Nematicity with a twist: rotational symmetry breaking in a moiré superlattice

Abstract

Motivated by recent reports of nematic order in twisted bilayer graphene (TBG), we investigate the impact of the triangular moiré 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 (C3z) of the moiré superlattice. We find that even in the presence of static strain that explicitly breaks the C3z 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 moiré superlattice.

Parquet renormalization group analysis of weak-coupling instabilities with multiple high-order Van Hove points inside the Brillouin zone

“…At higher orders in the expansion, the prefactors c (4) and c (8) are positive, while c (6) is negative. The anisotropic terms exist and select particular directions under spontaneous C 3z rotation symmetry breaking [62]. Since the octic order terms are perturbatively smaller than the sextic order ones, the free energy minima occur at θ ∆ = nπ/3 with n = 0, 1, 2.…”

Competing orders at higher-order Van Hove points

“…For d-wave charge Pomeranchuck order, we introduce two real order parameters ϕ 2 , ϕ 3 and the total order parameter is ϕ c = ϕ 2 Γ 2 + ϕ 3 Γ 3 . A hexagonal lattice allows for a cubic term in the free energy [27][28][29][30][31][32] . Keeping this term and neglecting ϕ 4 terms, we obtain…”

“…Each state selects one particular HOVH point where the order is largest. Such a state breaks lattice C 3 rotational symmetry and is a charge nematic [27][28][29][30][31][32] .…”