Emergent Quantum Phases and Superconductivity in Flatband-land

The discovery of superconductivity in twisted bilayer graphene in 2018 ignited a new field of condensed matter physics (“twistronics”), driven by the urge to uncover new useful electronic emergent phases by twisting layers of weakly-coupled atoms. The so-called magic-angle twisted bilayer graphene (MA-TBG) with rotational misalignment close to 1.1° between two graphene sheets features both insulating phases and superconductivity, despite the fact that isolated graphene layers do not. In fact, MA-TBG hosts a remarkably rich phase diagram of electronically correlated insulating, superconducting, magnetic, and topological quantum states. The origin of these emergent quantum phases remains controversial, but most likely it is rooted in the existence of exceedingly flat electronic bands at this misalignment angle. In a nutshell this proposal builds on the hypothesis that all these phases, including superconductivity, are driven by a particularly novel low-energy emergent electron-electron interaction in flatband systems such as MA-TBG. We will apply modern quantum many-body methods to solve this problem, and connect to existing experimental puzzles. The topic of the proposed research is not restricted to MA-TBG, but addresses also new “flatband” systems, including other twisted systems (double-bilayers and mirror-symmetric graphene trilayers) and superconducting Kagome metals, discovered in 2020. In addition, the project addresses the fundamental question of whether or not superconductivity can arise from repulsive interactions. Its impact is far-reaching, with important consequences for our understanding of correlated electron systems.