Abstract
Atomically thin transition metal dichalcogenides (TMDs) are 2D semiconductors with tightly bound excitons and correspondingly strong light–matter interactions. Owing to the weak van der Waals bonding between layers, TMDs can be isolated and stacked together to form synthetic heterostructures with emergent electronic and excitonic properties. In this Review, we focus on the emergent exciton physics in moiré superlattices and in TMD heterobilayers coupled to optical cavities, where exciton behaviour can be dramatically modified by the environment. In moiré superlattices, a small twist angle or lattice mismatch between the layers introduces a periodic variation in the interlayer alignment that leads to exciton localization, modified optical selection rules and strong correlations. In cavity–heterostructure systems, light–matter interaction is enhanced and exciton states can couple to the cavity to form exciton-polaritons, whose properties depend on the specific TMD layers involved and their alignment. Here, we discuss recent theoretical and experimental progress towards realizing exotic exciton states in TMD heterobilayers and comment on future scientific and technological directions.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$32.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 digital issues and online access to articles
$119.00 per year
only $9.92 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout








Similar content being viewed by others
References
Novoselov, K. S., Mishchenko, A., Carvalho, A. & Castro Neto, A. H. 2D materials and van der Waals heterostructures. Science 353, aac9439 (2016).
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).
Kim, K. et al. van der Waals heterostructures with high accuracy rotational alignment. Nano Lett. 16, 1989–1995 (2016).
Frisenda, R. et al. Recent progress in the assembly of nanodevices and van der Waals heterostructures by deterministic placement of 2D materials. Chem. Soc. Rev. 47, 53–68 (2018).
Fang, H. et al. Strong interlayer coupling in van der Waals heterostructures built from single-layer chalcogenides. Proc. Natl Acad. Sci. USA 111, 6198–6202 (2014).
Rivera, P. et al. Observation of long-lived interlayer excitons in monolayer MoSe2–WSe2 heterostructures. Nat. Commun. 6, 6242 (2015).
Yu, H. et al. Moiré excitons: from programmable quantum emitter arrays to spin–orbit-coupled artificial lattices. Sci. Adv. 3, e1701696 (2017).
Jin, C. et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019).
Seyler, K. L. et al. Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers. Nature 567, 66–70 (2019).
Zhang, L. et al. Highly valley-polarized singlet and triplet interlayer excitons in van der Waals heterostructure. Phys. Rev. B 100, 041402 (2019).
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).
Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).
Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020).
Xu, Y. et al. Correlated insulating states at fractional fillings of moiré superlattices. Nature 587, 214–218 (2020).
Xia, F., Wang, H., Xiao, D., Dubey, M. & Ramasubramaniam, A. Two-dimensional material nanophotonics. Nat. Photonics 8, 899–907 (2014).
Mak, K. F. & Shan, J. Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides. Nat. Photonics 10, 216–226 (2016).
Zhang, L. et al. Twist-angle dependence of moiré excitons in WS2/MoSe2 heterobilayers. Nat. Commun. 11, 5888 (2020).
Sidler, M. et al. Fermi polaron-polaritons in charge-tunable atomically thin semiconductors. Nat. Phys. 13, 255–261 (2017).
Zhang, L. et al. Van der Waals heterostructure polaritons with moiré-induced nonlinearity. Nature 591, 61–65 (2021).
Emmanuele, R. P. A. et al. Highly nonlinear trion-polaritons in a monolayer semiconductor. Nat. Commun. 11, 3589 (2020).
Gu, J. et al. Enhanced nonlinear interaction of polaritons via excitonic Rydberg states in monolayer WSe2. Nat. Commun. 12, 2269 (2021).
Tan, L. B. et al. Interacting polaron-polaritons. Phys. Rev. X 10, 021011 (2020).
Mueller, T. & Malic, E. Exciton physics and device application of two-dimensional transition metal dichalcogenide semiconductors. NPJ 2D Mater. Appl. 2, 29 (2018).
Wang, G. et al. Colloquium: Excitons in atomically thin transition metal dichalcogenides. Rev. Mod. Phys. 90, 21001 (2018).
Splendiani, A. et al. Emerging photoluminescence in monolayer MoS2. Nano Lett. 10, 1271–1275 (2010).
Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: a new direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).
Xiao, D., Yao, W. & Niu, Q. Valley-contrasting physics in graphene: magnetic moment and topological transport. Phys. Rev. Lett. 99, 236809 (2007).
