The distribution of electrons in two parallel twohyphen;dimensional electron sheets in close proximity at low temperatures is investigated. We find that due to the exchange interaction a symmetric structure may have a ground state in which all electrons are transferred to one of the sheets. This occurs if the separation between the two systems is sufficiently small and the twohyphen;dimensional electron gas density is sufficiently low. The exchange interaction consequently leads to a bistability with respect to electron population in the twohyphen;sheet system which may be useful for future electronic devices, such as memory elements.
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