Quantum interference on graphs controlled by an external electric field

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Abstract
The authors consider the motion of a charged quantum particle on a loop with two external leads which is placed into an electrostatic field. The loop Hamiltonian is chosen in the simplest possible way; in order to join it to the free Hamiltonians describing the leads, they employ a method based on self-adjoint extensions. Under a symmetry requirement, the resulting full Hamiltonian contains four free parameters; each junction is characterised by a pair of them. The system under consideration represents a model of metallic or semiconductor structure that can be fabricated by presently available technologies. Assuming the ballistic regime for electrons in such a structure, the authors calculate the resistance dependence on intensity of the external field. The results suggest the possibility of constructing quantum interference transistors whose size and switching voltage would be much smaller than in current microchips.