Yao, W., Xiao, D. & Niu, Q. Valley-dependent optoelectronics from inversion symmetry breaking. Phys. Rev. B 77, 235406 (2008).
Wu, F., Qu, F. & Macdonald, A. H. Exciton band structure of monolayer MoS2. Phys. Rev. B 91, 075310 (2015).
Ramasubramaniam, A. Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides. Phys. Rev. B 86, 115409 (2012).
Chernikov, A. et al. Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2. Phys. Rev. Lett. 113, 076802 (2014).
Ye, Z. et al. Probing excitonic dark states in single-layer tungsten disulphide. Nature 513, 214–218 (2014).
Cao, T. et al. Valley-selective circular dichroism of monolayer molybdenum disulphide. Nat. Commun. 3, 887 (2012).
Mak, K. F., He, K., Shan, J. & Heinz, T. F. Control of valley polarization in monolayer MoS2 by optical helicity. Nat. Nanotechnol. 7, 494–498 (2012).
Zeng, H., Dai, J., Yao, W., Xiao, D. & Cui, X. Valley polarization in MoS2 monolayers by optical pumping. Nat. Nanotechnol. 7, 490–493 (2012).
Sallen, G. et al. Robust optical emission polarization in MoS2 monolayers through selective valley excitation. Phys. Rev. B 86, 081301 (2012).
Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys. 10, 343–350 (2014).
Mak, K. F., Xiao, D. & Shan, J. Light–valley interactions in 2D semiconductors. Nat. Photonics 12, 451–460 (2018).
Zhu, Z. Y., Cheng, Y. C. & Schwingenschlögl, U. Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors. Phys. Rev. B 84, 153402 (2011).
Xiao, D. et al. Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012).
Liu, G. B., Xiao, D., Yao, Y., Xu, X. & Yao, W. Electronic structures and theoretical modelling of two-dimensional group-VIB transition metal dichalcogenides. Chem. Soc. Rev. 44, 2643–2663 (2015).
Zhao, W. et al. Evolution of electronic structure in atomically thin sheets of WS2 and WSe2. ACS Nano 7, 791–797 (2013).
Zeng, H. et al. Optical signature of symmetry variations and spin-valley coupling in atomically thin tungsten dichalcogenides. Sci. Rep. 3, 1608 (2013).
Echeverry, J. P., Urbaszek, B., Amand, T., Marie, X. & Gerber, I. C. Splitting between bright and dark excitons in transition metal dichalcogenide monolayers. Phys. Rev. B 93, 121107 (2016).
Komider, K., González, J. W. & Fernández-Rossier, J. Large spin splitting in the conduction band of transition metal dichalcogenide monolayers. Phys. Rev. B 88, 245436 (2013).
Malic, E. et al. Dark excitons in transition metal dichalcogenides. Phys. Rev. Mater. 2, 014002 (2018).
Robert, C. et al. Measurement of the spin-forbidden dark excitons in MoS2 and MoSe2 monolayers. Nat. Commun. 11, 4037 (2020).
Klein, J. et al. Controlling exciton many-body states by the electric-field effect in monolayer MoS2. Phys. Rev. Res. 3, L022009 (2021).
Zhang, X. X., You, Y., Zhao, S. Y. F. & Heinz, T. F. Experimental evidence for dark excitons in monolayer WSe2. Phys. Rev. Lett. 115, 257403 (2015).
Berghäuser, G. et al. Mapping of the dark exciton landscape in transition metal dichalcogenides. Phys. Rev. B 98, 020301 (2018).
Merkl, P. et al. Ultrafast transition between exciton phases in van der Waals heterostructures. Nat. Mater. 18, 691–696 (2019).
Wong, E. L., Al-mahboob, A., Chan, N. S. & Karmakar, A. Directly visualizing the momentum-forbidden dark excitons and their dynamics in atomically thin semiconductors. Science 370, 1199–1204 (2020).
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).
Edelberg, D. et al. Approaching the intrinsic limit in transition metal diselenides via point defect control. Nano Lett. 19, 4371–4379 (2019).
He, Y. M. et al. Single quantum emitters in monolayer semiconductors. Nat. Nanotechnol. 10, 497–502 (2015).
Srivastava, A. et al. Optically active quantum dots in monolayer WSe2. Nat. Nanotechnol. 10, 491–496 (2015).
