Enhanced second-order Stark effect in twisted bilayer graphene quantum dots

External electric field and interlayer twist introduce diverse changes in their confined electronic states of bilayer graphene quantum dots. Using a quantum-dot model, the band gaps of twisted bilayer graphene in finite sizes of about 1.4–2.4 nm with varying twist angles are studied in the presence of an electrostatic field perpendicular to the flakes by means of first-principles calculations. The size-dependent gaps are widened by the interlayer twist, but narrowed by the applied field. Their coupling, however, results in an enhanced Stark response in the twisted structures of which the field-induced band-gap variations are about 3–4 times as large as that of the corresponding untwisted structures under the same field strength. The exceptional Stark shifts come from the field-induced asynchronous shifts in their occupied and virtual energy levels, which are further enhanced by strong interlayer coupling at specific twist angles. Moreover, the shift of band gaps with the field strength follows the quadratic Stark response with large second-order shifting coefficients. The enhanced and tunable Stark shift suggests a gateway to the band engineering of bilayer graphene quantum dots by tuning their sizes, twist angles and their coupling with applied field.