Projected and Solvable Topological Heavy Fermion Model of Twisted Bilayer Graphene
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2025
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| author | Hu, Haoyu Song, Zhi-Da Bernevig, B. Andrei |
| author_facet | Hu, Haoyu Song, Zhi-Da Bernevig, B. Andrei |
| contents | 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 ($U_1$) 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 $U_1\ll γ$ limit. Nonetheless, we find that the local moments remain stable as long as $U_1 \gg Δ(ω)$ for $|ω|\lesssim U_1$, where $Δ(ω)\sim γ^2 N(ω)$ 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 $U_1$ 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 is always larger than the gap. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_14039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Projected and Solvable Topological Heavy Fermion Model of Twisted Bilayer Graphene Hu, Haoyu Song, Zhi-Da Bernevig, B. Andrei Strongly Correlated Electrons Mesoscale and Nanoscale Physics 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 ($U_1$) 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 $U_1\ll γ$ limit. Nonetheless, we find that the local moments remain stable as long as $U_1 \gg Δ(ω)$ for $|ω|\lesssim U_1$, where $Δ(ω)\sim γ^2 N(ω)$ 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 $U_1$ 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 is always larger than the gap. |
| title | Projected and Solvable Topological Heavy Fermion Model of Twisted Bilayer Graphene |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2502.14039 |