Higher-dimensional Fermiology in bulk moiré metals
Mak, K. F. & Shan, J. Semiconductor moiré materials. Nat. Nanotechnol. 17, 686–695 (2022).Article
ADS
CAS
PubMed
Google Scholar
Nuckolls, K. P. & Yazdani, A. A microscopic perspective on moiré materials. Nat. Rev. Mater. 9, 460–480 (2024).Article
ADS
Google Scholar
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).Article
ADS
CAS
PubMed
Google Scholar
Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023).Article
ADS
CAS
PubMed
Google Scholar
Yasuda, K., Wang, X., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Stacking-engineered ferroelectricity in bilayer boron nitride. Science 372, 1458–1462 (2021).Article
ADS
CAS
Google Scholar
Vizner Stern, M. et al. Interfacial ferroelectricity by van der Waals sliding. Science 372, 1462–1466 (2021).Article
ADS
CAS
Google Scholar
Song, T. et al. Direct visualization of magnetic domains and moiré magnetism in twisted 2D magnets. Science 374, 1140–1144 (2021).Article
ADS
CAS
PubMed
Google Scholar
Zhao, S. Y. F. et al. Time-reversal symmetry breaking superconductivity between twisted cuprate superconductors. Science 382, 1422–1427 (2023).Article
ADS
CAS
PubMed
Google Scholar
Cummins, H. Z. Experimental studies of structurally incommensurate crystal phases. Phys. Rep. 185, 211–409 (1990).Article
ADS
CAS
Google Scholar
Smaalen, S. V. Incommensurate Crystallography (Oxford Univ. Press, 2007).Janssen, T., Chapuis, G. & de Boissieu, M. Aperiodic Crystals: From Modulated Phases to Quasicrystals: Structure and Properties 2nd edn (Oxford Univ. Press, 2018).Onsager, L. Interpretation of the de Haas-van Alphen effect. Lond. Edinb. Dublin Philos. Mag. J. Sci. 43, 1006–1008 (1952).Article
Google Scholar
Lifshitz, I. M. & Kosevich, A. M. On the theory of magnetic susceptibility of metals at low temperatures. Zh. Eksp. Teor. Fiz. 29, 730–742 (1955).
Google Scholar
Leeb, V., Huber, N., Pfleiderer, C., Knolle, J. & Wilde, M. A. A field guide to non-Onsager quantum oscillations in metals. Adv. Phys. Res. 4, 2400134 (2025).Article
Google Scholar
de Wolff, P. M. The pseudo-symmetry of modulated crystal structures. Acta Crystallogr. A 30, 777–785 (1974).Article
ADS
Google Scholar
Janner, A. & Janssen, T. Symmetry of periodically distorted crystals. Phys. Rev. B 15, 643–658 (1977).Article
ADS
CAS
Google Scholar
Hazzard, K. R. A. & Gadway, B. Synthetic dimensions. Phys. Today 76, 62–63 (2023).Article
Google Scholar
Ozawa, T. & Price, H. M. Topological quantum matter in synthetic dimensions. Nat. Rev. Phys. 1, 349–357 (2019).Article
Google Scholar
Sugawa, S., Salces-Carcoba, F., Perry, A. R., Yue, Y. & Spielman, I. B. Second Chern number of a quantum-simulated non-Abelian Yang monopole. Science 360, 1429–1434 (2018).Article
ADS
MathSciNet
CAS
PubMed
PubMed Central
Google Scholar
Sakai, S., Takemori, N., Koga, A. & Arita, R. Superconductivity on a quasiperiodic lattice: extended-to-localized crossover of Cooper pairs. Phys. Rev. B 95, 024509 (2017).Article
ADS
Google Scholar
Cao, Y. et al. Kohn-Luttinger mechanism driven exotic topological superconductivity on the Penrose lattice. Phys. Rev. Lett. 125, 017002 (2020).Article
ADS
MathSciNet
CAS
PubMed
Google Scholar
Evans, H. T. & Allmann, R. The crystal structure and crystal chemistry of valleriite. Z. Kristallogr. Cryst. Mater. 127, 73–93 (1968).Article
CAS
Google Scholar
Yadav, A. K. et al. Observation of polar vortices in oxide superlattices. Nature 530, 198–201 (2016).Article
ADS
CAS
PubMed
Google Scholar
Wiegers, G. A. Misfit layer compounds: structures and physical properties. Prog. Solid State Chem. 24, 1–139 (1996).Article
CAS
Google Scholar
Shechtman, D., Blech, I., Gratias, D. & Cahn, J. W. Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951–1953 (1984).Article
ADS
CAS
Google Scholar
Goldman, A. I. & Kelton, R. F. Quasicrystals and crystalline approximants. Rev. Mod. Phys. 65, 213–230 (1993).Article
ADS
Google Scholar
