- Letter
- Open Access
Coulomb-mediated interactions of charge-transfer excitons in TMD lateral heterostructures
Phys. Rev. B 114, L171407 – Published 23 September, 2026
DOI: https://doi.org/10.1103/wm33-yhyl
Abstract
Lateral heterostructures of transition-metal dichalcogenides (TMDs) host spatially separated charge-transfer (CT) excitons. While analogous to interlayer excitons in vertical TMD heterostructures, these interfacial excitons possess much larger in-plane dipoles of several nanometers and an additional center-of-mass quantization. Here, we investigate mutual interactions between these highly dipolar CT excitons using a quantum mechanical approach. Accounting for the dipolar and quantum exchange interactions, we evaluate the experimentally accessible density-dependent energy renormalization and predict a net energy blueshift of a few meV for bound CT excitons. Interestingly, for small dipole moments, the energy renormalization displays a quadratic dependence with respect to the dipole moment, in contrast to the linear dependence found in vertical TMD heterostructures. We show that spatial energy offset and temperature are the key tuning knobs for controlling the density-dependent excitonic response. Overall, our results contribute to a better microscopic understanding of CT excitons and their interactions in lateral TMD heterostructures.
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References (68)
- X. Duan, C. Wang, J. C. Shaw, R. Cheng, Y. Chen, H. Li, X. Wu, Y. Tang, Q. Zhang, A. Pan, J. Jiang, R. Yu, Y. Huang, and X. Duan, Lateral epitaxial growth of two-dimensional layered semiconductor heterojunctions, Nat. Nanotechnol. 9, 1024 (2014).
- Y. Gong, J. Lin, X. Wang, G. Shi, S. Lei, Z. Lin, X. Zou, G. Ye, R. Vajtai, B. I. Yakobson, H. Terrones, M. Terrones, B. Tay, J. Lou, S. T. Pantelides, Z. Liu, W. Zhou, and P. M. Ajayan, Vertical and in-plane heterostructures from / monolayers, Nat. Mater. 13, 1135 (2014).
- C. Huang, S. Wu, A. M. Sanchez, J. J. P. Peters, R. Beanland, J. S. Ross, P. Rivera, W. Yao, D. H. Cobden, and X. Xu, Lateral heterojunctions within monolayer semiconductors, Nat. Mater. 13, 1096 (2014).
- M.-Y. Li, Y. Shi, C.-C. Cheng, L.-S. Lu, Y.-C. Lin, H.-L. Tang, M.-L. Tsai, C.-W. Chu, K.-H. Wei, J.-H. He, W.-H. Chang, K. Suenaga, and L.-J. Li, Epitaxial growth of a monolayer lateral p-n junction with an atomically sharp interface, Science 349, 524 (2015).
- H. Heo, J. H. Sung, G. Jin, J.-H. Ahn, K. Kim, M.-J. Lee, S. Cha, H. Choi, and M.-H. Jo, 2D materials: Rotation-misfit-free heteroepitaxial stacking and stitching growth of hexagonal transition-metal dichalcogenide monolayers by nucleation kinetics controls, Adv. Mater. 27, 3839 (2015).
- C. Zhang, M.-Y. Li, J. Tersoff, Y. Han, Y. Su, L.-J. Li, D. A. Muller, and C.-K. Shih, Strain distributions and their influence on electronic structures of laterally strained heterojunctions, Nat. Nanotechnol. 13, 152 (2018).
- P. K. Sahoo, S. Memaran, Y. Xin, L. Balicas, and H. R. Gutiérrez, One-pot growth of two-dimensional lateral heterostructures via sequential edge-epitaxy, Nature (London) 553, 63 (2018).
- A. Fali, T. Zhang, J. P. Terry, E. Kahn, K. Fujisawa, B. Kabius, S. Koirala, Y. Ghafouri, D. Zhou, W. Song, L. Yang, M. Terrones, and Y. Abate, Photodegradation protection in 2D in-plane heterostructures revealed by hyperspectral nanoimaging: The role of nanointerface 2D alloys, ACS Nano 15, 2447 (2021).
