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Recent years have witnessed the fabrication of various non-covalent interaction-based molecular electronic devices. In the non-covalent interaction-based molecular devices, the strength of the interfacial coupling between molecule and electrode is weakened compared to that of the covalent interaction-based molecular devices, which provides wide applications in fabricating versatile molecular devices. In this review, we start with the methods capable of fabricating graphene-based nanogaps, and the following routes to construct non-covalent interaction-based molecular junctions with graphene electrodes. Then we give an introduction to the reported non-covalent interaction-based molecular devices with graphene electrodes equipped with different electrical functions. Moreover, we summarize the recent progress in the design and fabrication of new-type molecular devices based on graphene and graphene-like two-dimensional (2D) materials. The review ends with a prospect on the challenges and opportunities of non-covalent interaction-based molecular electronics in the near future.
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