Twist angle dependence of flatbands in trilayer graphene: A first-principles study

Among the most classical two-dimensional (2D) heterostructures, graphene stands out to exhibit unique electronic properties through manipulations of stacking layers, twist angles, strain, and external electric and magnetic fields. In this work, we present a theoretical investigation of twisted trilayer graphene (tTLG) using first-principles calculations, considering various twist angles θ12, which is the angle between the bottom and middle layers, and θ23, which is the angle between the top and middle layers. For trilayer configurations AÃA, where θ23 = θ12, and AÃÃ′, where θ23≠θ12, supercells as large as containing 23 338 atoms are built to capture the impact of twist angles on the electronic properties in tTLG using RESCU+. We discover that flatbands (with bandwidths less than 100 meV) can emerge when the twist angles approach certain magic angles while θ12⋅θ23 > 0. The bandwidth minimizes near these magic angles and varies smoothly with the twist angle, exhibiting no abrupt changes. Despite the symmetry being affected by the shift of the bottom and top layers leading to the changes in the Dirac cones, the flatbands exhibit remarkable robustness and retain their distinct properties. Our findings explain why the correlated states can also exist at twist angles slightly away from the exact magic angles.