Edge-state-transmission duality relation and its implication for measurements

摘要

The duality in the Chalker-Coddington network model is examined. We are able to write down a duality relation for the edge-state-transmission coefficient, but only for a specific symmetric Hall geometry. Looking for broader implication of the duality, we calculate the transmission coefficient T in terms of the conductivity sigma(xx) and sigma(xy) in the diffusive limit. The edge-state scattering problem is reduced to solving the diffusion equation with two boundary conditions [partial derivative(y)-(sigma(xy)/sigma(xx))]partial derivative(x) phi=0 and {partial derivative(x)+[(sigma(xy)-sigma(xy)(lead))/sigma(xx)]partial derivative(y)}phi=0. We find that the resistances in the geometry considered are not necessarily measures of the resistivity and rho(xx), =(W/L)(R/T)hle(2)(R=1-T) holds only when p(xy) is quantized. We conclude that duality alone is not sufficient to explain the experimental findings of Shahar et al. and that Landauer-Buttiker argument does not render the additional condition, contrary to previous expectation. [S0163-1829(98)06015-9]. [References: 39]