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Interplay between many-body correlations, strain, and lattice relaxation in twisted bilayer graphene
Phys. Rev. B 113, L241112 – Published 17 June, 2026
DOI: https://doi.org/10.1103/x2mz-hm8y
Abstract
In twisted bilayer graphene, a unified understanding of the mechanisms governing temperature-dependent electronic spectra and thermodynamic properties remains controversial despite extensive theoretical efforts. Here, we present a comprehensive theoretical framework that quantitatively accounts for scanning tunneling spectroscopy, quantum twisting microscopy, and thermodynamic properties of magic angle twisted bilayer graphene. We demonstrate that the observed behavior arises from the interplay between electron correlations and external symmetry breaking induced by strain and lattice relaxation. These effects act cooperatively to shape the emergent electronic behavior, leaving characteristic signatures across spectroscopy, compressibility, and entropy.
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References (56)
- K. P. Nuckolls, R. L. Lee, M. Oh, D. Wong, T. Soejima, J. P. Hong, D. Călugăru, J. Herzog-Arbeitman, B. A. Bernevig, K. Watanabe, T. Taniguchi, N. Regnault, M. P. Zaletel, and A. Yazdani, Quantum textures of the many-body wavefunctions in magic-angle graphene, Nature (London) 620, 525 (2023).
- A. Kerelsky, L. J. McGilly, D. M. Kennes, L. Xian, M. Yankowitz, S. Chen, K. Watanabe, T. Taniguchi, J. Hone, C. Dean, A. Rubio, and A. N. Pasupathy, Maximized electron interactions at the magic angle in twisted bilayer graphene, Nature (London) 572, 95 (2019).
- S. Turkel, J. Swann, Z. Zhu, M. Christos, K. Watanabe, T. Taniguchi, S. Sachdev, M. S. Scheurer, E. Kaxiras, C. R. Dean, and A. N. Pasupathy, Orderly disorder in magic-angle twisted trilayer graphene, Science 376, 193 (2022).
- N. P. Kazmierczak, M. Van Winkle, C. Ophus, K. C. Bustillo, S. Carr, H. G. Brown, J. Ciston, T. Taniguchi, K. Watanabe, and D. K. Bediako, Strain fields in twisted bilayer graphene, Nat. Mater. 20, 956 (2021).
- Z. Zhang, S. Wu, D. Călugăru, H. Hu, T. Taniguchi, K. Wanatabe, A. B. Bernevig, and E. Y. Andrei, Heavy fermions, mass renormalization and local moments in magic-angle twisted bilayer graphene via planar tunneling spectroscopy, arXiv:2503.17875.
- Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature (London) 556, 80 (2018).
- K. P. Nuckolls, M. Oh, D. Wong, B. Lian, K. Watanabe, T. Taniguchi, B. A. Bernevig, and A. Yazdani, Strongly correlated Chern insulators in magic-angle twisted bilayer graphene, Nature (London) 588, 610 (2020).
- P. Stepanov, M. Xie, T. Taniguchi, K. Watanabe, X. Lu, A. H. MacDonald, B. A. Bernevig, and D. K. Efetov, Competing zero-field Chern insulators in superconducting twisted bilayer graphene, Phys. Rev. Lett. 127, 197701 (2021).
- D. Wong, K. P. Nuckolls, M. Oh, B. Lian, Y. Xie, S. Jeon, K. Watanabe, T. Taniguchi, B. A. Bernevig, and A. Yazdani, Cascade of electronic transitions in magic-angle twisted bilayer graphene, Nature (London) 582, 198 (2020).
- Y. Xie, B. Lian, B. Jäck, X. Liu, C.-L. Chiu, K. Watanabe, T. Taniguchi, B. A. Bernevig, and A. Yazdani, Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene, Nature (London) 572, 101 (2019).
