Pressure-induced metal-insulator transition in twisted bilayer graphene

Recent experiments on twisted bilayer graphene (TBLG) have observed insulating states for two and three unit charges per moir\'e supercell, whereas the quarter-filling state (QFS) remained metallic. Subsequent experiments show that under hydrostatic pressure the QFS turns insulating for a certain window of pressure. In fact, the resistivity of the 1/2-filling and 3/4-filling states are also enhanced in the same pressure-window. Using pressure-dependent band structure calculations we compute the ratio of the potential to the kinetic energy, rₛ. We find a window of pressure for which rₛ crosses the threshold for a triangular Wigner crystal, thereby corroborating our previous work that the insulating states in TBLG are driven by Wigner physics, A key prediction of this work is that the window for the onset of the hierarchy of Wigner states that obtains at commensurate fillings conforms to a dome shape under pressure. We also predict the optimal condition for Wigner crystallization to be around 1.50.28em0exGPa. Consequently, TBLG provides a new platform for the exploration of Wigner physics and its relationship with superconductivity.