Abstract

We investigate the topological heavy-fermion (THF) model of magic-angle twisted bilayer graphene (MATBG) in the projected limit, where only the flat bands are present in the low-energy spectrum. Such limit has been previously analyzed in momentum-space Bistritzer-MacDonald-type continuum models, but not in a real-space formalism. In this regime, the Hubbard interaction (U₁) of the f-electrons is larger than the bandwidth (2M) of the flat bands but smaller than the gap (γ) between the flat and remote bands. In the THF model, concentrated charge (in real space) and concentrated Berry curvature (in momentum space) are respectively realized by exponentially localized f-orbitals and itinerant Dirac c-electrons. Local moments naturally arise from f-orbitals. Hybridizing the f-electrons with c-electrons produces power-law tails of the flat-band Wannier functions, raising the question of relevance of the local moment picture in the projected U₁ ≪γ limit. Nonetheless, we find that the local moments remain stable as long as U₁ ≫∆(ω) for |ω| ≲U1, where ∆(ω) ∼γ2N(ω) is the hybridization function seen by each f-site, and N(ω) is the density of states of the Dirac c-bands. Notably, the comparison between U₁ and γ is irrelevant to the local moment formation if N(ω) is unknown. Within the framework of THF, we also derive the correlated self-energy of the flat bands using the Hubbard-I approximation, and estimate the coupling strength between the local moments. Finally, we comment that, in the regime of extremely concentrated Berry curvature, the single-particle gap between flat bands and remote bands vanishes and the interaction strength is always larger than the gap.

Abstract

We investigate the topological heavy-fermion (THF) model of magic-angle twisted bilayer graphene (MATBG) in the projected limit, where only the flat bands are present in the low-energy spectrum. Such limit has been previously analyzed in momentum-space Bistritzer-MacDonald-type continuum models, but not in a real-space formalism. In this regime, the Hubbard interaction (U₁) of the f-electrons is larger than the bandwidth (2M) of the flat bands but smaller than the gap (γ) between the flat and remote bands. In the THF model, concentrated charge (in real space) and concentrated Berry curvature (in momentum space) are respectively realized by exponentially localized f-orbitals and itinerant Dirac c-electrons. Local moments naturally arise from f-orbitals. Hybridizing the f-electrons with c-electrons produces power-law tails of the flat-band Wannier functions, raising the question of relevance of the local moment picture in the projected U₁ ≪γ limit. Nonetheless, we find that the local moments remain stable as long as U₁ ≫∆(ω) for |ω| ≲U1, where ∆(ω) ∼γ2N(ω) is the hybridization function seen by each f-site, and N(ω) is the density of states of the Dirac c-bands. Notably, the comparison between U₁ and γ is irrelevant to the local moment formation if N(ω) is unknown. Within the framework of THF, we also derive the correlated self-energy of the flat bands using the Hubbard-I approximation, and estimate the coupling strength between the local moments. Finally, we comment that, in the regime of extremely concentrated Berry curvature, the single-particle gap between flat bands and remote bands vanishes and the interaction strength is always larger than the gap.

Abstract

We investigate the topological heavy-fermion (THF) model of magic-angle twisted bilayer graphene (MATBG) in the projected limit, where only the flat bands are present in the low-energy spectrum. Such limit has been previously analyzed in momentum-space Bistritzer-MacDonald-type continuum models, but not in a real-space formalism. In this regime, the Hubbard interaction (U₁) of the f-electrons is larger than the bandwidth (2M) of the flat bands but smaller than the gap (γ) between the flat and remote bands. In the THF model, concentrated charge (in real space) and concentrated Berry curvature (in momentum space) are respectively realized by exponentially localized f-orbitals and itinerant Dirac c-electrons. Local moments naturally arise from f-orbitals. Hybridizing the f-electrons with c-electrons produces power-law tails of the flat-band Wannier functions, raising the question of relevance of the local moment picture in the projected U₁ ≪γ limit. Nonetheless, we find that the local moments remain stable as long as U₁ ≫∆(ω) for |ω| ≲U1, where ∆(ω) ∼γ2N(ω) is the hybridization function seen by each f-site, and N(ω) is the density of states of the Dirac c-bands. Notably, the comparison between U₁ and γ is irrelevant to the local moment formation if N(ω) is unknown. Within the framework of THF, we also derive the correlated self-energy of the flat bands using the Hubbard-I approximation, and estimate the coupling strength between the local moments. Finally, we comment that, in the regime of extremely concentrated Berry curvature, the single-particle gap between flat bands and remote bands vanishes and the interaction strength is always larger than the gap.

Abstract

We investigate the topological heavy-fermion (THF) model of magic-angle twisted bilayer graphene (MATBG) in the projected limit, where only the flat bands are present in the low-energy spectrum. Such limit has been previously analyzed in momentum-space Bistritzer-MacDonald-type continuum models, but not in a real-space formalism. In this regime, the Hubbard interaction (U₁) of the f-electrons is larger than the bandwidth (2M) of the flat bands but smaller than the gap (γ) between the flat and remote bands. In the THF model, concentrated charge (in real space) and concentrated Berry curvature (in momentum space) are respectively realized by exponentially localized f-orbitals and itinerant Dirac c-electrons. Local moments naturally arise from f-orbitals. Hybridizing the f-electrons with c-electrons produces power-law tails of the flat-band Wannier functions, raising the question of relevance of the local moment picture in the projected U₁ ≪γ limit. Nonetheless, we find that the local moments remain stable as long as U₁ ≫∆(ω) for |ω| ≲U1, where ∆(ω) ∼γ2N(ω) is the hybridization function seen by each f-site, and N(ω) is the density of states of the Dirac c-bands. Notably, the comparison between U₁ and γ is irrelevant to the local moment formation if N(ω) is unknown. Within the framework of THF, we also derive the correlated self-energy of the flat bands using the Hubbard-I approximation, and estimate the coupling strength between the local moments. Finally, we comment that, in the regime of extremely concentrated Berry curvature, the single-particle gap between flat bands and remote bands vanishes and the interaction strength is always larger than the gap.