Komsa, H. P. & Krasheninnikov, A. V. Electronic structures and optical properties of realistic transition metal dichalcogenide heterostructures from first principles. Phys. Rev. B 88, 085318 (2013).
Koåmider, K. & Fernández-Rossier, J. Electronic properties of the MoS2-WS2 heterojunction. Phys. Rev. B 87, 075451 (2013).
Gong, C. et al. Band alignment of two-dimensional transition metal dichalcogenides: application in tunnel field effect transistors. Appl. Phys. Lett. 103, 053513 (2013).
Zhang, C. et al. Systematic study of electronic structure and band alignment of monolayer transition metal dichalcogenides in Van der Waals heterostructures. 2D Mater. 4, 015026 (2017).
Raja, A. et al. Coulomb engineering of the bandgap and excitons in two-dimensional materials. Nat. Commun. 8, 15251 (2017).
Waldecker, L. et al. Rigid band shifts in two-dimensional semiconductors through external dielectric screening. Phys. Rev. Lett. 123, 206403 (2019).
Rivera, P. et al. Valley-polarized exciton dynamics in a 2D semiconductor heterostructure. Science 351, 688–691 (2016).
Wu, F. C., Xue, F. & Macdonald, A. H. Theory of two-dimensional spatially indirect equilibrium exciton condensates. Phys. Rev. B 92, 165121 (2015).
Wang, Z. et al. Evidence of high-temperature exciton condensation in two-dimensional atomic double layers. Nature 574, 76–80 (2019).
Heo, H. et al. Interlayer orientation-dependent light absorption and emission in monolayer semiconductor stacks. Nat. Commun. 6, 7372 (2015).
Nayak, P. K. et al. Probing evolution of twist-angle-dependent interlayer excitons in MoSe2/WSe2 van der waals heterostructures. ACS Nano 11, 4041–4050 (2017).
Yan, W. et al. Probing angle-dependent interlayer coupling in twisted bilayer WS2. J. Phys. Chem. C 123, 30684–30688 (2019).
Deilmann, T. & Thygesen, K. S. Interlayer excitons with large optical amplitudes in layered van der Waals materials. Nano Lett. 18, 2984–2989 (2018).
Peimyoo, N. et al. Electrical tuning of optically active interlayer excitons in bilayer MoS2. Nat. Nanotechnol. 16, 888–893 (2021).
Leisgang, N. et al. Giant Stark splitting of an exciton in bilayer MoS2. Nat. Nanotechnol. 15, 901–907 (2020).
Hong, X. et al. Ultrafast charge transfer in atomically thin MoS2/WS2 heterostructures. Nat. Nanotechnol. 9, 682–686 (2014).
Ceballos, F., Bellus, M. Z., Chiu, H. Y. & Zhao, H. Ultrafast charge separation and indirect exciton formation in a MoS2–MoSe2 van der Waals heterostructure. ACS Nano 8, 12717–12724 (2014).
Ross, J. S. et al. Interlayer exciton optoelectronics in a 2D heterostructure p–n junction. Nano Lett. 17, 638–643 (2017).
Jauregui, L. A. et al. Electrical control of interlayer exciton dynamics in atomically thin heterostructures. Science 366, 870–875 (2019).
Liu, K. et al. Evolution of interlayer coupling in twisted molybdenum disulfide bilayers. Nat. Commun. 5, 4966 (2014).
Van Der Zande, A. M. et al. Tailoring the electronic structure in bilayer molybdenum disulfide via interlayer twist. Nano Lett. 14, 3869–3875 (2014).
Meckbach, L., Stroucken, T. & Koch, S. W. Influence of the effective layer thickness on the ground-state and excitonic properties of transition-metal dichalcogenide systems. Phys. Rev. B 97, 035425 (2018).
Arora, A. et al. Interlayer excitons in a bulk van der Waals semiconductor. Nat. Commun. 8, 639 (2017).
Horng, J. et al. Observation of interlayer excitons in MoSe2 single crystals. Phys. Rev. B 97, 241404 (2018).
Wang, Z., Chiu, Y. H., Honz, K., Mak, K. F. & Shan, J. Electrical tuning of interlayer exciton gases in WSe2 bilayers. Nano Lett. 18, 137–143 (2018).
Wu, F., Lovorn, T. & Macdonald, A. H. Topological exciton bands in moiré heterojunctions. Phys. Rev. Lett. 118, 147401 (2017).