- Y. Zhang, Q. Lv, H. Wang, S. Zhao, Q. Xiong, R. Lv, and X. Zhang, Simultaneous electrical and thermal rectification in a monolayer lateral heterojunction, Science 378, 169 (2022).
- F. B. Sousa, B. A. L. Ferreira, S. K. Chakraborty, L. C. Carvalho, A. R. Cadore, B. Nayak, P. Ray, S. S. Alexandre, P. K. Sahoo, R. W. Nunes, and L. M. Malard, Enhanced light emission in lateral heterostructures in the electron–hole plasma regime, J. Phys. Chem. Lett. 16, 8227 (2025).
- B. Kundu, P. Mondal, D. Tebbe, M. N. Hasan, S. K. Chakraborty, M. Metzelaars, P. Kögerler, D. Karmakar, G. K. Pradhan, C. Stampfer, B. Beschoten, L. Waldecker, and P. K. Sahoo, Electrically controlled excitons, charge transfer induced trions, and narrowband emitters in lateral heterostructure, Nano Lett. 24, 14615 (2024).
- S. Shradha, R. Rosati, H. Lamsaadi, J. Picker, I. Paradisanos, M. T. Hossain, L. Krelle, L. F. Oswald, N. Engel, D. I. Markina, K. Watanabe, T. Taniguchi, P. K. Sahoo, L. Lombez, X. Marie, P. Renucci, V. Paillard, J.-M. Poumirol, A. Turchanin, E. Malic, et al., 2D excitonics with atomically thin lateral heterostructures, Rep. Prog. Phys. 89, 046501 (2026).
- B. Kundu, P. Chakrabarty, A. Dhara, R. Rosati, C. Samanta, S. K. Chakraborty, S. Sahoo, S. P. Dash, S. Dhara, E. Malic, S. Lodha, and P. K. Sahoo, Trion-engineered multimodal photo-transistors in two-dimensional lateral heterostructures, Adv. Funct. Mater. 36, e17486 (2026).
- M. Kaur, N. T. Sandino, J. P. Terry, M. Ghafariasl, and Y. Abate, Excitonic landscapes in monolayer lateral heterostructures revealed by unsupervised machine learning, Adv. Opt. Mater. 14, e03674 (2026).
- Q. Huang, Z. Wang, R. Liu, H. Yao, C. Ni, T. Bo, S. Wu, F. Sun, F. Fan, and M. V. Mirkin, In situ imaging reveals efficient charge separation in monolayer type-II heterojunctions, J. Am. Chem. Soc. 148, 8417 (2026).
- Y. Guo and J. Robertson, Band engineering in transition metal dichalcogenides: Stacked versus lateral heterostructures, Appl. Phys. Lett. 108, 233104 (2016).
- K. W. Lau, Calvin, Z. Gong, H. Yu, and W. Yao, Interface excitons at lateral heterojunctions in monolayer semiconductors, Phys. Rev. B 98, 115427 (2018).
- R. Rosati, I. Paradisanos, L. Huang, Z. Gan, A. George, K. Watanabe, T. Taniguchi, L. Lombez, P. Renucci, A. Turchanin, et al., Interface engineering of charge-transfer excitons in 2D lateral heterostructures, Nat. Commun. 14, 2438 (2023).
- L. Yuan, B. Zheng, Q. Zhao, R. Kempt, T. Brumme, A. B. Kuc, C. Ma, S. Deng, A. Pan, and L. Huang, Strong dipolar repulsion of one-dimensional interfacial excitons in monolayer lateral heterojunctions, ACS Nano 17, 15379 (2023).
- R. Rosati, S. Shradha, J. Picker, A. Turchanin, B. Urbaszek, and E. Malic, Impact of charge-transfer excitons on unidirectional exciton transport in lateral TMD heterostructures, Nano Lett. 25, 11319 (2025).
- M. V. Durnev and D. S. Smirnov, Intervalley mixing of interface excitons at lateral heterojunctions, Phys. Rev. B 111, 205403 (2025).
