Two-dimensional (2D) materials for their versatile band structures and strictly 2D nature have attracted considerable attention over the past decade. Graphene is a robust material for spintronics owing to its weak spin-orbit and hyperfine interactions, while monolayer transition metal dichalcogenides (TMDs) possess a Zeeman effect-like band splitting in which the spin and valley degrees of freedom are nondegenerate. The surface states of topological insulators (TIs) exhibit a spin-momentum locking that opens up the possibility of controlling the spin degree of freedom in the absence of an external magnetic field. Nanostructures made of these materials are also viable for use in quantum computing applications involving the superposition and entanglement of individual charge and spin quanta. In this article, we review a selection of transport studies addressing the confinement and manipulation of charges in nanostructures fabricated from various 2D materials. We supply the entry-level knowledge for this field by first introducing the fundamental properties of 2D bulk materials followed by the theoretical background relevant to the physics of nanostructures. Subsequently, a historical review of experimental development in this field is presented, from the early demonstration of graphene nanodevices on SiO2 substrate to more recent progress in utilizing hexagonal boron nitride to reduce substrate disorder. In the second part of this article, we extend our discussion to TMDs and TI nanostructures. We aim to outline the current challenges and suggest how future work will be geared towards developing spin qubits in 2D materials.
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