Zhang, C. et al. Interlayer couplings, Moiré patterns, and 2D electronic superlattices in MoS2/WSe2 hetero-bilayers. Sci. Adv. 3, e1601459 (2017).
Wu, F., Lovorn, T., Tutuc, E. & MacDonald, A. H. Hubbard model physics in transition metal dichalcogenide moiré bands. Phys. Rev. Lett. 121, 026402 (2018).
Naik, M. H. & Jain, M. Ultraflatbands and shear solitons in moiré patterns of twisted bilayer transition metal dichalcogenides. Phys. Rev. Lett. 121, 266401 (2018).
Gillen, R. & Maultzsch, J. Interlayer excitons in MoSe2/WSe2 heterostructures from first principles. Phys. Rev. B 97, 165306 (2018).
Naik, M. H., Maity, I., Maiti, P. K. & Jain, M. Kolmogorov–Crespi potential for multilayer transition-metal dichalcogenides: capturing structural transformations in moiré superlattices. J. Phys. Chem. C 123, 9770–9778 (2019).
Naik, M. H., Kundu, S., Maity, I. & Jain, M. Origin and evolution of ultraflat bands in twisted bilayer transition metal dichalcogenides: realization of triangular quantum dots. Phys. Rev. B 102, 075413 (2020).
Shabani, S. et al. Deep moiré potentials in twisted transition metal dichalcogenide bilayers. Nat. Phys. 17, 720–725 (2021).
Enaldiev, V. V., Zólyomi, V., Yelgel, C., Magorrian, S. J. & Fal’ko, V. I. Stacking domains and dislocation networks in marginally twisted bilayers of transition metal dichalcogenides. Phys. Rev. Lett. 124, 206101 (2020).
Tong, Q., Chen, M., Xiao, F., Yu, H. & Yao, W. Interferences of electrostatic moiré potentials and bichromatic superlattices of electrons and excitons in transition metal dichalcogenides. 2D Mater. 8, 025007 (2021).
Weston, A. et al. Atomic reconstruction in twisted bilayers of transition metal dichalcogenides. Nat. Nanotechnol. 15, 592–597 (2020).
McGilly, L. J. et al. Visualization of moiré superlattices. Nat. Nanotechnol. 15, 580–584 (2020).
Rosenberger, M. R. et al. Twist angle-dependent atomic reconstruction and moiré patterns in transition metal dichalcogenide heterostructures. ACS Nano 14, 4550–4558 (2020).
Zhang, Z. et al. Flat bands in twisted bilayer transition metal dichalcogenides. Nat. Phys. 16, 1093–1096 (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).
Li, H. et al. Imaging moiré flat bands in three-dimensional reconstructed WSe2/WS2 superlattices. Nat. Mater. 20, 945–950 (2021).
Stansbury, C. H. et al. Visualizing electron localization of WS2/WSe2 moiré superlattices in momentum space. Sci. Adv. 7, eabf4387 (2021).
Tang, Y. et al. Tuning layer-hybridized moiré excitons by the quantum-confined Stark effect. Nat. Nanotechnol. 16, 52–57 (2021).
Andersen, T. I. et al. Excitons in a reconstructed moiré potential in twisted WSe2/WSe2 homobilayers. Nat. Mater. 20, 480–487 (2021).
MacNeill, D. et al. Breaking of valley degeneracy by magnetic field in monolayer MoSe2. Phys. Rev. Lett. 114, 037401 (2015).
Srivastava, A. et al. Valley Zeeman effect in elementary optical excitations of monolayer WSe2. Nat. Phys. 11, 141–147 (2015).
Aivazian, G. et al. Magnetic control of valley pseudospin in monolayer WSe2. Nat. Phys. 11, 148–152 (2015).
Kim, J. et al. Ultrafast generation of pseudo-magnetic field for valley excitons in WSe2 monolayers. Science 346, 1205–1208 (2014).
Sie, E. J. et al. Valley-selective optical Stark effect in monolayer WS2. Nat. Mater. 14, 290–294 (2015).
Yu, H., Wang, Y., Tong, Q., Xu, X. & Yao, W. Anomalous light cones and valley optical selection rules of interlayer excitons in twisted heterobilayers. Phys. Rev. Lett. 115, 187002 (2015).
Lu, X., Li, X. & Yang, L. Modulated interlayer exciton properties in a two-dimensional moiré crystal. Phys. Rev. B 100, 155416 (2019).
