Combined Minivalley and Layer Control in Twisted Double Bilayer Graphene.

Control over minivalley polarization and interlayer coupling is demonstrated in double bilayer graphene twisted with an angle of 2.37°. This intermediate angle is small enough for the minibands to form and large enough such that the charge carrier gases in the layers can be tuned independently. Using a dual-gated geometry we identify and control all possible combinations of minivalley polarization via the population of the two bilayers. An applied displacement field opens a band gap in either of the two bilayers, allowing us to even obtain full minivalley polarization. In addition, the carriers, formerly separated by their minivalley character, are mixed by tuning through a Lifshitz transition, where the Fermi surface topology changes. The high degree of control over the minivalley character of the bulk charge transport in twisted double bilayer graphene offers new opportunities for realizing valleytronics devices such as valley valves, filters, and logic gates.