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

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Science Advances  05 Aug 2020:
Vol. 6, no. 32, eaba8834
DOI: 10.1126/sciadv.aba8834


  • Fig. 1 Nematic order in a moiré superlattice.

    (A) The triangular moiré superlattice of TBG (blue bonds), formed by the AA stacking regions (black dots). (B) In the presence of nematic order, one of the superlattice bonds becomes different (red bond), while the other two remain equivalent. (C) The symmetries of the moiré superlattice involve twofold rotations with respect to orthogonal in-plane axes (C2x and C2y) and sixfold rotations with respect to the z axis (C6z). (D) Nematic director n̂=(cosθ,sinθ): black (red) corresponds to γ < 0 (γ > 0) in the action in Eq. 1. Note that n̂ and n̂ (dashed arrows) are identified. (E) Bond order pattern and lattice distortion pattern associated with each nematic director.

  • Fig. 2 Nematic transition in the presence of static strain.

    (A) Schematic temperature versus strain phase diagram with strain applied along the y axis (α = π/2) and λ < 0, γ > 0. For compressive strain (ε < 0), because the director is fixed at θ0 = π/2, which is a minimum of the cubic term, no phase transition occurs, and only a crossover temperature Tnem* survives. For tensile strain (ε > 0), the director is at θ0 = 0, which is a maximum of the cubic term, for T>Tnemflop, and at ±θ¯0 for T<Tnemflop. Thus, Tnemflop marks an Ising-like nematic-flop transition in which the twofold rotational symmetries C2x and C2y are spontaneously broken. The sixfold rotation C6z is explicitly broken to C2z everywhere for ε ≠ 0. (B) Evolution of the bond order patterns as temperature is lowered in the cases of compressive and tensile strain. Only in the latter case, the three bonds become inequivalent at low temperatures, signaling the breaking of C2x and C2y.

  • Fig. 3 Phonon-mediated nemato-orbital coupling.

    Momentum directional dependence of the nematic susceptibility χnem(q0,q^) caused by the nemato-orbital coupling, with q^=(cosζq,sinζq). Light blue (dark blue) denotes softer (harder) directions, corresponding to higher (lower) susceptibility. While for a rigid crystal, vT < vL, the soft direction is rotated by ±π/4 with respect to the nematic director n (red arrow), for TBG, vT > vL, the rotation is 0, π/2. Note that the director can point in any of the directions θ of Fig. 1B.

  • Fig. 4 Fermi surface distortion and nematic hot spots.

    (A) Fermi surface of the six-band model in (51); red and black correspond to the two valleys. The two pairs of hot spots are marked by open and full symbols. (B) Distortion of the Fermi surface in the presence of intravalley Potts-nematic order, with nematic director n along the x axis. (C) Same as (B), but for intervalley nematic order. In (B) and (C), the undistorted Fermi surface is shown by the dashed lines.

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