Geng, W. T., Wang, V., Liu, Y. C., Ohno, T. & Nara, J. Moiré potential, lattice corrugation, and band gap spatial variation in a twist-free MoTe2/MoS2 heterobilayer. J. Phys. Chem. Lett. 11, 2637–2646 (2020).
Joe, A. Y. et al. Electrically controlled emission from singlet and triplet exciton species in atomically thin light emitting diodes. Phys. Rev. B 103, 17–21 (2021).
Ciarrocchi, A. et al. Polarization switching and electrical control of interlayer excitons in two-dimensional van der Waals heterostructures. Nat. Photonics 13, 131–136 (2019).
Wang, T. et al. Giant valley-Zeeman splitting from spin-singlet and spin-triplet interlayer excitons in WSe2/MoSe2 heterostructure. Nano Lett. 20, 694–700 (2020).
Miller, B. et al. Long-lived direct and indirect interlayer excitons in van der Waals heterostructures. Nano Lett. 17, 5229–5237 (2017).
Hanbicki, A. T. et al. Double indirect interlayer exciton in a MoSe2/WSe2 van der Waals heterostructure. ACS Nano 12, 4719–4726 (2018).
Tran, K. et al. Evidence for moiré excitons in van der Waals heterostructures. Nature 567, 71–75 (2019).
Calman, E. V. et al. Indirect excitons and trions in MoSe2/WSe2 van der Waals heterostructures. Nano Lett. 20, 1869–1875 (2020).
Bai, Y. et al. Excitons in strain-induced one-dimensional moiré potentials at transition metal dichalcogenide heterojunctions. Nat. Mater. 19, 1068–1073 (2020).
Wang, J. et al. Diffusivity reveals three distinct phases of interlayer excitons in MoSe2/WSe2 heterobilayers. Phys. Rev. Lett. 126, 106804 (2021).
Förg, M. et al. Moiré excitons in MoSe2-WSe2 heterobilayers and heterotrilayers. Nat. Commun. 12, 1656 (2021).
Kunstmann, J. et al. Momentum-space indirect interlayer excitons in transition-metal dichalcogenide van der Waals heterostructures. Nat. Phys. 14, 801–805 (2018).
Yuan, L. et al. Twist-angle-dependent interlayer exciton diffusion in WS2–WSe2 heterobilayers. Nat. Mater. 19, 617–623 (2020).
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).
Baek, H. et al. Highly energy-tunable quantum light from moiré-trapped excitons. Sci. Adv. 6, eaba8526 (2020).
Brotons-Gisbert, M. et al. Spin–layer locking of interlayer excitons trapped in moiré potentials. Nat. Mater. 19, 630–636 (2020).
Koperski, M. et al. Single photon emitters in exfoliated WSe2 structures. Nat. Nanotechnol. 10, 503–506 (2015).
Chakraborty, C., Kinnischtzke, L., Goodfellow, K. M., Beams, R. & Vamivakas, A. N. Voltage-controlled quantum light from an atomically thin semiconductor. Nat. Nanotechnol. 10, 507–511 (2015).
Merkl, P. et al. Twist-tailoring Coulomb correlations in van der Waals homobilayers. Nat. Commun. 11, 2167 (2020).
Brem, S. et al. Hybridized intervalley moiré excitons and flat bands in twisted WSe2 bilayers. Nanoscale 12, 11088–11094 (2020).
Scuri, G. et al. Electrically tunable valley dynamics in twisted WSe2/WSe2 bilayers. Phys. Rev. Lett. 124, 217403 (2020).
Ruiz-Tijerina, D. A. & Fal’ko, V. I. Interlayer hybridization and moiré superlattice minibands for electrons and excitons in heterobilayers of transition-metal dichalcogenides. Phys. Rev. B 99, 30–32 (2019).
Alexeev, E. M. et al. Resonantly hybridized excitons in moiré superlattices in van der Waals heterostructures. Nature 567, 81–86 (2019).
Sung, J. et al. Broken mirror symmetry in excitonic response of reconstructed domains in twisted MoSe2/MoSe2 bilayers. Nat. Nanotechnol. 15, 750–754 (2020).
Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiré heterostructure. Nature 580, 472–477 (2020).
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).
Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Chen, G. et al. Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice. Nat. Phys. 15, 237–241 (2019).
Pisoni, R. et al. Interactions and magnetotransport through spin-valley coupled landau levels in monolayer MoS2. Phys. Rev. Lett. 121, 247701 (2018).
