Spectroscopy and Correlation Effect at Magic Angle

The twisted bilayer graphene (TBG) near the magic angle develops topological flat electron bands at low energies, and exhibits both superconducting and correlated insulating phases at low temperatures. The STM spectroscopy measurements of magic angle TBG shows that the differential tunneling conductances dI/dV at both low and relatively high temperatures have a strong dependence on the doping density in the flat bands. We show that the Hartree Fock mean field theory with spontaneous spin/valley polarization and strain effect fails to capture the spectroscopy at the magic angle. Instead, we show that charge correlation effects beyond the mean field theory are significant for explaining the spectroscopy data, and can be demonstrated in the exact diagonalization of a phenomenological Hubbard model. We also discuss the possible effects of phonon-mediated electron interaction. Lastly, we talk about the effects of the TBG band topology on the Hofstadter butterfly and the interacting phases.