Wang, Z. et al. Evidence of high-temperature exciton condensation in two-dimensional atomic double layers. Nature 574, 76–80 (2019).
Wang, J. et al. Optical generation of high carrier densities in 2D semiconductor heterobilayers. Sci. Adv. 5, eaax0145 (2019).
Li, W., Lu, X., Dubey, S., Devenica, L. & Srivastava, A. Dipolar interactions between localized interlayer excitons in van der Waals heterostructures. Nat. Mater. 19, 624–629 (2020).
Kremser, M. et al. Discrete interactions between a few interlayer excitons trapped at a MoSe2–WSe2 heterointerface. Npj 2D Mater. Appl. 4, 8 (2020).
Yu, H., Liu, G.-B., Tang, J., Xu, X. & Yao, W. Moiré excitons: from programmable quantum emitter arrays to spin–orbit-coupled artificial lattices. Sci. Adv. 3, e1701696 (2017).
Liu, X. & Hersam, M. C. 2D materials for quantum information science. Nat. Rev. Mater. 4, 669–684 (2019).
Kennes, D. M. et al. Moiré heterostructures as a condensed-matter quantum simulator. Nat. Phys. 17, 155–163 (2021).
Rivera, P. et al. Interlayer valley excitons in heterobilayers of transition metal dichalcogenides. Nat. Nanotechnol. 13, 1004 (2018).
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).
Karni, O. et al. Infrared interlayer exciton emission in MoS2/WSe2 heterostructures. Phys. Rev. Lett. 123, 247402 (2019).
Zhang, L. et al. Highly valley-polarized singlet and triplet interlayer excitons in van der Waals heterostructure. Phys. Rev. B 100, 041402 (2019).
Fogler, M. M., Butov, L. V. & Novoselov, K. S. High-temperature superfluidity with indirect excitons in van der Waals heterostructures. Nat. Commun. 5, 4555 (2014).
Wu, F., Lovorn, T. & MacDonald, A. H. Theory of optical absorption by interlayer excitons in transition metal dichalcogenide heterobilayers. Phys. Rev. B 97, 035306 (2018).
Jin, C. et al. Identification of spin, valley and moiré quasi-angular momentum of interlayer excitons. Nat. Phys. 15, 1140–1144 (2019).
Jin, C. et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019).
Gillen, R. & Maultzsch, J. Interlayer excitons in MoSe2/WSe2 heterostructures from first principles. Phys. Rev. B 97, 165306 (2018).
Shabani, S. et al. Deep moiré potentials in twisted transition metal dichalcogenide bilayers. Nat. Phys. 17, 720–725 (2021).
Man, M. K. L. et al. Experimental measurement of the intrinsic excitonic wave function. Sci. Adv. 7, eabg0192 (2021).
Dong, S. et al. Direct measurement of key exciton properties: energy, dynamics, and spatial distribution of the wave function. Nat. Sci. 1, e10010 (2021).
Wallauer, R. et al. Momentum-resolved observation of exciton formation dynamics in monolayer WS2. Nano Lett. 21, 5867–5873 (2021).
Li, H. et al. Imaging moiré flat bands in three-dimensional reconstructed WSe2/WS2 superlattices. Nat. Mater. 20, 945–950 (2021).
Madéo, J. et al. Directly visualizing the momentum-forbidden dark excitons and their dynamics in atomically thin semiconductors. Science 370, 1199–1204 (2020).
Schönhense, G., Medjanik, K. & Elmers, H.-J. Space-, time- and spin-resolved photoemission. J. Electron. Spectrosc. Relat. Phenom. 200, 94–118 (2015).
Medjanik, K. et al. Direct 3D mapping of the Fermi surface and Fermi velocity. Nat. Mater. 16, 615–621 (2017).
Kunstmann, J. et al. Momentum-space indirect interlayer excitons in transition-metal dichalcogenide van der Waals heterostructures. Nat. Phys. 14, 801–805 (2018).
