Quantum Hall Conductivity and the Electronic States in Cylinder Geometry with Finite Width

概要

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The two-dimensional electronic states and the quantum Hall conductivity on thecylinder surface with finite width are analyzed numerically. A parameter 0 characteriz-ing the generalized boundary condition in the ,v-direction is introduced. For each 0the sum of the ,v-component of the center of mass x,.(0) over the states v involved inthe lowest Landau subband is shown to satisfy a sum rule and to be stable against randomness. Through different interpretations of 0, the numerical data for x.,(0) can beused to discuss the Hall conductivity in two different cases. One is an infinitely longstrip system with finite periodicity L, in the ,v-direction; 0 is the generalized Blochmomentum in this case. The other is a real cylinder with the Aharonov-Bohm fluxpenetrating the cylinder along the axis, where 0 represents the flux. In the latter casewe can discuss the fluctuation of the Hall conductivity with respect to the flux.
社団法人日本物理学会の論文
1989-03-15