic potentials. (English) Zbl 0978.81086

Summary: 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 tunneling 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 \(B\).

MSC:

81V70 Many-body theory; quantum Hall effect
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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