Larentis, S. et al. Large effective mass and interaction-enhanced Zeeman splitting of K-valley electrons in MoSe2. Phys. Rev. B 97, 201407 (2018).
Fallahazad, B. et al. Shubnikov–de Haas oscillations of high-mobility holes in monolayer and bilayer WSe2: Landau level degeneracy, effective mass, and negative compressibility. Phys. Rev. Lett. 116, 086601 (2016).
Allain, A., Kang, J., Banerjee, K. & Kis, A. Electrical contacts to two-dimensional semiconductors. Nat. Mater. 14, 1195–1205 (2015).
Ross, J. S. et al. Electrical control of neutral and charged excitons in a monolayer semiconductor. Nat. Commun. 4, 1474 (2013).
Mak, K. F. et al. Tightly bound trions in monolayer MoS2. Nat. Mater. 12, 207–211 (2013).
Li, H. et al. Imaging two-dimensional generalized Wigner crystals. Nature 597, 650–654 (2021).
Jin, C. et al. Stripe phases in WSe2/WS2 moiré superlattices. Nat. Mater. 20, 940–944 (2021).
Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).
Shimazaki, Y. et al. Optical signatures of periodic charge distribution in a Mott-like correlated insulator state. Phys. Rev. X 11, 021027 (2021).
Yamamoto, Y., Tassone, F. & Cao, H. Semiconductor Cavity Quantum Electrodynamics (Springer, 2000).
Purcell, E. M. Spontaneous emission proababilities at radio frequencies. Phys. Rev. 69, 681 (1946).
Liu, X. et al. Strong light–matter coupling in two-dimensional atomic crystals. Nat. Photonics 9, 30–34 (2014).
Dufferwiel, S. et al. Exciton–polaritons in van der Waals heterostructures embedded in tunable microcavities. Nat. Commun. 6, 8579 (2015).
Basov, D. N., Fogler, M. M. & García De Abajo, F. J. Polaritons in van der Waals materials. Science 354, aag1992 (2016).
Flatten, L. C. et al. Room-temperature exciton-polaritons with two-dimensional WS2. Sci. Rep. 6, 33134 (2016).
Liu, X. et al. Control of coherently coupled exciton polaritons in monolayer tungsten disulphide. Phys. Rev. Lett. 119, 027403 (2017).
Chen, Y. J., Cain, J. D., Stanev, T. K., Dravid, V. P. & Stern, N. P. Valley-polarized exciton–polaritons in a monolayer semiconductor. Nat. Photonics 11, 431–435 (2017).
Dufferwiel, S. et al. Valley-addressable polaritons in atomically thin semiconductors. Nat. Photonics 11, 497–501 (2017).
Zhang, L., Gogna, R., Burg, W., Tutuc, E. & Deng, H. Photonic-crystal exciton-polaritons in monolayer semiconductors. Nat. Commun. 9, 713 (2018).
Förg, M. et al. Cavity-control of interlayer excitons in van der Waals heterostructures. Nat. Commun. 10, 3697 (2019).
Latini, S., Ronca, E., De Giovannini, U., Hübener, H. & Rubio, A. Cavity control of excitons in two-dimensional materials. Nano Lett. 19, 3473–3479 (2019).
Rivera, P. et al. Coupling of photonic crystal cavity and interlayer exciton in heterobilayer of transition metal dichalcogenides. 2D Mater. 7, 015027 (2020).
Liu, Y. et al. Room temperature nanocavity laser with interlayer excitons in 2D heterostructures. Sci. Adv. 5, eaav4506 (2019).
Paik, E. Y. et al. Interlayer exciton laser of extended spatial coherence in atomically thin heterostructures. Nature 576, 80–84 (2019).
Blatt, J. M., Böer, K. W. & Brandt, W. Bose-Einstein condensation of excitons. Phys. Rev. 126, 1691 (1962).
Keldysh, L. V. & Kozlov, A. N. Collective properties of excitons in semiconductors. Sov. Phys. JETP 27, 521 (1968).
Lozovik, Y. E. & Yudson, V. I. A new mechanism for superconductivity: pairing between spatially separated electrons and holes. Zh. Eksp. Teor. Fiz. 71, 738–753 (1976).
Fukuzawa, T., Mendez, E. E. & Hong, J. M. Phase transition of an exciton system in GaAs coupled quantum wells. Phys. Rev. Lett. 64, 3066 (1990).
