Abstract
Narrow and even flat energy bands reflect strong electronic correlation which brings in novel physical properties. Pursuing flatter band has recently attracted a lot of attention. Along this line, we theoretically investigate low-energy band structures and concomitant topological properties of twisted bilayer graphene at the first magic angle based on a continuum model. By considering an external moir\'e electric potential, in addition to the intrinsic Hartree potential, we find that the lowest bands can be further flattened by this electric potential and a superflat band structure is obtained. In such bands, the extremely small ratio between the bandwidth and the interaction strength will enhance the strong correlation. These superflat energy bands give nearly perfect nesting at the half-filling, then it benefits the formation of Cooper pairs and the rise of superconducting temperature. Moreover, combining with a perfectly aligned boron nitride substrate, the system undergoes a topological phase transition by modulating the relevant parameters of the electric potential. The topological phase transition can be well explained using simplified analytical treatments near the Dirac points.
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