Multiple flat bands and topological Hofstadter butterfly in twisted bilayer graphene close to the second magic angle

Moire superlattices in two-dimensional van der Waals heterostructures provide an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer graphene (tBLG) has made this moire system one of the most renowned condensed matter platforms. So far studies of tBLG have been mostly focused on the lowest two flat moire bands at the first magic angle theta(m1) similar to 1.1 degrees, leaving highorder moire bands and magic angles largely unexplored. Here we report an observation of multiple well-isolated flat moire bands in tBLG close to the second magic angle theta(m2) similar to 0.5 degrees, which cannot be explained without considering electron-election interactions. With high magnetic field magnetotransport measurements we further reveal an energetically unbound Hofstadter butterfly spectrum in which continuously extended quantized Landau level gaps cross all trivial band gaps. The connected Hofstadter butterfly strongly evidences the topologically nontrivial textures of the multiple moire bands. Overall, our work provides a perspective for understanding the quantum phases in tBLG and the fractal Hofstadter spectra of multiple topological bands.