Zhu, X., Littlewood, P. B., Hybertsen, M. S. & Rice, T. M. Exciton condensate in semiconductor quantum well structures. Phys. Rev. Lett. 74, 1633 (1995).
Alexandrou, A. et al. Electric-field effects on exciton lifetimes in symmetric coupled GaAs/Al0.3Ga0.7As double quantum wells. Phys. Rev. B 42, 9225 (1990).
Butov, L. V., Zrenner, A., Abstreiter, G., Böhm, G. & Weimann, G. Condensation of indirect excitons in coupled AlAs/GaAs quantum wells. Phys. Rev. Lett. 73, 304 (1994).
Butov, L. V., Gossard, A. C. & Chemla, D. S. Macroscopically ordered state in an exciton system. Nature 418, 751–754 (2002).
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).
Fisher, D. S. & Hohenberg, P. C. Dilute Bose gas in two dimensions. Phys. Rev. B 37, 4936 (1988).
Prokof’ev, N., Ruebenacker, O. & Svistunov, B. Critical point of a weakly interacting two-dimensional Bose gas. Phys. Rev. Lett. 87, 270402 (2001).
Filinov, A., Prokof’Ev, N. V. & Bonitz, M. Berezinskii-Kosterlitz-Thouless transition in two-dimensional dipole systems. Phys. Rev. Lett. 105, 070401 (2010).
Perali, A., Neilson, D. & Hamilton, A. R. High-temperature superfluidity in double-bilayer graphene. Phys. Rev. Lett. 110, 146803 (2013).
Su, J.-J. & MacDonald, A. H. Spatially indirect exciton condensate phases in double bilayer graphene. Phys. Rev. B 95, 45416 (2017).
Burg, G. W. et al. Strongly enhanced tunneling at total charge neutrality in double-bilayer graphene-WSe2 heterostructures. Phys. Rev. Lett. 120, 177702 (2018).
Xie, M. & MacDonald, A. H. Electrical reservoirs for bilayer excitons. Phys. Rev. Lett. 121, 67702 (2018).
Zeng, Y. & MacDonald, A. H. Electrically controlled two-dimensional electron-hole fluids. Phys. Rev. B 102, 85154 (2020).
Ma, L. et al. Strongly correlated excitonic insulator in atomic double layers. Nature 598, 585–589 (2021).
Eisenstein, J. P. & MacDonald, A. H. Bose–Einstein condensation of excitons in bilayer electron systems. Nature 432, 691–694 (2004).
Spielman, I. B., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Resonantly enhanced tunneling in a double layer quantum Hall ferromagnet. Phys. Rev. Lett. 84, 5808 (2000).
Kellogg, M., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Vanishing Hall resistance at high magnetic field in a double-layer two-dimensional electron system. Phys. Rev. Lett. 93, 36801 (2004).
Tutuc, E., Shayegan, M. & Huse, D. A. Counterflow measurements in strongly correlated GaAs hole bilayers: evidence for electron-hole pairing. Phys. Rev. Lett. 93, 36802 (2004).
Fisher, M. P. A., Weichman, P. B., Grinstein, G. & Fisher, D. S. Boson localization and the superfluid-insulator transition. Phys. Rev. B 40, 546–570 (1989).
Greiner, M. et al. Quantum phase transition from a superfluid to a Mott insulator in an ultracold gas of atoms. Phys. B Condens. Matter 329–333, 11–12 (2003).
Jung, J., Raoux, A., Qiao, Z. & Macdonald, A. H. Ab initio theory of moiré superlattice bands in layered two-dimensional materials. Phys. Rev. B 89, 205414 (2014).
Togan, E., Lim, H. T., Faelt, S., Wegscheider, W. & Imamoglu, A. Enhanced Interactions between dipolar polaritons. Phys. Rev. Lett. 121, 227402 (2018).
Tsintzos, S. I. et al. Electrical tuning of nonlinearities in exciton-polariton condensates. Phys. Rev. Lett. 121, 37401 (2018).
Cristofolini, P. et al. Coupling quantum tunneling with cavity photons. Science 336, 704–707 (2012).
Delteil, A. et al. Towards polariton blockade of confined exciton–polaritons. Nat. Mater. 18, 219–222 (2019).
Muñoz-Matutano, G. et al. Emergence of quantum correlations from interacting fibre-cavity polaritons. Nat. Mater. 18, 213–218 (2019).
