  We theoretically study transport signatures associated with a spontaneous
2-valley to 1-valley quantum phase transition in a two-dimensional electron gas
(2DEG) tuned by decreasing the 2D carrier density, as claimed in a recent
experiment [Phys. Rev. Lett. 127, 116601 (2021)]. The key issue we focus on is
whether the experimentally measured 2D resistivity as a function of carrier
density is consistent (or not) with an underlying spontaneous
valley-polarization transition as assumed uncritically in the experimental
report. Our theoretical analysis is particularly germane since the experiment
does not directly measure the change in the Fermi surface resulting from the
valley polarization transition, but infers such a transition indirectly through
transport measurements. We validate the experimental claim, showing that indeed
the observed sudden change in the 2D resistivity is quantitatively consistent
with a sudden change in the valley polarization from 2 to 1 at the critical
density.
