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

TL;DR

This paper investigates the nature of insulating states in magic angle twisted bilayer graphene at integer fillings, revealing a novel Kramers intervalley-coherent insulator with unique symmetry properties through analytical and numerical methods.

Contribution

It introduces the K-IVC insulator as the ground state at charge neutrality, combining strong-coupling analysis with Hartree-Fock calculations including remote bands.

Findings

K-IVC state exhibits circulating currents and orbital magnetization density wave.

Symmetry analysis reveals a preserved Kramers time reversal symmetry.

Other insulators and metallic states can be stabilized by perturbations.

Abstract

In magic angle twisted bilayer graphene, 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 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 exhibits a pattern of alternating circulating currents which 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 approximate ${\rm U}(4) \times {\rm U}(4)$ symmetry, resulting from the remarkable properties of the tBG band structure, which helps select a low energy manifold of states, which are further split to favor the K-IVC. 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 semi-metallic state, and discuss the ground state at half filling and a comparison with experiments.