Electron-phonon superconductivity and Landau levels in twisted bilayer graphene

In the first half of the presentation, we show the analytical calculation of the electron-phonon coupling in twisted bilayer graphene (TBG), which was recently experimentally observed to exhibit superconductivity around the magic twist angle $\theta\approx 1.05^\circ$. We show that phonon-mediated electron electron attraction at the magic angle is strong enough to induce a conventional intervalley pairing between graphene valleys $K$ and $K'$ with a superconducting critical temperature $T_c\sim1K$, in agreement with the experiment. In the second half of the talk, we show the existence of topological Landau levels at large magnetic fields due to nontrivial topology of the flat bands.