Perturbative renormalization group approach to magic-angle twisted bilayer graphene using topological heavy fermion model
arXiv:2507.17751 · doi:10.1103/2px8-h7c2
Abstract
We develop a perturbative renormalization group (RG) theory for the topological heavy fermion (THF) model, describing magic-angle twisted bilayer graphene (MATBG) as an emergent Anderson lattice. Our theory focuses on an energy window where the interactions can be treated perturbatively within the THF model, providing insights into the low-energy physics. In particular, the realistic parameters place MATBG near an intermediate regime where the Hubbard interaction and the hybridization energy are comparable, motivating the need for RG analysis. Our approach analytically tracks the flow of single-particle parameters and Coulomb interactions within an energy window below eV, providing implications for distinguishing between Kondo-like () and projected-limit/Mott-semimetal () scenarios at low energies. We show that the RG flows generically lower the ratio and drive MATBG toward the chiral limit, consistent with the previous numerical study based on the Bistritzer-MacDonald model. The framework presented here also applies to other moiré systems and stoichiometric materials that admit a THF description, including magic-angle twisted trilayer graphene, twisted checkerboard model, and Lieb lattice, among others, providing a foundation for developing low-energy effective theories relevant to a broad class of topological flat-band materials.
22 pages, 15 figures
References in corpus (56)
- Magic-angle graphene superlattices: a new platform for unconventional superconductivity
- Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
- Moire bands in twisted double-layer graphene
- Tuning superconductivity in twisted bilayer graphene
- Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
- Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
- Intrinsic quantized anomalous Hall effect in a moiré heterostructure
- Magic Angle Spectroscopy
- Tunable Phase Boundaries and Ultra-Strong Coupling Superconductivity in Mirror Symmetric Magic-Angle Trilayer Graphene
- Graphene Bilayers with a Twist
- Imaging Electronic Correlations in Twisted Bilayer Graphene near the Magic Angle
- Charge-Order and Broken Rotational Symmetry in Magic Angle Twisted Bilayer Graphene
- Spectroscopic signatures of many-body correlations in magic angle twisted bilayer graphene
- Spin-polarized Correlated Insulator and Superconductor in Twisted Double Bilayer Graphene
- Strange metal in magic-angle graphene with near Planckian dissipation
- Electric field tunable unconventional superconductivity in alternating twist magic-angle trilayer graphene
- Cascade of electronic transitions in magic-angle twisted bilayer graphene
- Cascade of Phase Transitions and Dirac Revivals in Magic Angle Graphene
- Superconductivity in rhombohedral trilayer graphene
- Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
- Phonon scattering dominated electron transport in twisted bilayer graphene
- Nematicity and Competing Orders in Superconducting Magic-Angle Graphene
- Superconductivity without insulating states in twisted bilayer graphene stabilized by monolayer WSe
- Band Structure of Twisted Bilayer Graphene: Emergent Symmetries, Commensurate Approximants and Wannier Obstructions
- Many-body instability of Coulomb interacting bilayer graphene: RG approach
- MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
- Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening
- Quantum critical scaling in graphene
- Flavour Hund's Coupling, Correlated Chern Gaps, and Diffusivity in Moiré Flat Bands
- Twisted bilayer graphene. II. Stable symmetry anomaly
- Towards the hidden symmetry in Coulomb interacting twisted bilayer graphene: renormalization group approach
- Quantum textures of the many-body wavefunctions in magic-angle graphene
- Graphene via large N I: Renormalization
- Anomalous thermodynamics of Coulomb interacting massless Dirac fermions in two spatial dimensions
- Why does graphene behave as a weakly interacting system?
- Kondo lattice model in magic-angle twisted bilayer graphene
- Derivation of Wannier orbitals and minimal-basis tight-binding hamiltonians for twisted bilayer graphene: a first-principles approach
- Heavy fermion representation for twisted bilayer graphene systems
- Kondo Lattice Model of Magic-Angle Twisted-Bilayer Graphene: Hund's Rule, Local-Moment Fluctuations, and Low-Energy Effective Theory
- Effective field theory, three-loop perturbative expansion, and their experimental implications in graphene many-body effects
- Superconductivity in Twisted Double Bilayer Graphene Stabilized by WSe
- Heavy quasiparticles and cascades without symmetry breaking in twisted bilayer graphene
- Interactions in the 8-orbital model for twisted bilayer graphene
- Symmetric Kondo Lattice States in Doped Strained Twisted Bilayer Graphene
- Spontaneous time-reversal symmetry breaking in twisted double bilayer graphene
- Dynamical correlations and order in magic-angle twisted bilayer graphene
- Magic-Angle Twisted Symmetric Trilayer Graphene as Topological Heavy Fermion Problem
- Kondo Phase in Twisted Bilayer Graphene -- A Unified Theory for Distinct Experiments
- TBG as Topological Heavy Fermion: II. Analytical approximations of the model parameters
- Topological Mixed Valence Model for Twisted Bilayer Graphene
- Nonlocal Moments in the Chern Bands of Twisted Bilayer Graphene
- Scaling theory of intrinsic Kondo and Hund's rule interactions in magic-angle twisted bilayer graphene
- Topological Mixed Valence Model in Magic-Angle Twisted Bilayer Graphene
- Fractional Chern insulator candidate in twisted bilayer checkboard lattice
- Symmetry-based classification of exact flat bands in single and bilayer moiré systems
- Nonflat bands and chiral symmetry in magic-angle twisted bilayer graphene