Quantum oscillations of electrical conductivity of two-dimensional ballistic contacts

Am exactly solvable model of a two-dimensional ballistic contact with sharp edges is considered along with its generalization to other models of two- and three-dimensional contacts. This model is used for calculating the effect of the contact shape, temperature and magnetic field on the quantization of conductance as a function of the contact diameter. The conditions of existence of conduction quantization are specified. It is shown that the structure of conductance steps qualitatively depends on the contact topology: G = (2e2/h)n for a contact with zero boundary conditions with respect to transverse coordinate, and G = (2e2/h)(2 n + 1), n = 0, 1, 2, ..., in the case of cyclic boundary conditions. It is concluded that there is no universal quantization of conductance in three-dimensional point contacts.

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