Moser, S. An experimentalist’s guide to the matrix element in angle resolved photoemission. J. Electron. Spectrosc. Relat. Phenom. 214, 29–52 (2017).
Beaulieu, S. et al. Revealing hidden orbital pseudospin texture with time-reversal dichroism in photoelectron angular distributions. Phys. Rev. Lett. 125, 216404 (2020).
Rustagi, A. & Kemper, A. F. Photoemission signature of excitons. Phys. Rev. B 97, 235310 (2018).
Ohnishi, H., Tomita, N. & Nasu, K. Direct determination of exciton wavefunction amplitudes by the momentum-resolved photo-electron emission experiment. Int. J. Mod. Phys. B 32, 1850094 (2017).
Wang, Y. H., Steinberg, H., Jarillo-Herrero, P. & Gedik, N. Observation of Floquet–Bloch states on the surface of a topological insulator. Science 342, 453–457 (2013).
Mahmood, F. et al. Selective scattering between Floquet–Bloch and Volkov states in a topological insulator. Nat. Phys. 12, 306–310 (2016).
Cui, X. et al. Transient excitons at metal surfaces. Nat. Phys. 10, 505–509 (2014).
Liu, E. et al. Signatures of moiré trions in WSe2/MoSe2 heterobilayers. Nature 594, 46–50 (2021).
Hybertsen, M. S. & Louie, S. G. Electron correlation in semiconductors and insulators: band gaps and quasiparticle energies. Phys. Rev. B 34, 5390–5413 (1986).
Rohlfing, M. & Louie, S. G. Electron–hole excitations and optical spectra from first principles. Phys. Rev. B 62, 4927–4944 (2000).
Meckbach, L., Stroucken, T. & Koch, S. W. Giant excitation induced bandgap renormalization in TMDC monolayers. Appl. Phys. Lett. 112, 061104 (2018).
Sun, D. et al. Observation of rapid exciton–exciton annihilation in monolayer molybdenum disulfide. Nano Lett. 14, 5625–5629 (2014).
Wu, F., Lovorn, T., Tutuc, E. & MacDonald, A. H. Hubbard model physics in transition metal dichalcogenide moiré bands. Phys. Rev. Lett. 121, 026402 (2018).
Brown, D. Decentering distortion of lenses. Photogramm. Eng. 32, 444–462 (1966).
Xian, R. P., Rettig, L. & Ernstorfer, R. Symmetry-guided nonrigid registration: the case for distortion correction in multidimensional photoemission spectroscopy. Ultramicroscopy 202, 133–139 (2019).
Ye, Z. et al. Efficient generation of neutral and charged biexcitons in encapsulated WSe2 monolayers. Nat. Commun. 9, 3718 (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).
Schlipf, M. & Gygi, F. Optimization algorithm for the generation of ONCV pseudopotentials. Comput. Phys. Commun. 196, 36–44 (2015).
Ismail-Beigi, S. Truncation of periodic image interactions for confined systems. Phys. Rev. B 73, 233103 (2006).
Dion, M., Rydberg, H., Schröder, E., Langreth, D. C. & Lundqvist, B. I. Van der Waals density functional for general geometries. Phys. Rev. Lett. 92, 246401 (2004).
Cooper, V. R. Van der Waals density functional: an appropriate exchange functional. Phys. Rev. B 81, 161104 (2010).
Deslippe, J. et al. BerkeleyGW: a massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures. Comput. Phys. Commun. 183, 1269–1289 (2012).
da Jornada, F. H., Qiu, D. Y. & Louie, S. G. Nonuniform sampling schemes of the Brillouin zone for many-electron perturbation-theory calculations in reduced dimensionality. Phys. Rev. B 95, 035109 (2017).
Alexeev, E. M. et al. Resonantly hybridized excitons in moiré superlattices in van der Waals heterostructures. Nature 567, 81–86 (2019).
Zhang, C. et al. Interlayer couplings, Moiré patterns, and 2D electronic superlattices in MoS2/WSe2 hetero-bilayers. Sci. Adv. 3, e1601459 (2017).