Abstract

Interplay of strong correlation and flat topological band has been a central problem in moiré 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 (THFM). We label the valence of the f orbital in the AA site based on its occupation nf. At ν = −2, we show that the f orbital is not in the simple f 2+ valence expected from a trivial Mott localization picture. 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. Based on this picture, we dub the phase as mixed valence Mott insulator. This unconventional insulator still has a large hybridization ⟨c†f⟩ ≠ 0 and is sharply distinct from the usual Kondo breakdown picture. In most of the momentum space away from the Γ point, there is a Mott gap equal to the Hubbard U. On the other hand, at the Γ point, we only 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+⟩⟨f 2+| and |f 2+⟩⟨f 3+| with a sign structure such that it is orthogonal to the microscopic f operator. At ν = 0, similar approach leads to the description of a Mott semimetal.

Abstract

Interplay of strong correlation and flat topological band has been a central problem in moiré 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 (THFM). We label the valence of the f orbital in the AA site based on its occupation nf. At ν = −2, we show that the f orbital is not in the simple f 2+ valence expected from a trivial Mott localization picture. 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. Based on this picture, we dub the phase as mixed valence Mott insulator. This unconventional insulator still has a large hybridization ⟨c†f⟩ ≠ 0 and is sharply distinct from the usual Kondo breakdown picture. In most of the momentum space away from the Γ point, there is a Mott gap equal to the Hubbard U. On the other hand, at the Γ point, we only 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+⟩⟨f 2+| and |f 2+⟩⟨f 3+| with a sign structure such that it is orthogonal to the microscopic f operator. At ν = 0, similar approach leads to the description of a Mott semimetal.

Abstract

Interplay of strong correlation and flat topological band has been a central problem in moiré 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 (THFM). We label the valence of the f orbital in the AA site based on its occupation nf. At ν = −2, we show that the f orbital is not in the simple f 2+ valence expected from a trivial Mott localization picture. 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. Based on this picture, we dub the phase as mixed valence Mott insulator. This unconventional insulator still has a large hybridization ⟨c†f⟩ ≠ 0 and is sharply distinct from the usual Kondo breakdown picture. In most of the momentum space away from the Γ point, there is a Mott gap equal to the Hubbard U. On the other hand, at the Γ point, we only 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+⟩⟨f 2+| and |f 2+⟩⟨f 3+| with a sign structure such that it is orthogonal to the microscopic f operator. At ν = 0, similar approach leads to the description of a Mott semimetal.

Abstract

Interplay of strong correlation and flat topological band has been a central problem in moiré 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 (THFM). We label the valence of the f orbital in the AA site based on its occupation nf. At ν = −2, we show that the f orbital is not in the simple f 2+ valence expected from a trivial Mott localization picture. 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. Based on this picture, we dub the phase as mixed valence Mott insulator. This unconventional insulator still has a large hybridization ⟨c†f⟩ ≠ 0 and is sharply distinct from the usual Kondo breakdown picture. In most of the momentum space away from the Γ point, there is a Mott gap equal to the Hubbard U. On the other hand, at the Γ point, we only 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+⟩⟨f 2+| and |f 2+⟩⟨f 3+| with a sign structure such that it is orthogonal to the microscopic f operator. At ν = 0, similar approach leads to the description of a Mott semimetal.