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Quantum mechanics predicts that two distinguishable quantum states can be realized by confining a single electron within an ultrasmall space. However, scaling down such devices paradoxically amplifies fringe capacitance effects, which hinders the experimental observation of single-electron memory. We report a two-dimensional single-electron memory device based on a coplanar drain-channel-source structure that suppressed fringe capacitance, exhibiting a nonvolatile threshold voltage shift of 0.5 volts after the change of a single electron. Two intriguing quantum behaviors have also been verified regarding the programming voltage. 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