Emergent heavy fermion and superconductivity near Mott transition in twisted bilayer graphene

Abstract

Near a bandwidth-tuned Mott transition, the Fermi velocity $v_F$ and quasiparticle residue $Z$ of a metal often vanish. Here, we show that analogous phenomena emerge in twisted bilayer graphene (TBG) at integer fillings and can be captured by an emergent heavy-fermion framework within a projective active-band limit. Unlike models incorporating remote bands, our effective heavy-fermion description arises from \textit{mixed-valence Mott} physics via decoupled charge and local-moment sectors. In the charge sector, active bands $c(\mathbf{k})$ hybridize with an emergent \emph{orthogonal fermion} $\psi (\mathbf{k})$ to open a large Mott gap at $|\mathbf{k}|>k_{\ast }$ ($k_{\ast }$ sets the momentum-patch size) and a quadratic band-touching semimetal near $\mathbf{k}=0$ at neutrality ($\nu =0$). The orthogonal fermion is a linear combination of the doublon and holon excitations and may be written as ${\psi }_i\sim (\delta n_i^f+\frac{1}{2}{)}^{-1}{f}_i$. An emergent Kondo coupling $J_K\sim U$ ($U$ is the local Hubbard interaction) between $\psi$ and local moments ${\psi }^{\prime }$ frames the Mott transition as a Kondo screening transition, tuned by the twist angle $\theta$. Away from the magic angle, a Kondo-screened heavy semimetal develops below $T_K$ (the Kondo temperature) with vanishing $Z$. Introducing anti-Hund's coupling $J_A$ generates an s-wave fully gapped or nematic, nodally gapped superconducting dome near the Mott boundary even at $\nu =0$. At other integer fillings $\nu =\pm 1,\pm 2$, increasing bandwidth first drives the small-gap Mott state into an intermediate quadratic band-touching semimetal before entering a heavy Fermi liquid with large Fermi surfaces. Our results establish a unified framework for emergent heavy fermion physics with both itinerant carriers and local moments from the $f$ orbital.

5+15 pages