Critical Nematic Phase with Pseudogaplike Behavior in Twisted Bilayers

The crystallographic restriction theorem constrains two-dimensional nematicity to display either Ising (Z2) or three-state-Potts (Z3) critical behaviors, both of which are dominated by amplitude fluctuations. Here, we use group theory and microscopic modeling to show that this constraint is circumvented in a 30°-twisted hexagonal bilayer due to its emergent quasicrystalline symmetries. We find a critical phase dominated by phase fluctuations of a Z6 nematic order parameter and bounded by two Berezinskii-Kosterlitz-Thouless (BKT) transitions, which displays only quasi-long-range nematic order. The electronic spectrum in the critical phase displays a thermal pseudogaplike behavior, whose properties depend on the anomalous critical exponent. We also show that an out-of-plane magnetic field induces nematic phase fluctuations that suppress the two BKT transitions via a mechanism analogous to the Hall viscoelastic response of the lattice, giving rise to a putative nematic quantum critical point with emergent continuous symmetry. Finally, we demonstrate that even in the case of an untwisted bilayer, a critical phase emerges when the nematic order parameter changes sign between the two layers, establishing an odd-parity nematic state.