Particle-hole asymmetric phases in doped twisted bilayer graphene

Twisted bilayer graphene (TBG) has emerged as a paradigmatic platform for exploring the interplay between strong interactions in a multi-band system with nearly flat bands, while offering unprecedented control over the filling fraction of electron/hole carriers. Despite much theoretical work, developing a comprehensive ab initio model for this system has proven challenging due to the inherent trade-off between accurately describing the band structure and incorporating the interactions within the Hamiltonian. Here, we constructed an extended multi-orbital Hubbard model, and performed Hartree-Fock (HF) calculations to explore its phase diagram across commensurate fillings. We found several nearly-degenerate insulating states at charge neutrality, all of which exhibit orbital orders. We also observed that most of the Hartree–Fock ground states exhibit a generalized valley Hund’s-like rule, resulting in valley polarization. Importantly, we show that the incorporation of the intra-valley and inter-valley exchange interactions is crucial to properly stabilize the ordered symmetry-broken states. In agreement with experiments, we find significant particle-hole asymmetry, which underscores the importance of using particle-hole asymmetric models.. Authors: Hou, Run [Rice University, Houston, TX (United States)] (ORCID:000000033090277X); Sur, Shouvik [Rice University, Houston, TX (United States)] (ORCID:0000000312613261); Wagner, Lucas K. [University of Illinois, Urbana-Champaign, IL (United States)] (ORCID:000000023755044X); Nevidomskyy, Andriy H. [Rice University, Houston, TX (United States)] (ORCID:0000000286847979). DOE Contract: SC0020177; SC0025047; SC0025247. Subjects: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Extended Hubbard model; Hartree-Fock methods; Mean field theory; Topology; Twisted bilayer graphene