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Numerical confirmation of universality of transmission micro-symmetry relations in a four-probe quantum dot

We study the crossover behavior of the Hall resistance between the integer quantum Hall regime and a regime dominated by the Aharonov-Bohm oscillations, in a system of 4-probe quantum dot with an artificial impurity confined inside. In a previous study [M. Lei, N.J. Zhu and Hong Guo, Phys. Rev. B. 52, 16784, (1995)], a peculiar set of symmetry relations between various scattering probabilities were found in this crossover regime. In this paper we examine the universality of this set of symmetry relations using different shapes of the quantum dot and positions of the artificial impurity. The symmetry holds for these changes and we conclude that in this transport regime the general behavior of the Hall resistance is determined by the competition of the quantum Hall and Aharonov-Bohm effects, rather than by the detailed shapes of the structure.