Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).
Zhang, C. et al. Interlayer couplings, Moiré patterns, and 2D electronic superlattices in MoS2/WSe2 hetero-bilayers. Sci. Adv. 3, e1601459 (2017).
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
Jin, C. et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019).
Tran, K. et al. Evidence for moiré excitons in van der Waals heterostructures. Nature 567, 71–75 (2019).
Seyler, K. L. et al. Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers. Nature 567, 66–70 (2019).
Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).
Zhang, Z. et al. Flat bands in twisted bilayer transition metal dichalcogenides. Nat. Phys. 16, 1093–1096 (2020).
Zhang, L. et al. Twist-angle dependence of moiré excitons in WS2/MoSe2 heterobilayers. Nat. Commun. 11, 5888 (2020).
Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).
Xie, Y. et al. Fractional Chern insulators in magic-angle twisted bilayer graphene. Nature 600, 439–443 (2021).
Li, H. et al. Imaging moiré flat bands in three-dimensional reconstructed WSe2/WS2 superlattices. Nat. Mater. 20, 945–950 (2021).
Bai, Y. et al. Excitons in strain-induced one-dimensional moiré potentials at transition metal dichalcogenide heterojunctions. Nat. Mater. 19, 1068–1073 (2020).
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).
Oh, M. et al. Evidence for unconventional superconductivity in twisted bilayer graphene. Nature 600, 240–245 (2021).
Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641–646 (2021).
Choi, Y. et al. Correlation-driven topological phases in magic-angle twisted bilayer graphene. Nature 589, 536–541 (2021).
Wang, X. et al. Interfacial ferroelectricity in rhombohedral-stacked bilayer transition metal dichalcogenides. Nat. Nanotechnol. 17, 367–371 (2022).
Törmä, P., Peotta, S. & Bernevig, B. A. Superconductivity, superfluidity and quantum geometry in twisted multilayer systems. Nat. Rev. Phys. 4, 528–542 (2022).
Weston, A. et al. Interfacial ferroelectricity in marginally twisted 2D semiconductors. Nat. Nanotechnol. 17, 390–395 (2022).
Rozhkov, A. V., Sboychakov, A. O., Rakhmanov, A. L. & Nori, F. Electronic properties of graphene-based bilayer systems. Phys. Rep. 648, 1–104 (2016).
Lopes dos Santos, J. M. B., Peres, N. M. R. & Castro Neto, A. H. Continuum model of the twisted graphene bilayer. Phys. Rev. B 86, 155449 (2012).
Mele, E. J. Commensuration and interlayer coherence in twisted bilayer graphene. Phys. Rev. B 81, 161405 (2010).
Sboychakov, A. O., Rakhmanov, A. L., Rozhkov, A. V. & Nori, F. Electronic spectrum of twisted bilayer graphene. Phys. Rev. B 92, 075402 (2015).
Rozhkov, A. V., Sboychakov, A. O., Rakhmanov, A. L. & Nori, F. Single-electron gap in the spectrum of twisted bilayer graphene. Phys. Rev. B 95, 045119 (2017).
Ahn, S. J. et al. Dirac electrons in a dodecagonal graphene quasicrystal. Science 361, 782–786 (2018).
Yao, W. et al. Quasicrystalline 30° twisted bilayer graphene as an incommensurate superlattice with strong interlayer coupling. Proc. Natl Acad. Sci. USA 115, 6928–6933 (2018).
Pezzini, S. et al. 30°-twisted bilayer graphene quasicrystals from chemical vapor deposition. Nano Lett. 20, 3313–3319 (2020).
Nguyen, P. V. et al. Visualizing electrostatic gating effects in two-dimensional heterostructures. Nature 572, 220–223 (2019).
Bisri, S. Z., Shimizu, S., Nakano, M. & Iwasa, Y. Endeavor of iontronics: from fundamentals to applications of ion‐controlled electronics. Adv. Mater. 29, 1607054 (2017).
Zhang, C. et al. Probing critical point energies of transition metal dichalcogenides: surprising indirect gap of single layer WSe2. Nano Lett. 15, 6494–6500 (2015).
Koren, E. et al. Coherent commensurate electronic states at the interface between misoriented graphene layers. Nat. Nanotechnol. 11, 752–757 (2016).
Inbar, A. et al. The quantum twisting microscope. Nature 614, 682–687 (2023).
Chari, T., Ribeiro-Palau, R., Dean, C. R. & Shepard, K. Resistivity of rotated graphite–graphene contacts. Nano Lett. 16, 4477–4482 (2016).
Zhao, X. et al. Strong moiré excitons in high-angle twisted transition metal dichalcogenide homobilayers with robust commensuration. Nano Lett. 22, 203–210 (2022).
Weston, A. et al. Atomic reconstruction in twisted bilayers of transition metal dichalcogenides. Nat. Nanotechnol. 15, 592–597 (2020).
McCreary, K. M. et al. Stacking-dependent optical properties in bilayer WSe2. Nanoscale 14, 147–156 (2022).
Hsu, W.-T. et al. Quantitative determination of interlayer electronic coupling at various critical points in bilayer MoS2. Phys. Rev. B 106, 125302 (2022).
Hsu, W.-T. et al. Tailoring excitonic states of van der Waals bilayers through stacking configuration, band alignment, and valley spin. Sci. Adv. 5, eaax7407 (2019).
Zhang, Y., Devakul, T. & Fu, L. Spin-textured Chern bands in AB-stacked transition metal dichalcogenide bilayers. Proc. Natl Acad. Sci. USA 118, e2112673118 (2021).
Uri, A. et al. Superconductivity and strong interactions in a tunable moiré quasicrystal. Nature 620, 762–767 (2023).
Lin, Y.-C. et al. Realizing large-scale, electronic-grade two-dimensional semiconductors. ACS Nano 12, 965–975 (2018).
Giannozzi, P. et al. Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).
Giannozzi, P. et al. Advanced capabilities for materials modelling with Quantum ESPRESSO. J. Phys. Condens. Matter 29, 465901 (2017).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Hamann, D. R. Optimized norm-conserving Vanderbilt pseudopotentials. Phys. Rev. B 88, 085117 (2013).
van Setten, M. J. et al. The PseudoDojo: training and grading a 85 element optimized norm-conserving pseudopotential table. Comput. Phys. Commun. 226, 39–54 (2018).
Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H–Pu. J. Chem. Phys. 132, 154104 (2010).
Medeiros, P. V. C., Stafström, S. & Björk, J. Effects of extrinsic and intrinsic perturbations on the electronic structure of graphene: retaining an effective primitive cell band structure by band unfolding. Phys. Rev. B 89, 041407 (2014).
Medeiros, P. V. C., Tsirkin, S. S., Stafström, S. & Björk, J. Unfolding spinor wave functions and expectation values of general operators: introducing the unfolding-density operator. Phys. Rev. B 91, 041116 (2015).
Iraola, M. et al. IrRep: symmetry eigenvalues and irreducible representations of ab initio band structures. Comput. Phys. Commun. 272, 108226 (2022).
Dr. Thomas Hughes is a UK-based scientist and science communicator who makes complex topics accessible to readers. His articles explore breakthroughs in various scientific disciplines, from space exploration to cutting-edge research.