- E. Vandoolaeghe, F. Fortuna, S. K. Chakraborty, B. Nayak, T. Taniguchi, K. Watanabe, P. K. Sahoo, T. Chervy, and P. A. Murthy, Dipolar excitonic quantum wires at atomically sharp lateral interfaces, Nano Lett. (2026), doi: 10.1021/acs.nanolett.6c02624.
- M. V. Durnev and D. S. Smirnov, Tunable linear polarization of interface excitons at lateral heterojunctions, Phys. Rev. B 114, 045419 (2026).
- V. Suri, S. Singla, S. K. Chakraborty, V. Jakhar, S. Sarkar, P. K. Sahoo, B. Chakraborty, and S. Korbel, Strongly bound charge-transfer interface excitons in lateral monolayer heterostructures, Nano Lett. 26, 11634 (2026).
- E. Najafidehaghani, Z. Gan, A. George, T. Lehnert, G. Q. Ngo, C. Neumann, T. Bucher, I. Staude, D. Kaiser, T. Vogl, U. Hübner, U. Kaiser, F. Eilenberger, and A. Turchanin, 1D junction electronic and optoelectronic devices from transition metal dichalcogenide lateral heterostructures grown by one-pot chemical vapor deposition synthesis, Adv. Funct. Mater. 31, 2101086 (2021).
- S. Xie, L. Tu, Y. Han, L. Huang, K. Kang, K. U. Lao, P. Poddar, C. Park, D. A. Muller, R. A. DiStasio, and J. Park, Coherent, atomically thin transition-metal dichalcogenide superlattices with engineered strain, Science 359, 1131 (2018).
- N. Ichinose, T. Hotta, M. Maruyama, Z. Liu, R. Canton-Vitoria, S. Okada, F. Zeng, F. Zhang, T. Taniguchi, K. Watanabe, et al., Two-dimensional atomic-scale ultrathin lateral heterostructures, arXiv:2208.12696.
- D. Beret, I. Paradisanos, H. Lamsaadi, Z. Gan, E. Najafidehaghani, A. George, T. Lehnert, J. Biskupek, U. Kaiser, S. Shree, A. Estrada-Real, D. Lagarde, X. Marie, P. Renucci, K. Watanabe, T. Taniguchi, S. Weber, V. Paillard, L. Lombez, J.-M. Poumirol, et al., Exciton spectroscopy and unidirectional transport in lateral heterostructures encapsulated in hexagonal boron nitride, npj 2D Mater. Appl. 6, 84 (2022).
- R. Rosati, I. Paradisanos, E. Malic, and B. Urbaszek, Two dimensional semiconductors: Optical and electronic properties, in Comprehensive Semiconductor Science and Technology, 2nd ed. (Elsevier, Oxford, 2025), pp. 312–351.
- Y. Wu, J. Tan, H. Fang, and R. Lv, Manipulating interfacial excitonic landscapes for exciton transport in two-dimensional lateral heterostructures, Adv. Funct. Mater. 36, e77200 (2026).
- H. Lamsaadi, D. Beret, I. Paradisanos, P. Renucci, D. Lagarde, X. Marie, B. Urbaszek, Z. Gan, A. George, K. Watanabe, et al., Kapitza-resistance-like exciton dynamics in atomically flat lateral heterojunction, Nat. Commun. 14, 5881 (2023).
- M. Z. Bellus, M. Mahjouri-Samani, S. D. Lane, A. D. Oyedele, X. Li, A. A. Puretzky, D. Geohegan, K. Xiao, and H. Zhao, Photocarrier transfer across monolayer lateral heterojunctions, ACS Nano 12, 7086 (2018).
- M. Shimasaki, T. Nishihara, K. Matsuda, T. Endo, Y. Takaguchi, Z. Liu, Y. Miyata, and Y. Miyauchi, Directional exciton-energy transport in a lateral heteromonolayer of , ACS Nano 16, 8205 (2022).
- H. Lamsaadi, A. Cuche, G. Agez, I. Paradisanos, D. Beret, L. Lombez, P. Renucci, D. Lagarde, X. Marie, Z. Gan, A. George, K. Watanabe, T. Taniguchi, A. Turchanin, N. Combe, B. Urbaszek, V. Paillard, and J.-M. Poumirol, Exciton collimation, focusing and trapping using complex transition metal dichalcogenide lateral heterojunctions, Adv. Opt. Mater. 13, 2403009 (2025).
