We theoretically study transport signatures associated with a spontaneous two-valley to one-valley quantum phase transition in a two-dimensional electron gas (2DEG) tuned by decreasing the 2D carrier density, as claimed in a recent experiment [M. S. Hossain et al., 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.

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• Phase transitions
• Two-dimensional electron system
• Critical phenomena