Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).
Waters, D. et al. Flat bands and mechanical deformation effects in the moiré superlattice of MoS2-WSe2 heterobilayers. ACS Nano 14, 7564–7573 (2020).
Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).
Zhang, Z. et al. Flat bands in twisted bilayer transition metal dichalcogenides. Nat. Phys. 16, 1093–1096 (2020).
Li, H. et al. Imaging moiré flat bands in three-dimensional reconstructed WSe2/WS2 superlattices. Nat. Mater. 20, 945–950 (2021).
Ghiotto, A. et al. Quantum criticality in twisted transition metal dichalcogenides. Nature 597, 345–349 (2021).
Huang, X. et al. Correlated insulating states at fractional fillings of the WS2/WSe2 moiré lattice. Nat. Phys. 17, 715–719 (2021).
Anderson, E. et al. Programming correlated magnetic states via gate controlled moiré geometry. Science 381, 325–330 (2023).
Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023).
Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023).
Zeng, Y. et al. Thermodynamic evidence of fractional Chern insulator in moiré MoTe2. Nature 622, 69–73 (2023).
Xu, F. et al. Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2. Phys. Rev. X 13, 031037 (2023).
Kang, K. et al. Evidence of the fractional quantum spin Hall effect in moiré MoTe2. Nature 628, 522–526 (2024).
Park, H. et al. Ferromagnetism and topology of the higher flat band in a fractional Chern insulator. Nat. Phys. https://doi.org/10.1038/s41567-025-02804-0 (2025).
Xu, F. et al. Interplay between topology and correlations in the second moiré band of twisted bilayer MoTe2. Nat. Phys. https://doi.org/10.1038/s41567-025-02803-1 (2025).
Foutty, B. A. et al. Mapping twist-tuned multi-band topology in bilayer WSe2. Science 384, 343–347 (2024).
Li, H. et al. Imaging two-dimensional generalized Wigner crystals. Nature 597, 650–654 (2021).
Li, H. et al. Mapping charge excitations in generalized Wigner crystals. Nat. Nanotechnol. 19, 618–623 (2024).
Redekop, E. et al. Direct magnetic imaging of fractional Chern insulators in twisted MoTe2. Nature 635, 584–589 (2024).
Ji, Z. et al. Local probe of bulk and edge states in a fractional Chern insulator. Nature 635, 578–583 (2024).
Zhang, X.-W. et al. Polarization-driven band topology evolution in twisted MoTe2 and WSe2. Nat. Commun. 15, 4223 (2024).
Wu, F., Lovorn, T., Tutuc, E., Martin, I. & MacDonald, A. H. Topological insulators in twisted transition metal dichalcogenide homobilayers. Phys. Rev. Lett. 122, 086402 (2019).
Yu, H., Chen, M. & Yao, W. Giant magnetic field from moiré induced Berry phase in homobilayer semiconductors. Natl Sci. Rev. 7, 12–20 (2020).
Wang, X. et al. Interfacial ferroelectricity in rhombohedral-stacked bilayer transition metal dichalcogenides. Nat. Nanotechnol. 17, 367–371 (2022).
Molino, L. et al. Ferroelectric switching at symmetry-broken interfaces by local control of dislocations networks. Adv. Mater. 35, 2207816 (2023).
Zhang, S. et al. Visualizing moiré ferroelectricity via plasmons and nano-photocurrent in graphene/twisted-WSe2 structures. Nat. Commun. 14, 6200 (2023).
Duerloo, K.-A. N., Ong, M. T. & Reed, E. J. Intrinsic piezoelectricity in two-dimensional materials. J. Phys. Chem. Lett. 3, 2871–2876 (2012).
McGilly, L. J. et al. Visualization of moiré superlattices. Nat. Nanotechnol. 15, 580–584 (2020).
Enaldiev, V. V. et al. Stacking domains and dislocation networks in marginally twisted bilayers of transition metal dichalcogenides. Phys. Rev. Lett. 124, 206101 (2020).
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).
Pan, Y. et al. Quantum-confined electronic states arising from moiré pattern of MoS2-WSe2 heterobilayers. Nano Lett. 18, 1849–1855 (2018).
Tilak, N., Li, G., Taniguchi, T., Watanabe, K. & Andrei, E. Y. Moiré potential, lattice relaxation, and layer polarization in marginally twisted MoS2 bilayers. Nano Lett. 23, 73–81 (2023).
Al Ezzi, M. M., Pallewela, G. N., De Beule, C., Mele, E. J., & Adam, S. Analytical model for atomic relaxation in twisted moiré materials. Phys. Rev. Lett. 133, 266201 (2024).