- R. Rosati, K. Sonowal, and E. Malic, Exciton trapping at the interface of lateral TMD heterostructures, in 2D Photonic Materials and Devices IX (SPIE, San Francisco, CA, 2026), Vol. 13898, p. 8.
- X. Sun, E. Malic, and Y. Lu, Dipolar many-body complexes and their interactions in stacked 2D heterobilayers, Nat. Rev. Phys. 6, 439 (2024).
- Q. Lin et al., Moiré-engineered light-matter interactions in heterobilayers at room temperature, Nat. Commun. 15, 8762 (2024).
- D. Erkensten, S. Brem, and E. Malic, Exciton-exciton interaction in transition metal dichalcogenide monolayers and van der Waals heterostructures, Phys. Rev. B 103, 045426 (2021).
- D. Erkensten, S. Brem, R. Perea-Causín, and E. Malic, Microscopic origin of anomalous interlayer exciton transport in van der Waals heterostructures, Phys. Rev. Mater. 6, 094006 (2022).
- Z. Sun, A. Ciarrocchi, F. Tagarelli, J. F. Gonzalez Marin, K. Watanabe, T. Taniguchi, and A. Kis, Excitonic transport driven by repulsive dipolar interaction in a van der Waals heterostructure, Nat. Photonics 16, 79 (2022).
- J. Hagel, S. Brem, C. Linderälv, P. Erhart, and E. Malic, Exciton landscape in van der Waals heterostructures, Phys. Rev. Res. 3, 043217 (2021).
- R. Perea-Causin, D. Erkensten, J. M. Fitzgerald, J. J. Thompson, R. Rosati, S. Brem, and E. Malic, Exciton optics, dynamics, and transport in atomically thin semiconductors, APL Mater. 10, 100701 (2022).
- D. Schmitt, J. P. Bange, W. Bennecke, A. AlMutairi, G. Meneghini, K. Watanabe, T. Taniguchi, D. Steil, D. R. Luke, R. T. Weitz, et al., Formation of moiré interlayer excitons in space and time, Nature (London) 608, 499 (2022).
- D. Erkensten, S. Brem, R. Perea-Causín, J. Hagel, F. Tagarelli, E. Lopriore, A. Kis, and E. Malic, Electrically tunable dipolar interactions between layer-hybridized excitons, Nanoscale 15, 11064 (2023).
- A. Steinhoff, E. Wietek, M. Florian, T. Schulz, T. Taniguchi, K. Watanabe, S. Zhao, A. Högele, F. Jahnke, and A. Chernikov, Exciton-exciton interactions in van der Waals heterobilayers, Phys. Rev. X 14, 031025 (2024).
- C. Ciuti, V. Savona, C. Piermarocchi, A. Quattropani, and P. Schwendimann, Role of the exchange of carriers in elastic exciton-exciton scattering in quantum wells, Phys. Rev. B 58, 7926 (1998).
- F. Lengers, R. Rosati, T. Kuhn, and D. E. Reiter, Spatiotemporal dynamics of Coulomb-correlated carriers in semiconductors, Phys. Rev. B 99, 155306 (2019).
- S. Grisard, A. V. Trifonov, T. Hahn, T. Kuhn, O. Hordiichuk, M. V. Kovalenko, D. R. Yakovlev, M. Bayer, and I. A. Akimov, Spin-dependent exciton–exciton interactions in a mixed lead halide perovskite crystal, ACS Photonics 11, 2930 (2024).
- V. Shahnazaryan, I. Iorsh, I. A. Shelykh, and O. Kyriienko, Exciton-exciton interaction in transition-metal dichalcogenide monolayers, Phys. Rev. B 96, 115409 (2017).
- J. C. König-Otto, M. Mittendorff, T. Winzer, F. Kadi, E. Malic, A. Knorr, C. Berger, W. A. de Heer, A. Pashkin, H. Schneider, M. Helm, and S. Winnerl, Slow noncollinear Coulomb scattering in the vicinity of the Dirac point in graphene, Phys. Rev. Lett. 117, 087401 (2016).