Bancel, P. A., Heiney, P. A., Stephens, P. W., Goldman, A. I. & Horn, P. M. Structure of rapidly quenched Al-Mn. Phys. Rev. Lett. 54, 2422–2425 (1985).Article
ADS
CAS
PubMed
Google Scholar
Zhang, Y., Maharaj, A. V. & Kivelson, S. Disruption of quantum oscillations by an incommensurate charge density wave. Phys. Rev. B 91, 085105 (2015).Article
ADS
Google Scholar
Suárez Morell, E., Correa, J. D., Vargas, P., Pacheco, M. & Barticevic, Z. Flat bands in slightly twisted bilayer graphene: tight-binding calculations. Phys. Rev. B 82, 121407 (2010).Article
ADS
Google Scholar
Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. 108, 12233–12237 (2011).Article
ADS
CAS
PubMed
PubMed Central
Google Scholar
Devarakonda, A. et al. Clean 2D superconductivity in a bulk van der Waals superlattice. Science 370, 231–236 (2020).Article
ADS
CAS
PubMed
Google Scholar
Ma, K. et al. Two-dimensional superconductivity in a bulk superlattice van der Waals material Ba6Nb11Se28. Phys. Rev. Mater. 6, 044806 (2022).Article
CAS
Google Scholar
Devarakonda, A. et al. Evidence of striped electronic phases in a structurally modulated superlattice. Nature 631, 526–530 (2024).Article
ADS
CAS
PubMed
Google Scholar
Yoo, H. et al. Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene. Nat. Mater. 18, 448–453 (2019).Article
ADS
CAS
PubMed
Google Scholar
Lau, C. N., Bockrath, M. W., Mak, K. F. & Zhang, F. Reproducibility in the fabrication and physics of moiré materials. Nature 602, 41–50 (2022).Article
ADS
CAS
PubMed
Google Scholar
Khasanova, N. R. et al. A new structure type of the ternary sulfide Eu1.3Nb1.9S5. J. Solid State Chem. 164, 345–353 (2002).Article
ADS
CAS
Google Scholar
Everson, M. P., Johnson, A., Lu, H.-A., Coleman, R. V. & Falicov, L. M. Magnetoquantum oscillations, magnetic breakdown, and Fermi-surface modifications in NbSe3. Phys. Rev. B. 36, 6953–6962 (1987).Article
ADS
CAS
Google Scholar
Hill, S. et al. Quantum limit and anomalous field-induced insulating behavior in η-Mo4O11. Phys. Rev. B. 55, 2018–2031 (1997).Article
ADS
CAS
Google Scholar
Huber, N. et al. Quantum oscillations of the quasiparticle lifetime in a metal. Nature 621, 276–281 (2023).Article
ADS
CAS
PubMed
Google Scholar
Gerhardts, R. R., Weiss, D. & Klitzing, K. V. Novel magnetoresistance oscillations in a periodically modulated two-dimensional electron gas. Phys. Rev. Lett. 62, 1173–1176 (1989).Article
ADS
CAS
PubMed
Google Scholar
Janssen, T. Aperiodic crystals: a contradictio in terminis? Phys. Rep. 168, 55–113 (1988).Article
ADS
MathSciNet
Google Scholar
Boada, O., Celi, A., Latorre, J. I. & Lewenstein, M. Quantum simulation of an extra dimension. Phys. Rev. Lett. 108, 133001 (2012).Article
ADS
CAS
PubMed
Google Scholar
Lohse, M., Schweizer, C., Price, H. M., Zilberberg, O. & Bloch, I. Exploring 4D quantum Hall physics with a 2D topological charge pump. Nature 553, 55–58 (2018).Article
ADS
CAS
PubMed
Google Scholar
Zilberberg, O. et al. Photonic topological boundary pumping as a probe of 4D quantum Hall physics. Nature 553, 59–62 (2018).Article
ADS
CAS
PubMed
Google Scholar
Lu, J. P. & Birman, J. L. Electronic structure of a quasiperiodic system. Phys. Rev. B. 36, 4471–4474 (1987).Article
ADS
CAS
Google Scholar
Batalla, E., Razavi, F. S. & Datars, W. R. Fermi surface of Hg3−δAsF6 and Hg3−δSbF6. Phys. Rev. B. 25, 2109–2118 (1982).Article
ADS
CAS
Google Scholar
Kawamoto, T. et al. Fermi surface of the organic superconductor (MDT–ST)(I3)0.417 reconstructed by incommensurate potential. Phys. Rev. B 73, 024503 (2006).Article
ADS
Google Scholar
Schnars, U. & Jüptner, W. Direct recording of holograms by a CCD target and numerical reconstruction. Appl. Opt. 33, 179–181 (1994).Article
ADS
CAS
PubMed
Google Scholar
Bousso, R. The holographic principle. Rev. Mod. Phys. 74, 825–874 (2002).Article
ADS
MathSciNet
Google Scholar
Pastawski, F., Yoshida, B., Harlow, D. & Preskill, J. Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence. J. High Energy Phys. 2015, 149 (2015).Article
MathSciNet
Google Scholar