- Y. Choi, J. Kemmer, Y. Peng, A. Thomson, H. Arora, R. Polski, Y. Zhang, H. Ren, J. Alicea, G. Refael, F. von Oppen, K. Watanabe, T. Taniguchi, and S. Nadj-Perge, Electronic correlations in twisted bilayer graphene near the magic angle, Nat. Phys. 15, 1174 (2019).
- Z. Hao, A. M. Zimmerman, P. Ledwith, E. Khalaf, D. H. Najafabadi, K. Watanabe, T. Taniguchi, A. Vishwanath, and P. Kim, Electric field–tunable superconductivity in alternating-twist magic-angle trilayer graphene, Science 371, 1133 (2021).
- J. Yu, B. A. Foutty, Y. H. Kwan, M. E. Barber, K. Watanabe, T. Taniguchi, Z.-X. Shen, S. A. Parameswaran, and B. E. Feldman, Spin skyrmion gaps as signatures of strong-coupling insulators in magic-angle twisted bilayer graphene, Nat. Commun. 14, 6679 (2023).
- R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, Proc. Natl. Acad. Sci. USA 108, 12233 (2011).
- J. Herzog-Arbeitman, J. Yu, D. Calugaru, H. Hu, N. Regnault, O. Vafek, J. Kang, and B. A. Bernevig, Topological heavy fermion model as an efficient representation of atomistic strain and relaxation in twisted bilayer graphene, Phys. Rev. B 112, 125128 (2025).
- J. Xiao, A. Inbar, J. Birkbeck, N. Gershon, Y. Zamir, Y. Vituri, T. Taniguchi, K. Watanabe, E. Berg, and S. Ilani, Imaging the flat bands of magic-angle graphene reshaped by interactions, Nature (London) 653, 68 (2026).
- A. Rozen, J. M. Park, U. Zondiner, Y. Cao, D. Rodan-Legrain, T. Taniguchi, K. Watanabe, Y. Oreg, A. Stern, E. Berg, P. Jarillo-Herrero, and S. Ilani, Entropic evidence for a Pomeranchuk effect in magic-angle graphene, Nature (London) 592, 214 (2021).
- Y. Saito, F. Yang, J. Ge, X. Liu, T. Taniguchi, K. Watanabe, J. I. A. Li, E. Berg, and A. F. Young, Isospin Pomeranchuk effect in twisted bilayer graphene, Nature (London) 592, 220 (2021).
- I. Das, X. Lu, J. Herzog-Arbeitman, Z.-D. Song, K. Watanabe, T. Taniguchi, B. A. Bernevig, and D. K. Efetov, Symmetry-broken Chern insulators and Rashba-like Landau-level crossings in magic-angle bilayer graphene, Nat. Phys. 17, 710 (2021).
- A. T. Pierce, Y. Xie, J. M. Park, E. Khalaf, S. H. Lee, Y. Cao, D. E. Parker, P. R. Forrester, S. Chen, K. Watanabe, T. Taniguchi, A. Vishwanath, P. Jarillo-Herrero, and A. Yacoby, Unconventional sequence of correlated Chern insulators in magic-angle twisted bilayer graphene, Nat. Phys. 17, 1210 (2021).
- Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices, Nature (London) 556, 43 (2018).
- X. Lu, P. Stepanov, W. Yang, M. Xie, M. A. Aamir, I. Das, C. Urgell, K. Watanabe, T. Taniguchi, G. Zhang, A. Bachtold, A. H. MacDonald, and D. K. Efetov, Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene, Nature (London) 574, 653 (2019).
- M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watanabe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, Tuning superconductivity in twisted bilayer graphene, Science 363, 1059 (2019).
- Z.-D. Song and B. A. Bernevig, Magic-angle twisted bilayer graphene as a topological heavy fermion problem, Phys. Rev. Lett. 129, 047601 (2022).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/x2mz-hm8y for additional information on the model, solution method, and interplay between strain and level splitting, which includes Refs. [52, 53, 54, 55, 56].
