Nematicity with a twist: rotational symmetry breaking in a moir\'e superlattice

TL;DR

This paper explores how the unique triangular moiré superlattice in twisted bilayer graphene influences nematic order, revealing a threefold symmetry-breaking mechanism and phase transition characteristics distinct from conventional crystals.

Contribution

It introduces a Potts-like nematic order parameter in TBG, analyzes the effects of strain and elastic fluctuations, and demonstrates the first-order nature of the nematic transition in moiré superlattices.

Findings

Nematic order in TBG has a 3-state Potts character due to $C_{3z}$ symmetry.

Elastic fluctuations induce a first-order nematic transition.

Soft directions in momentum space enhance coupling to nematic fluctuations.

Abstract

Motivated by recent reports of nematic order in twisted bilayer graphene (TBG), we investigate the impact of the triangular moir\'e superlattice degrees of freedom on nematicity. In TBG, the nematic order parameter is not Ising-like, as it is the case in tetragonal crystals, but has a 3-state Potts character related to the threefold rotational symmetry ($C_{3z}$) of the moir\'e superlattice. We find that even in the presence of static strain that explicitly breaks the $C_{3z}$ symmetry, the system can still undergo a nematic-flop phase transition that spontaneously breaks in-plane twofold rotations. Moreover, elastic fluctuations, manifested as acoustic phonons, mediate a nemato-orbital coupling that ties the orientation of the nematic director to certain soft directions in momentum space, rendering the Potts-nematic transition mean-field and first-order. In contrast to the case of rigid crystals, the Fermi-surface hot-spots associated with these soft directions are maximally coupled to the low-energy nematic fluctuations in the case of the moir\'e superlattice.