Speaker
Description
We study strongly correlated superconductivity in magic-angle twisted bilayer graphene (MATBG) using a variational Gutzwiller wavefunction $\ket{\Psi_G} = \prod_{\vb{R}} \hat{P}_{\vb{R}}\ket{\Phi_0}$, where the Gutzwiller projector $\hat{P}_{\vb{R}}$ is allowed to break charge
U(1) symmetry to accommodate superconducting (SC) order. The ground state energy is evaluated via the \textit{Gutzwiller Approximation} applied to an 8-band model consisting of correlated $f$-orbitals and uncorrelated $c$-orbitals, with interactions including onsite Coulomb repulsion $U$, phonon-mediated anti-Hund's coupling $\hat{H}_{J_A}$, and intra-orbital Hund's coupling $\hat{H}_{J_H}$. At filling $\nu = 2.5$, we map out the phase diagram as a function of $U$ and $J_A$, and reveal a strongly correlated SC (SC-SC) phase dominates at large $U$,wherethe strong on-site interaction U strongly suppress the $f$-orbital charge fluctuations
while maintaining finite pairing order and a sizeable quasiparticle weight Z, distinguishing it from a conventional Mott insulator. For a range of $J_{\rm A}$, SC-SC transitions to FL as $U$ decreases, until the weakly correlated BCS-like SC (BCS-SC) re-enters as $U \to 0$. We further identify a novel small Fermi liquid (sFL) state with effective Fermi surface formed by $c$-orbitals, which is essentially different with the normal Fermi liquid. %volume $=\nu+2$.
Interestingly, in the intermediate- ($U \lesssim 40$ meV) and large-$U$ ($U \gtrsim 40$ meV)
regimes, the conventional FL and the sFL are the lowest-energy normal phases, respectively,potentially serve as the parent states of the SC-SC phase. These results illuminate the interplay between strong correlations and unconventional pairing in MATBG, and establish a versatile Gutzwiller framework applicable to other strongly correlated superconductors.