- S. Carr, D. Massatt, S. B. Torrisi, P. Cazeaux, M. Luskin, and E. Kaxiras, Relaxation and domain formation in incommensurate two-dimensional heterostructures, Phys. Rev. B 98, 224102 (2018).
- O. Vafek and J. Kang, Continuum effective Hamiltonian for graphene bilayers for an arbitrary smooth lattice deformation from microscopic theories, Phys. Rev. B 107, 075123 (2023).
- J. Kang and O. Vafek, Analytical solution for the relaxed atomic configuration of twisted bilayer graphene including heterostrain, Phys. Rev. B 112, 125138 (2025).
- G. Rai, L. Crippa, D. Călugăru, H. Hu, F. Paoletti, L. de' Medici, A. Georges, B. A. Bernevig, R. Valentí, G. Sangiovanni, and T. Wehling, Dynamical correlations and order in magic-angle twisted bilayer graphene, Phys. Rev. X 14, 031045 (2024).
- A. Datta, M. J. Calderón, A. Camjayi, and E. Bascones, Heavy quasiparticles and cascades without symmetry breaking in twisted bilayer graphene, Nat. Commun. 14, 5036 (2023).
- H. Hu, G. Rai, L. Crippa, J. Herzog-Arbeitman, D. Călugăru, T. Wehling, G. Sangiovanni, R. Valentí, A. M. Tsvelik, and B. A. Bernevig, Symmetric Kondo lattice states in doped strained twisted bilayer graphene, Phys. Rev. Lett. 131, 166501 (2023).
- M. Wallerberger, A. Hausoel, P. Gunacker, A. Kowalski, N. Parragh, F. Goth, K. Held, and G. Sangiovanni, W2dynamics: Local one- and two-particle quantities from dynamical mean field theory, Comput. Phys. Commun. 235, 388 (2019).
- H. Kim, Y. Choi, É. Lantagne-Hurtubise, C. Lewandowski, A. Thomson, L. Kong, H. Zhou, E. Baum, Y. Zhang, L. Holleis, K. Watanabe, T. Taniguchi, A. F. Young, J. Alicea, and S. Nadj-Perge, Imaging inter-valley coherent order in magic-angle twisted trilayer graphene, Nature (London) 623, 942 (2023).
- X.-F. Zhou, Y.-W. Liu, C.-Y. Hao, C. Yan, Q. Zheng, Y.-N. Ren, Y.-X. Zhao, K. Watanabe, T. Taniguchi, and L. He, Coexistence of reconstructed and unreconstructed structures in the structural transition regime of twisted bilayer graphene, Phys. Rev. B 107, 125410 (2023).
- A. Inbar, J. Birkbeck, J. Xiao, T. Taniguchi, K. Watanabe, B. Yan, Y. Oreg, A. Stern, E. Berg, and S. Ilani, The quantum twisting microscope, Nature (London) 614, 682 (2023).
- M. Lee, I. Das, J. Herzog-Arbeitman, J. Papp, J. Li, M. Daschner, Z. Zhou, M. Bhatt, M. Currle, J. Yu, Y. Jiang, M. Becherer, R. Mittermeier, P. Altpeter, C. Obermayer, H. Lorenz, G. Chavez, B. T. Le, J. Williams, K. Watanabe, et al., Revealing electron-electron interactions in graphene at room temperature with the quantum twisting microscope, Nano Lett. 26, 4046 (2026).
- U. Zondiner, A. Rozen, D. Rodan-Legrain, Y. Cao, R. Queiroz, T. Taniguchi, K. Watanabe, Y. Oreg, F. von Oppen, A. Stern, E. Berg, P. Jarillo-Herrero, and S. Ilani, Cascade of phase transitions and Dirac revivals in magic-angle graphene, Nature (London) 582, 203 (2020).
- P. Stepanov, I. Das, X. Lu, A. Fahimniya, K. Watanabe, T. Taniguchi, F. H. L. Koppens, J. Lischner, L. Levitov, and D. K. Efetov, Untying the insulating and superconducting orders in magic-angle graphene, Nature (London) 583, 375 (2020).
