Multiple Flat Bands and Topological Hofstadter Butterfly in Twisted Bilayer Graphene Close to the Second Magic Angle

Abstract: Moir\'e superlattices in two-dimensional (2D) van der Waals (vdW) heterostructures provide 20 an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer graphene (tBLG) has built this moir\'e system one of the most renowned condensed matter platforms (1-10). So far the studies of tBLG has been mostly focused on the lowest two flat moir\'e bands at the first magic angle {\theta}m1 ~ 1.1{\deg}, leaving high-order moir\'e bands and magic angles largely unexplored. Here we report 25 an observation of multiple well-isolated flat moir\'e bands in tBLG close to the second magic angle {\theta}m2 ~ 0.5{\deg}, which cannot be explained without considering electron-election interactions. With high magnetic field magneto-transport measurements, we further reveal a qualitatively new, energetically unbound Hofstadter butterfly spectrum in which continuously extended quantized Landau level gaps cross all trivial band-gaps. The 30 connected Hofstadter butterfly strongly evidences the topologically nontrivial textures of the multiple moir\'e bands. Overall, our work provides a new perspective for understanding the quantum phases in tBLG and the fractal Hofstadter spectra of multiple topological bands.