  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, $r_s$. We find an
experimentally relevant window of pressure for which $r_s$ crosses the
threshold for a triangular Wigner crystal, thereby corroborating our previous
work [Nano Lett. (2018)] that the insulating states in TBLG are due to Wigner
rather than Mott 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 is dome-shaped as a function of the applied pressure, which can be
probed experimentally. Theoretically, we find a peak for crystallization around
$1.5$ GPa relative to the experimental optimal pressure of $1.33$ GPa for the
observation of the insulating states. Consequently, TBLG provides a new
platform for the exploration of Wigner physics and its relationship with
superconductivity.
