Hundness in twisted bilayer graphene: correlated gaps and pairing

We characterize gap-opening mechanisms in the topological heavy fermion (THF) model of magic-angle twisted bilayer graphene (MATBG), with and without electron-phonon coupling, using dynamical mean-field theory (DMFT) with the numerical renormalization group (NRG) impurity solver. In the presence of symmetry breaking associated with valley-orbital ordering (time-reversal-symmetric or Kramers intervalley coherent, or valley polarized), spin anti-Hund and orbital-angular-momentum Hund couplings, induced by the dynamical Jahn-Teller effect, result in a robust pseudogap at filling $2 \lesssim |\nu| \lesssim 2.5$. We also find that Hundness enhances the pairing susceptibilities for $1.6 \lesssim |\nu| \lesssim 2.8$, which might be a precursor to the superconducting phases neighboring $|\nu| = 2$.