We have studied the electron transport in a one-dimensional electron interferometer. It consists of a quantum dot, defined in a two-dimensional electron gas, to which quantum point contacts are attached. Discrete electronic states are formed due to the constructive interference of electron waves which travel along the circumference of the dot in one-dimensional magnetic edge channels. An artificial one-dimensional crystal has been fabricated, which consists of a sequence of 15 quantum dots, coupled by point contacts. The conductance of this device reveals the formation of a band structure, including the gaps between adjacent bands and the discrete electronic states from which the bands are constructed.
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