Multiple topological transitions in twisted bilayer graphene near the first magic angle

Kasra Hejazi; Chunxiao Liu; Hassan Shapourian; Xiao Chen; Leon Balents

doi:10.1103/PhysRevB.99.035111

paper

Multiple topological transitions in twisted bilayer graphene near the first magic angle

arXiv:1808.01568 · doi:10.1103/PhysRevB.99.035111

Abstract

Recent experiments have observed strongly correlated physics in twisted bilayer graphene (TBG) at very small angles, along with nearly flat electron bands at certain fillings. A good starting point in understanding the physics is a continuum model (CM) proposed by Lopes dos Santos et al. [Phys. Rev. Lett. 99, 256802 (2007)] and Bistritzer et al. [PNAS 108, 12233 (2011)] for TBG at small twist angles, which successfully predicts the bandwidth reduction of the middle two bands of TBG near the first magic angle $θ_{0} = 1.0 5^{\circ}$ . In this paper, we analyze the symmetries of the CM and investigate the low energy flat band structure in the entire moiré Brillouin zone near $θ_{0}$ . Instead of observing flat bands at only one "magic" angle, we notice that the bands remain almost flat within a small range around $θ_{0}$ , where multiple topological transitions occur. The topological transitions are caused by the creation and annihilation of Dirac nodes at either $K$ , $K^{'}$ , or $Γ$ points, or along the high symmetry lines in the moiré Brillouin zone. We trace the evolution of the nodes and find that there are several processes transporting them from $Γ$ to $K$ and $K^{'}$ . At the $Γ$ point, the lowest energy levels of the CM are doubly degenerate for some range of twisting angle around $θ_{0}$ , suggesting that the physics is not described by any two band model. Based on this observation, we propose an effective six-band model (up to second order in quasi-momentum) near the $Γ$ point with the full symmetries of the CM, which we argue is the minimal model that explains the motion of the Dirac nodes around $Γ$ as the twist angle is varied. By fitting the coefficients from the numerical results, we show that this six-band model captures the important physics over a wide range of angles near the first "magic" angle.

Multiple topological transitions in twisted bilayer graphene near the first magic angle

Abstract

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