- Open Access
Flat-band driven Kondo breakdown and reentrant effects in heavy-fermion moiré superlattices
Phys. Rev. B 113, 235153 – Published 26 June, 2026
DOI: https://doi.org/10.1103/85vr-blw1
Abstract
Moiré superlattices (MSLs) in van der Waals heterostructures have demonstrated their incredible power in driving emergent electronic phenomena, some of which are reminiscent of those usually only observed in bulk strongly correlated quantum materials. With the recent discovery of van der Waals -electron materials, the design of novel MSLs of intrinsic strong correlation is now within the reach. Here we study the novel electron phases of two-dimensional heavy-fermion MSL with increasingly diluted -electron local moments. By applying dynamical mean-field theory with numerical renormalization group as an impurity solver, we demonstrate the appearance of a different energy scale and a reentrant Kondo breakdown in connection with the emergence of a flat band in the system. We further compare our numerical findings with predictions derived from the Lieb-Mattis theorem and show the necessity of this energy scale to consistently reconcile the predictions with the conventional single-impurity limit for exceedingly large unit cells.
Physics Subject Headings (PhySH)
Article Text
References (77)
- N. Grewe, One particle excitation spectrum of the Kondo-lattice, Solid State Commun. 50, 19 (1984).
- F. Steglich, J. Aarts, C. D. Bredl, W. Lieke, D. Meschede, W. Franz, and H. Schäfer, Superconductivity in the presence of strong Pauli paramagnetism: , Phys. Rev. Lett. 43, 1892 (1979).
- H. v. Löhneysen, A. Rosch, M. Vojta, and P. Wölfle, Fermi-liquid instabilities at magnetic quantum phase transitions, Rev. Mod. Phys. 79, 1015 (2007).
- P. Gegenwart, Q. Si, and F. Steglich, Quantum criticality in heavy-fermion metals, Nat. Phys. 4, 186 (2008).
- S. Doniach, The Kondo lattice and weak antiferromagnetism, Physica B+C 91, 231 (1977).
- O. Trovarelli, C. Geibel, S. Mederle, C. Langhammer, F. M. Grosche, P. Gegenwart, M. Lang, G. Sparn, and F. Steglich, : Pronounced non-fermi-liquid effects above a low-lying magnetic phase transition, Phys. Rev. Lett. 85, 626 (2000).
- O. Stockert, H. V. Löhneysen, A. Rosch, N. Pyka, and M. Loewenhaupt, Two-Dimensional Fluctuations at the Quantum-Critical Point of , Phys. Rev. Lett. 80, 5627 (1998).
- H. R. Krishna-murthy, J. W. Wilkins, and K. G. Wilson, Renormalization-group approach to the Anderson model of dilute magnetic alloys. II. Static properties for the asymmetric case, Phys. Rev. B 21, 1044 (1980).
- K. G. Wilson, The renormalization group and critical phenomena, Rev. Mod. Phys. 55, 583 (1983).
- T. Pruschke, R. Bulla, and M. Jarrell, Low-energy scale of the periodic Anderson model, Phys. Rev. B 61, 12799 (2000).
- H. Kang, K. Haule, G. Kotliar, P. Coleman, and J.-H. Shim, Energy scales of the doped Anderson lattice model, Phys. Rev. B 99, 165115 (2019).
- A. Hewson, The Kondo Problem to Heavy Fermions (Cambridge University Press, Cambridge, 1993).
- L. A. Ponomarenko, R. V. Gorbachev, et al., Cloning of Dirac fermions in graphene superlattices, Nature (London) 497, 594 (2013).
- C. R. Dean, L. Wang, et al., Hofstadter's butterfly and the fractal quantum Hall effect in moiré superlattices, Nature (London) 497, 598 (2013).
- B. Hunt, J. D. Sanchez-Yamagishi, et al., Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure, Science 340, 1427 (2013).
- G. L. Yu, R. V. Gorbachev, et al., Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices, Nat. Phys. 10, 525 (2014).
- L. Wang, Y. Gao, et al., Evidence for a fractional fractal quantum Hall effect in graphene superlattices, Science 350, 1231 (2015).
- R. Krishna Kumar, X. Chen, et al., High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices, Science 357, 181 (2017).
- Y. Cao, V. Fatemi, et al., Unconventional superconductivity in magic-angle graphene superlattices, Nature (London) 556, 43 (2018).
- M. Yankowitz, S. Chen, et al. Tuning superconductivity in twisted bilayer graphene, Science 363, 1059 (2019).
- G. Chen, A. L. Sharpe, et al., Signatures of tunable superconductivity in a trilayer graphene moiré superlattice, Nature (London) 572, 215 (2019).
- Y. Cao, V. Fatemi, et al., Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature (London) 556, 80 (2018).
- L. Wang, E.-M. Shih, et al., Correlated electronic phases in twisted bilayer transition metal dichalcogenides, Nat. Mater. 19, 861 (2020).
- R. Celotta, S. B. Balakirsky, et al., Autonomous assembly of atomically perfect nanostructures using a scanning tunneling microscope, Rev. Sci. Instrum. 85, 121301 (2014).