- Y. Saito, J. Ge, K. Watanabe, T. Taniguchi, and A. F. Young, Independent superconductors and correlated insulators in twisted bilayer graphene, Nat. Phys. 16, 926 (2020).
- Y. H. Kwan, G. Wagner, T. Soejima, M. P. Zaletel, S. H. Simon, S. A. Parameswaran, and N. Bultinck, Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene, Phys. Rev. X 11, 041063 (2021).
- G. Wagner, Y. H. Kwan, N. Bultinck, S. H. Simon, and S. A. Parameswaran, Global phase diagram of the normal state of twisted bilayer graphene, Phys. Rev. Lett. 128, 156401 (2022).
- L. Rademaker, D. A. Abanin, and P. Mellado, Charge smoothening and band flattening due to Hartree corrections in twisted bilayer graphene, Phys. Rev. B 100, 205114 (2019).
- J. Zhu, I. Torre, M. Polini, and A. H. MacDonald, Weak-coupling theory of magic-angle twisted bilayer graphene, Phys. Rev. B 110, L121117 (2024).
- M. Xie and A. H. MacDonald, Weak-field Hall resistivity and spin-valley flavor symmetry breaking in magic-angle twisted bilayer graphene, Phys. Rev. Lett. 127, 196401 (2021).
- N. Bultinck, E. Khalaf, S. Liu, S. Chatterjee, A. Vishwanath, and M. P. Zaletel, Ground state and hidden symmetry of magic-angle graphene at even integer filling, Phys. Rev. X 10, 031034 (2020).
- L. L. H. Lau and P. Coleman, Topological mixed valence model for twisted bilayer graphene, Phys. Rev. X 15, 021028 (2025).
- A. Ghosh, S. Chakraborty, R. Dutta, A. Agarwala, K. Watanabe, T. Taniguchi, S. Banerjee, N. Trivedi, S. Mukerjee, and A. Das, Thermopower probes of emergent local moments in magic-angle twisted bilayer graphene, Nat. Phys. 21, 732 (2025).
- J.-Y. Zhao, B. Zhou, and Y.-H. Zhang, Topological Mott localization and pseudogap metal in twisted bilayer graphene, Phys. Rev. B 112, 085107 (2025).
- P. J. Ledwith, J. Dong, A. Vishwanath, and E. Khalaf, Nonlocal moments in the Chern bands of twisted bilayer graphene, Phys. Rev. X 15, 021087 (2025).
- G.-D. Zhou, Y.-J. Wang, N. Tong, and Z.-D. Song, Kondo phase in twisted bilayer graphene, Phys. Rev. B 109, 045419 (2024).
- L. Crippa, Figure data for interplay between many-body correlations, strain and lattice relaxation in twisted bilayer graphene [Data set], Zenodo (2026), https://doi.org/10.5281/zenodo.20427082.
- J. Kaufmann and K. Held, ana_cont: Python package for analytic continuation, Comput. Phys. Commun. 282, 108519 (2023).
- N. Wagner, L. Crippa, A. Amaricci, P. Hansmann, M. Klett, E. J. König, T. Schäfer, D. D. Sante, J. Cano, A. J. Millis, A. Georges, and G. Sangiovanni, Mott insulators with boundary zeros, Nat. Commun. 14, 7531 (2023).
- H. Shinaoka, Y. Nomura, S. Biermann, M. Troyer, and P. Werner, Negative sign problem in continuous-time quantum Monte Carlo: Optimal choice of single-particle basis for impurity problems, Phys. Rev. B 92, 195126 (2015).
- A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions, Rev. Mod. Phys. 68, 13 (1996).
- E. Gull, A. J. Millis, A. I. Lichtenstein, A. N. Rubtsov, M. Troyer, and P. Werner, Continuous-time Monte Carlo methods for quantum impurity models, Rev. Mod. Phys. 83, 349 (2011).