Mixed valence Mott insulator and composite excitation in twisted bilayer graphene

TL;DR

This paper constructs a theoretical model of a mixed valence Mott insulator in twisted bilayer graphene, revealing unconventional excitations and hybridization effects that differ from traditional Kondo physics.

Contribution

It introduces a novel parton mean field theory for a topological heavy fermion model, describing a mixed valence Mott insulator with unique composite excitations in TBG.

Findings

Identification of a mixed valence state with superposed $f^{2+}$ and $f^{3+}$ valences.

Discovery of a composite excitation dominating the top of the lower band.

Distinct Mott gap behavior at different momentum points.

Abstract

Interplay of strong correlation and flat topological band has been a central problem in moir\'e systems such as the magic angle twisted bilayer graphene (TBG). Recent studies show that Mott-like states may still be possible in TBG despite the Wannier obstruction. However, the nature of such unconventional states is still not well understood. In this work we construct the ground state wavefunction and exotic excitations of a symmetric correlated semimetal or insulator at even integer filling using a parton mean field theory of the topological heavy fermion model. We label the valence of the $f$ orbital based on its occupation $n_f$. At $\nu=-2$, we show that the $f$ orbital is not in the simple $f^{2+}$ valence expected from a trivial Mott localization. Instead, around $1/3$ of AA sites are self doped, with holes entering the $c$ orbitals away from AA sites. As a result, the $f$ orbital is in a superposition of $f^{2+}$ and $f^{3+}$ valences and should not be viewed as local moment. We dub the phase as \textit{mixed valence Mott insulator}. This unconventional insulator has a large hybridization $\langle c^\dagger f \rangle\neq 0$ and is sharply distinct from the usual `kondo breakdown' picture. In most of the momentum space away from the $\Gamma$ point, there is a Mott gap equal to the Hubbard $U$. At the $\Gamma$ point, we have a `charge transfer gap' much smaller than $U$. In particular, the top of the lower band is dominated by a composite excitation, which is a linear combination of $|f^{1+}\rangle\langle f^{2+}|$ and $|f^{2+}\rangle\langle f^{3+}|$ with a sign structure such that it is orthogonal to the microscopic $f$ operator. At $\nu=0$, similar approach leads to a Mott semimetal. We hope this work will inspire more explorations of the Anderson models with a large hybridization, a regime which may host new physics beyond the familiar Kondo or heavy fermion systems.