Kyriienko, O., Krizhanovskii, D. N. & Shelykh, I. A. Nonlinear quantum optics with trion polaritons in 2D monolayers: conventional and unconventional photon blockade. Phys. Rev. Lett. 125, 197402 (2020).
Dreismann, A. et al. A sub-femtojoule electrical spin-switch based on optically trapped polariton condensates. Nat. Mater. 15, 1074–1078 (2016).
Kavokin, A. & Lagoudakis, P. Exciton–polariton condensates: exciton-mediated superconductivity. Nat. Mater. 15, 599–600 (2016).
Cortese, E. et al. Excitons bound by photon exchange. Nat. Phys. 17, 31–35 (2021).
Paravicini-Bagliani, G. L. et al. Magneto-transport controlled by Landau polariton states. Nat. Phys. 15, 186–190 (2019).
Ashida, Y. et al. Quantum electrodynamic control of matter: cavity-enhanced ferroelectric phase transition. Phys. Rev. X 10, 041027 (2020).
Yu, H. & Yao, W. Electrically tunable topological transport of moiré polaritons. Sci. Bull. 65, 1555–1562 (2020).
Pei, J., Yang, J., Yildirim, T., Zhang, H. & Lu, Y. Many-body complexes in 2D semiconductors. Adv. Mater. 31, 1706945 (2019).
Laussy, F. P., Kavokin, A. V. & Shelykh, I. A. Exciton-polariton mediated superconductivity. Phys. Rev. Lett. 104, 106402 (2010).
Cotleţ, O., Zeytinolu, S., Sigrist, M., Demler, E. & Imamolu, A. Superconductivity and other collective phenomena in a hybrid Bose-Fermi mixture formed by a polariton condensate and an electron system in two dimensions. Phys. Rev. B 93, 054510 (2016).
Qiu, L., Chakraborty, C., Dhara, S. & Vamivakas, A. N. Room-temperature valley coherence in a polaritonic system. Nat. Commun. 10, 1513 (2019).
Yu, H., Liu, G.-B., Gong, P., Xu, X. & Yao, W. Dirac cones and Dirac saddle points of bright excitons in monolayer transition metal dichalcogenides. Nat. Commun. 5, 3876 (2014).
Yu, T. & Wu, M. W. Valley depolarization due to intervalley and intravalley electron-hole exchange interactions in monolayer MoS2. Phys. Rev. B 89, 205303 (2014).
Glazov, M. M. et al. Exciton fine structure and spin decoherence in monolayers of transition metal dichalcogenides. Phys. Rev. B 89, 201302 (2014).
Acknowledgements
E.Y.P., Y.Z., L.Z., J.Z., A.H.M., H.D. and F.W. acknowledge support from the US Army Research Office under MURI award W911NF-17-1-0312. E.Y.P., L.Z. and H.D. were also supported by the Air Force Office of Scientific Research under award FA2386-18-1-4086 and the National Science Foundation under award DMR 1838412. D.W. was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under contract number DE-AC02-05-CH11231 (van der Waals heterostructures programme, KCWF16). E.C.R. acknowledges support from the Department of Defense through the National Defense Science and Engineering Graduate (NDSEG) fellowship programme.
Author information
Authors and Affiliations
Contributions
The authors contributed equally to all aspects of the article.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature Reviews Materials thanks the anonymous reviewers for their contribution to the peer review of this work.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Regan, E.C., Wang, D., Paik, E.Y. et al. Emerging exciton physics in transition metal dichalcogenide heterobilayers. Nat Rev Mater 7, 778–795 (2022). https://doi.org/10.1038/s41578-022-00440-1
Accepted:
Published:
Issue date:
DOI: https://doi.org/10.1038/s41578-022-00440-1
This article is cited by
-
Efficient energy transfer and photoluminescence enhancement in 2D MoS2/bulk InSe van der Waals heterostructures
npj 2D Materials and Applications (2025)
-
Ferroelectric control of diverse hyperbolic polaritons in the visible spectrum
npj Computational Materials (2025)
-
Atomistic theory of twist-angle dependent intralayer and interlayer exciton properties in twisted bilayer materials
npj 2D Materials and Applications (2025)
-
Large exciton binding energy in a bulk van der Waals magnet from quasi-1D electronic localization
Nature Communications (2025)
-
Magnon-mediated exciton–exciton interaction in a van der Waals antiferromagnet
Nature Materials (2025)