We investigated the low temperature transport properties of AlGaAs/GaAsquantum dot arrays. The coupling between dots and the electron density are controlled by a single gate covering the array. Below 1 K, the current - voltage (I - V) curves show multiple discontinuous jumps in the current, or `switching events', between different insulating and conducting states, which occur at gate-voltage and temperature dependent thresholds. Each single switching event is accompanied by hysteresis, and multiple switching events result in a hierarchy of hysteresis loops. A possible mechanism for this behavior, involving gate-to-dot tunneling, is discussed.
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