- B. Jang, C. Lee, J.-X. Zhu, and J. H. Shim, Exploring two-dimensional van der Waals heavy-fermion material: Data mining theoretical approach, npj 2D Mater. Appl. 6, 80 (2022).
- V. A. Posey, S. Turkel, et al., Two-dimensional heavy fermions in the van der waals metal cesii, Nature (London) 625, 483 (2024).
- W. Zhao, B. Shen, Z. Tao, Z. Han, K. Kang, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Gate-tunable heavy fermions in a moiré kondo lattice, Nature (London) 616, 61 (2023).
- A. Ramires and J. L. Lado, Emulating heavy fermions in twisted trilayer graphene, Phys. Rev. Lett. 127, 026401 (2021).
- V. Vaňo, M. Amini, S. C. Ganguli, G. Chen, J. L. Lado, S. Kezilebieke, and P. Liljeroth, Artificial heavy fermions in a van der Waals heterostructure, Nature (London) 599, 582 (2021).
- 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).
- G. Kotliar and D. Vollhardt, Strongly correlated materials: Insights From Dynamical Mean-Field Theory, Phys. Today 57(3), 53 (2004).
- G. Diniz, G. S. Diniz, G. B. Martins, and E. Vernek, Reentrant Kondo effect for a quantum impurity coupled to a metal-semiconductor hybrid contact, Phys. Rev. B 101, 125115 (2020).
- P. Zalom and T. Novotný, Tunable reentrant Kondo effect in quantum dots coupled to metal-superconducting hybrid reservoirs, Phys. Rev. B 104, 035437 (2021).
- D. Guerci, J. Wang, J. Zang, J. Cano, J. H. Pixley, and A. Millis, Chiral Kondo lattice in doped bilayers, Sci. Adv. 9, eade7701 (2023).
- Z.-D. Song and B. A. Bernevig, Magic-angle twisted bilayer graphene as a topological heavy fermion problem, Phys. Rev. Lett. 129, 047601 (2022).
- H. Shi and X. Dai, Heavy-fermion representation for twisted bilayer graphene systems, Phys. Rev. B 106, 245129 (2022).
- H. Hu, B. A. Bernevig, and A. M. Tsvelik, Kondo lattice model of magic-angle twisted-bilayer graphene: Hund's rule, local-moment fluctuations, and low-energy effective theory, Phys. Rev. Lett. 131, 026502 (2023).
- Y.-Z. Chou and S. Das Sarma, Kondo lattice model in magic-angle twisted bilayer graphene, Phys. Rev. Lett. 131, 026501 (2023).
- 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).
- R. L. Merino, D. Călugăru, H. Hu, J. Díez-Mérida, A. Díez-Carlón, T. Taniguchi, K. Watanabe, P. Seifert, B. A. Bernevig, and D. K. Efetov, Interplay between light and heavy electron bands in magic-angle twisted bilayer graphene, Nat. Phys. 21, 1078 (2025).
- 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.
- D. Călugăru, H. Hu, R. L. Merino, N. Regnault, D. K. Efetov, and B. A. Bernevig, The thermoelectric effect and its natural heavy fermion explanation in twisted bilayer and trilayer graphene, arXiv:2402.14057.
- R. L. Merino, D. Calugaru, H. Hu, J. Diez-Merida, A. Diez-Carlon, T. Taniguchi, K. Watanabe, P. Seifert, B. A. Bernevig, and D. K. Efetov, Evidence of heavy fermion physics in the thermoelectric transport of magic angle twisted bilayer graphene, arXiv:2402.11749.
- S. Batlle-Porro, D. Calugaru, H. Hu, R. K. Kumar, N. C. H. Hesp, K. Watanabe, T. Taniguchi, B. A. Bernevig, P. Stepanov, and F. H. L. Koppens, Cryo-near-field photovoltage microscopy of heavy-fermion twisted symmetric trilayer graphene, arXiv:2402.12296.
- R. Žitko and T. Pruschke, Energy resolution and discretization artifacts in the numerical renormalization group, Phys. Rev. B 79, 085106 (2009).
- R. Zitko, NRG Ljubljana (8f90ac4), Zenodo (2021), https://doi.org/10.5281/zenodo.4841076.
- O. Parcollet, M. Ferrero, T. Ayral, H. Hafermann, I. Krivenko, L. Messio, and P. Seth, TRIQS: A toolbox for research on interacting quantum systems, Comput. Phys. Commun. 196, 398 (2015).
- W. C. Oliveira and L. N. Oliveira, Generalized numerical renormalization-group method to calculate the thermodynamical properties of impurities in metals, Phys. Rev. B 49, 11986 (1994).
- R. Peters, T. Pruschke, and F. B. Anders, Numerical renormalization group approach to Green's functions for quantum impurity models, Phys. Rev. B 74, 245114 (2006).
- A. Weichselbaum and J. von Delft, Sum-rule conserving spectral functions from the numerical renormalization group, Phys. Rev. Lett. 99, 076402 (2007).
