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 in tetragonal crystals, but has a three-state Potts character related to the threefold rotational symmetry (C 3z ) of the moiré 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 nematic director orientation 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 low-energy nematic fluctuations in the moiré superlattice case.
Highlights
Recent experiments in twisted bilayer graphene (TBG) have unveiled a rich phase diagram displaying phenomena often observed in strongly correlated systems, such as superconductivity, metal-insulator transition, nematicity, ferromagnetism, and the anomalous quantum Hall effect [1,2,3,4,5,6,7]
While a number of theoretical proposals have explored the possibility of such an electronic nematic phase [30,31,32,33,34], experimentally, it remains a difficult task to distinguish spontaneous nematic order from an explicit broken symmetry caused by strain, whose presence is ubiquitous in TBG [26, 35,36,37]
In systems with tetragonal symmetry, these two d-waves have distinct symmetries and must be treated as two independent Ising order parameters. This is markedly different in hexagonal systems, such as TBG with point group D6: The two nematic components belong to a single irreducible representation of D6 and transform as partners under its symmetries, defining a two-component order parameter = ( 1, 2)
Summary
Recent experiments in twisted bilayer graphene (TBG) have unveiled a rich phase diagram displaying phenomena often observed in strongly correlated systems, such as superconductivity, metal-insulator transition, nematicity, ferromagnetism, and the anomalous quantum Hall effect [1,2,3,4,5,6,7]. In contrast to correlated materials, in TBG, these phases can be precisely tuned with gating and twist angles, rather than doping and pressure. This offers a compelling venue to elucidate correlation-driven electronic orders [8,9,10,11,12,13,14,15,16,17,18,19,20,21], which avoids the typical complications related to bulk compounds. While a number of theoretical proposals have explored the possibility of such an electronic nematic phase [30,31,32,33,34], experimentally, it remains a difficult task to distinguish spontaneous nematic order from an explicit broken symmetry caused by strain, whose presence is ubiquitous in TBG [26, 35,36,37]
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