- H. Mittenzwey, A. Knorr, and T. Deilmann, Coulomb interaction in atomically thin semiconductors and density-independent exciton-scattering processes, arXiv:2602.13763.
- H. Mittenzwey, O. Voigt, and A. Knorr, Excitonic theory of the ultrafast optical response of 2D-quantum-confined semiconductors at elevated densities, Adv. Quantum Technol. 9, e70271 (2026).
- H. Haug and S. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 2004).
- F. Katsch, M. Selig, A. Carmele, and A. Knorr, Theory of exciton–exciton interactions in monolayer transition metal dichalcogenides, Phys. Status Solidi B 255, 1800185 (2018).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/wm33-yhyl for additional details on calculation of CT exciton wave functions, microscopic model, and analytical calculation of energy shifts, which includes Refs. [63, 64, 65, 66, 67, 68].
- L. Keldysh, Coulomb interaction in thin semiconductor and semimetal films, JETP Lett. 29, 658 (1979).
- N. S. Rytova, The screened potential of a point charge in a thin film, Phys. Astron. 30, 3 (1967).
- S. Ovesen, S. Brem, C. Linderälv, M. Kuisma, T. Korn, P. Erhart, M. Selig, and E. Malic, Interlayer exciton dynamics in van der Waals heterostructures, Commun. Phys. 2, 23 (2019).
- A. Steinhoff, M. Florian, M. Rösner, G. Schönhoff, T. O. Wehling, and F. Jahnke, Exciton fission in monolayer transition metal dichalcogenide semiconductors, Nat. Commun. 8, 1166 (2017).
- T. Siday, F. Sandner, S. Brem, M. Zizlsperger, R. Perea-Causin, F. Schiegl, S. Nerreter, M. Plankl, P. Merkl, F. Mooshammer, M. A. Huber, E. Malic, and R. Huber, Ultrafast nanoscopy of high-density exciton phases in , Nano Lett. 22, 2561 (2022).
- F. Tassone and Y. Yamamoto, Exciton-exciton scattering dynamics in a semiconductor microcavity and stimulated scattering into polaritons, Phys. Rev. B 59, 10830 (1999).
- J. Zipfel, J. Holler, A. A. Mitioglu, M. V. Ballottin, P. Nagler, A. V. Stier, T. Taniguchi, K. Watanabe, S. A. Crooker, P. C. M. Christianen, T. Korn, and A. Chernikov, Spatial extent of the excited exciton states in monolayers from diamagnetic shifts, Phys. Rev. B 98, 075438 (2018).
- S. Brem, A. Ekman, D. Christiansen, F. Katsch, M. Selig, C. Robert, X. Marie, B. Urbaszek, A. Knorr, and E. Malic, Phonon-assisted photoluminescence from indirect excitons in monolayers of transition-metal dichalcogenides, Nano Lett. 20, 2849 (2020).
- S. Brem, J. Zipfel, M. Selig, A. Raja, L. Waldecker, J. D. Ziegler, T. Taniguchi, K. Watanabe, A. Chernikov, and E. Malic, Intrinsic lifetime of higher excitonic states in tungsten diselenide monolayers, Nanoscale 11, 12381 (2019).
- F.-C. Wu, F. Xue, and A. H. MacDonald, Theory of two-dimensional spatially indirect equilibrium exciton condensates, Phys. Rev. B 92, 165121 (2015).
- R. Rosati, R. Perea-Causín, S. Brem, and E. Malic, Negative effective excitonic diffusion in monolayer transition metal dichalcogenides, Nanoscale 12, 356 (2020).
- R. Rosati and F. Rossi, Scattering nonlocality in quantum charge transport: Application to semiconductor nanostructures, Phys. Rev. B 89, 205415 (2014).
- A. Kormányos, G. Burkard, M. Gmitra, J. Fabian, V. Zólyomi, N. D. Drummond, and V. Fal'ko, theory for two-dimensional transition metal dichalcogenide semiconductors, 2D Mater. 2, 022001 (2015).