- R. Bulla, A. C. Hewson, and T. Pruschke, Numerical renormalization group calculations for the self-energy of the impurity Anderson model, J. Phys.: Condens. Matter 10, 8365 (1998).
- E. Lieb and D. Mattis, Ordering energy levels of interacting spin systems, J. Math. Phys. 3, 749 (1962).
- S.-Q. Shen, Total spin and antiferromagnetic correlation in the Kondo model, Phys. Rev. B 53, 14252 (1996).
- I. Titvinidze, A. Schwabe, and M. Potthoff, Ferromagnetism of magnetic impurities coupled indirectly via conduction electrons: Insights from various theoretical approaches, Phys. Rev. B 90, 045112 (2014).
- A. K. Zhuravlev, Negative impurity magnetic susceptibility and heat capacity in a Kondo model with narrow peaks in the local density of electron states, Phys. Met. Metall. 108, 107 (2009).
- F. Eickhoff and F. B. Anders, Kondo breakdown in multi-orbital Anderson lattices induced by destructive hybridization interference, SciPost Phys. 17, 069 (2024).
- D. Withoff and E. Fradkin, Phase transitions in gapless Fermi systems with magnetic impurities, Phys. Rev. Lett. 64, 1835 (1990).
- R. Bulla, T. Pruschke, and A. C. Hewson, Anderson impurity in pseudo-gap Fermi systems, J. Phys.: Condens. Matter 9, 10463 (1997).
- C. R. Cassanello and E. Fradkin, Kondo effect in flux phases, Phys. Rev. B 53, 15079 (1996).
- C. Gonzalez-Buxton and K. Ingersent, Renormalization-group study of Anderson and Kondo impurities in gapless Fermi systems, Phys. Rev. B 57, 14254 (1998).
- M. Vojta and R. Bulla, Kondo effect of impurity moments in -wave superconductors: Quantum phase transition and spectral properties, Phys. Rev. B 65, 014511 (2001).
- K. Ingersent and Q. Si, Critical local-moment fluctuations, anomalous exponents, and scaling in the kondo problem with a pseudogap, Phys. Rev. Lett. 89, 076403 (2002).
- L. Fritz and M. Vojta, Phase transitions in the pseudogap Anderson and Kondo models: Critical dimensions, renormalization group, and local-moment criticality, Phys. Rev. B 70, 214427 (2004).
- M. Vojta, Impurity quantum phase transitions, Philos. Mag. 86, 1807 (2006).
- A. Schröder, G. Aeppli, R. Coldea, M. Adams, O. Stockert, H. Löhneysen, E. Bucher, R. Ramazashvili, and P. Coleman, Onset of antiferromagnetism in heavy-fermion metals, Nature (London) 407, 351 (2000).
- F. Eickhoff and F. B. Anders, Strongly correlated multi-impurity models: The crossover from a single-impurity problem to lattice models, Phys. Rev. B 102, 205132 (2020).
- I. Affleck, The Kondo screening cloud: What it is and how to observe it, in Perspectives of Mesoscopic Physics (World Scientific, Singapore, 2010), pp. 1–44.
- I. V. Borzenets, J. Shim, J. C. H. Chen, A. Ludwig, A. D. Wieck, S. Tarucha, H.-S. Sim, and M. Yamamoto, Observation of the Kondo screening cloud, Nature (London) 579, 210 (2020).
- A. K. Mitchell, P. G. Derry, and D. E. Logan, Multiple magnetic impurities on surfaces: Scattering and quasiparticle interference, Phys. Rev. B 91, 235127 (2015).
- F. Eickhoff, J. Zhu, and B. Fauseweh, Figure and data for flat-band driven Kondo breakdown and reentrant effects in heavy-fermion moiré superlattices, Zenodo (2025), https://doi.org/10.5281/zenodo.14843480.
- J. Sherman and W. J. Morrison, Adjustment of an inverse matrix corresponding to a change in one element of a given matrix, Ann. Math. Stat. 21, 124 (1950).
- H. Lee, E. Plekhanov, D. Blackbourn, S. Acharya, and C. Weber, The Mott to Kondo transition in diluted Kondo superlattices, Commun. Phys. 2, 49 (2019).
- F. Eickhoff, Power-law spectra and asymptotic scaling in the orbital-selective Mott phase of a three-orbital Hubbard model, SciPost Phys. 20, 050 (2026).
- R. Bulla and M. Potthoff, “linearized” dynamical mean-field theory for the mott-hubbard transition, Eur. Phys. J. B 13, 257 (2000).
- M. A. Ruderman and C. Kittel, Indirect exchange coupling of nuclear magnetic moments by conduction electrons, Phys. Rev. 96, 99 (1954).
- T. Kasuya, A theory of metallic ferro- and antiferromagnetism on Zener's model, Prog. Theor. Phys. 16, 45 (1956),.
- F. Eickhoff, B. Lechtenberg, and F. B. Anders, Effective low-energy description of the two-impurity Anderson model: RKKY interaction and quantum criticality, Phys. Rev. B 98, 115103 (2018).