Since the successful exfoliation of graphene monolayer, the exotic and superior electrical properties of graphene have rendered it a promising potential candidate for the future electronics. In particular, the extremely high electron mobility and the rapid developments in mass-fabricating high-quality graphene might initiate a new electronic industry revolution with graphene-based next-generation electronics, namely high-speed field effect transistors (FET). However, the unique Dirac-conical band structure, which provides fascinating electronic features for graphene, turns out to be the primary obstacle that hinders the fabrication of graphene-based FET due to its lack of a band gap. Since a desirably large band gap is required for a high on-off ratio FET, physicists have been trying to figure out ways to open a controllable band gap in monolayer and multilayer graphene from the early stage of graphene research. Up till now, there are two major kinds of ways towards opening a band gap for graphene. The first is by directly violating the pristine electronic or geometrical properties of graphene, through doping, adatom, introducing periodic defects, constrictions, or other chemical treatments. These methods are generally destructive to graphene’s original electronic properties. The other way largely preserves the pristine electronic properties of graphene, such as breaking the intrinsic symmetries of graphene that protect the Dirac cone intact, either through substrate interaction, applying external field, etc., or through other mechanisms such as spin-orbit interaction, strain, and electron many-body effects. There might be multiple mechanisms appearing in various theoretical or experimental works that contribute to the opening of band gap, and this classification is far from clear-cut. Investigations toward this problem include various methodologies, including theoretical proposition, ab-initio calculations, density-function or other approximated calculations, and experimental verification using angular resolved photoemission spectroscopic, scanning tunneling spectroscopic and transport evidences. There are also intense theoretical and experimental works on bilayer or multilayer graphene band gap opening. Although there have been many successful examples of band gap opening in graphene, it is still far to say that graphene-based ideal FET is feasible. The major remaining challenges are increasing the band gap up to a desirable value, making the band gap precisely controllable, and more importantly, preserving the superior electronic properties of graphene. Given that band gap opening is a dramatic change of graphene’s electronic structure, it is still not clear which mechanism might ultimately resolve such dilemma, and more investigations are needed in this emergent and fruitful field.
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