Pressure-Induced Metal-Insulator Transition in Twisted Bi-layer Graphene

Understand

Recent experiments [arXiv: 1808.07865] on twisted bilayer graphene (TBLG) show that under hydrostatic pressure, an insulating state at quarter-filling of the moir\'e superlattice (i.e., one charge per supercell) emerges, in sharp contrast with the previous ambient pressure measurements of Cao et al.

• where the quarter--filling state (QFS) is a metal [Nature 556, 43 & 80 (2018)].
• In fact, the insulating state at the other commensurate fillings of two and three charges per supercell is also enhanced under applied pressure.
• Based on realistic computations of the band structure for TBLG which show that the bandwidth first shrinks and then expands with increasing hydrostatic pressure, we compute the ratio of the potential to the kinetic energy, $r_s$.