Event

The twisted bilayer graphene (TBG) near the magic twist angle 1.05 degrees is known to have extremely flat electron bands, and exhibits both superconductivity and correlated insulating phases. In the first part, we show that the electron-phonon coupling is enhanced by the twist structure, which is strong enough to induce conventional BCS superconductivity with a critical temperature around 1K. We further predict the possible BCS superconductivity at other twist angles and in higher electron bands. In the second part, we explore the Landau levels and Hofstadter butterfly of the TBG. We predict the nontrivial fragile topology of the two flat bands gives rise to two topological Landau levels of Chern number -1 separating away from the flat bands at magnetic fields above 15T, leading to an unbounded Hofstadter butterfly. Besides, we show the single-particle band theory with Zeeman splitting could result in Landau fans at both zero and half fillings, as observed in experiments.