Ground State and Hidden Symmetry of Magic-Angle Graphene at Even Integer Filling

• Published in: Physical review. X Vol. 10; no. 3; p. 031034
• Main Authors: Bultinck, Nick, Khalaf, Eslam, Liu, Shang, Chatterjee, Shubhayu, Vishwanath, Ashvin, Zaletel, Michael P.
• Format: Journal Article
• Language: English
• Published: College Park American Physical Society 12.08.2020
• Subjects: Bilayers; Broken symmetry; Density; Electrons; Graphene; Ground state; Hartree approximation; High temperature; Insulators; Integers; Kinetic energy; Manifolds; Mathematical analysis; Perturbation; Questions; Superconductivity; Symmetry; Unit cell
• ISSN: 2160-3308; 2160-3308
• DOI: 10.1103/PhysRevX.10.031034

In magic angle twisted bilayer graphene (TBG), electron-electron interactions play a central role, resulting in correlated insulating states at certain integer fillings. Identifying the nature of these insulators is a central question, and it is potentially linked to the relatively high-temperature superconductivity observed in the same devices. Here, we address this question using a combination of analytical strong-coupling arguments and a comprehensive Hartree-Fock numerical calculation, which includes the effect of remote bands. The ground state we obtain at charge neutrality is an unusual ordered state, which we call the Kramers intervalley-coherent (K-IVC) insulator. In its simplest form, the K-IVC order exhibits a pattern of alternating circulating currents that triples the graphene unit cell, leading to an “orbital magnetization density wave.” Although translation and time-reversal symmetry are broken, a combined “Kramers” time-reversal symmetry is preserved. Our analytic arguments are built on first identifying an approximateU(4)×U(4)symmetry, resulting from the remarkable properties of the TBG band structure, which helps select a low-energy manifold of states that are further split to favor the K-IVC state. This low-energy manifold is also found in the Hartree-Fock numerical calculation. We show that symmetry-lowering perturbations can stabilize other insulators and the semimetallic state, and we discuss the ground state at half-filling and give a comparison with experiments.