Topological Invariant and the Quantization of the Hall Conductance
نویسنده
چکیده
The topological aspects of wavefunctions for electrons in a two dimensional periodic potential with a magnetic field are discussed. Special attention is paid to the linear response formula for the Hall conductance cxY. It is shown that the quantized value of gxY is related to the number of zeros of wavefunctions in the magnetic Brillouin zone. A phase of wavefunctions cannot be determined in a unique and smooth way over the entire magnetic Brillouin zone unless the magnetic subband carries no Hall current. ,c: 1985 Academic Press. Inc.
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