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.
Highlights
In twisted bilayer graphene (TBG), two sheets of graphene twisted by a small angle θ create a moirelattice, resulting in electronic minibands
In the absence of dispersion and with full sublattice polarization, there is a Uð4Þ × Uð4Þ symmetry coming from each “zeroth Landau level (ZLL).” much intuition from the theory of U(4) quantum-Hall ferromagnetism in MLG [26] can be translated to TBG, albeit with the novel twist of time-reversal symmetry: Unlike a single ZLL, unfrustrated Cooper pairs can form from one electron in each copy
To summarize, based on both numerical and analytical arguments, we propose that the insulating state observed at charge neutrality in pristine MATBG [5] is the Kramers intervalley-coherent (K-IVC) state, i.e., an intervalleycoherent state with an emergent spinless Kramers time-reversal symmetry T 0
Summary
In twisted bilayer graphene (TBG), two sheets of graphene twisted by a small angle θ create a moirelattice, resulting in electronic minibands. In the absence of dispersion and with full sublattice polarization, there is a Uð4Þ × Uð4Þ symmetry coming from each “ZLL.” much intuition from the theory of U(4) quantum-Hall ferromagnetism in MLG [26] can be translated to TBG, albeit with the novel twist of time-reversal symmetry: Unlike a single ZLL, unfrustrated Cooper pairs can form from one electron in each copy. This doubled-ZLL picture brings us back to the tension between the QH and Hubbard paradigms. Taking into account the finite sublattice polarization, the K-IVC state that remains a “generalized ferromagnet” is favored relative to the valley-Hall state
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