Zhao, W. et al. Direct measurement of the electronic structure and band gap nature of atomic-layer-thick 2H-MoTe2. Preprint at https://doi.org/10.48550/arXiv.2001.05894 (2020).
Liu, G.-B., Shan, W.-Y., Yao, Y., Yao, W. & Xiao, D. Three-band tight-binding model for monolayers of group-vib transition metal dichalcogenides. Phys. Rev. B 88, 085433 (2013).
Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotechnol. 8, 899–911 (2013).
Mao, N. et al. Transfer learning relaxation, electronic structure and continuum model for twisted bilayer MoTe2. Commun. Phys. 7, 262 (2024).
Wang, T. et al. Topology, magnetism and charge order in twisted MoTe2 at higher integer hole fillings. Preprint at https://doi.org/10.48550/arXiv.2312.12531 (2023).
Wang, C. et al. Fractional Chern insulator in twisted bilayer MoTe2. Phys. Rev. Lett. 132, 036501 (2024).
Jia, Y. et al. Moiré fractional Chern insulators. I. First-principles calculations and continuum models of twisted bilayer MoTe2. Phys. Rev. B 109, 205121 (2024).
Ahn, C.-E., Lee, W., Yananose, K., Kim, Y. & Cho, G. Y. First Landau level physics in second moiré band of 2.1° twisted bilayer MoTe2. Preprint at https://arxiv.org/html/2403.19155v1 (2024).
Xu, C., Mao, N., Zeng, T. & Zhang, Y. Multiple Chern bands in twisted MoTe2 and possible non-abelian states. Preprint at https://doi.org/10.48550/arXiv.2403.17003 (2024).
Liu, Z. et al. Continuously tunable uniaxial strain control of van der Waals heterostructure devices. J. Appl. Phys. 135, 204306 (2024).
Choi, Y. et al. Electronic correlations in twisted bilayer graphene near the magic angle. Nat. Phys. 15, 1174 (2019).
Wallace, P. R. The band theory of graphite. Phys. Rev. 71, 622–634 (1947).
Li, G., Luican, A. & Andrei, E. Y. Self-navigation of a scanning tunneling microscope tip toward a micron-sized graphene sample. Rev. Sci. Instrum. 82, 073701 (2011).
Li, G., Luican, A. & Andrei, E. Y. Scanning tunneling spectroscopy of graphene on graphite. Phys. Rev. Lett. 102, 176804 (2009).
Tersoff, J. & Hamann, D. R. Theory of the scanning tunneling microscope. Phys. Rev. B 31, 805–813 (1985).
Selloni, A., Carnevali, P., Tosatti, E. & Chen, C. D. Voltage-dependent scanning-tunneling microscopy of a crystal surface: graphite. Phys. Rev. B 31, 2602–2605 (1985).
Huder, L., Mesple, F. & Renard, V. T. Scanning tunneling microscopy analysis in Python. Zenodo https://doi.org/10.5281/zenodo.7991365 (2023).
Artaud, A. et al. Universal classification of twisted, strained and sheared graphene moiré superlattices. Sci. Rep. 6, 25670 (2016).
Huder, L. et al. Electronic spectrum of twisted graphene layers under heterostrain. Phys. Rev. Lett. 120, 156405 (2018).
Kerelsky, A. et al. Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature 572, 95–100 (2019).
Zhang, L., Han, J., Wang, H., Car, R. & Weinan, E. Deep potential molecular dynamics: a scalable model with the accuracy of quantum mechanics. Phys. Rev. Lett. 120, 143001 (2018).
Wang, H., Zhang, L., Han, J. & Weinan, E. DeePMD-kit: a deep learning package for many-body potential energy representation and molecular dynamics. Comput. Phys. Commun. 228, 178–184 (2018).
Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).
Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27, 1787–1799 (2006).
Thompson, A. P. et al. LAMMPS-a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput. Phys. Commun. 271, 108171 (2022).
Soler, J. M. et al. The siesta method for ab initio order-n materials simulation. J. Phys.: Condens. Matter 14, 2745 (2002).
Hamann, D. Optimized norm-conserving Vanderbilt pseudopotentials. Phys. Rev. B 88, 085117 (2013).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).
Aftab, S. et al. Carrier polarity modulation of molybdenum ditelluride (MoTe2) for phototransistor and switching photodiode applications. Nanoscale 12, 15687–15696 (2020).
Mleczko, M. J. et al. Contact engineering high-performance n-type MoTe2 transistors. Nano Lett. 19, 6352–6362 (2019). PMID: 31314531.
Yu, Y.-J. et al. Tuning the graphene work function by electric field effect. Nano Lett. 9, 3430–3434 (2009).
Edelberg, D. et al. Approaching the intrinsic limit in transition metal diselenides via point defect control. Nano Lett. 19, 4371–4379 (2019).