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Persistence of Charge Ordering Instability to Coulomb Engineering in the Excitonic Insulator Candidate TiSe2

Sebastian Buchberger1,2, Yann in ’t Veld3, Akhil Rajan1, Philip A. E. Murgatroyd1, Brendan Edwards1, Bruno K. Saika1, Naina Kushwaha1,4, Maria H. Visscher1,2, Jan Berges5 et al.

Dina Carbone6, Jacek Osiecki6, Craig Polley6, Tim Wehling3,7,*, and Phil D. C. King1,†

  • *Contact author: tim.wehling@physik.uni-hamburg.de
  • †Contact author: pdk6@st-andrews.ac.uk
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Phys. Rev. X 15, 041028 – Published 12 November, 2025

DOI: https://doi.org/10.1103/9trc-9865

Abstract

TiSe2 has long been considered one of the best candidate materials to host the elusive excitonic insulator (EI) phase. However, a finite coupling to the lattice can generically be expected, while a lack of “smoking-gun” signatures for the importance of the electron-hole interaction in driving the phase transition has rendered it challenging to distinguish the EI from the conventional charge-density wave (CDW) phase. Here, we demonstrate a new approach, exploiting the susceptibility of excitons to dielectric screening. We combine mechanical exfoliation with molecular-beam epitaxy to fabricate ultraclean van der Waals heterostructures of monolayer (ML) TiSe2/graphite and ML TiSe2/h-BN. We observe how the modified substrate screening environment drives a renormalization of the quasiparticle band gap of the TiSe2 layer, signifying its susceptibility to Coulomb engineering. The temperature-dependent evolution of its electronic structure, however, remains unaffected, indicating that excitons are not required to drive the CDW transition in TiSe2.

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Popular Summary

The layered material titanium diselenide (TiSe2) displays a charge-density wave, a quantum state where both electrons and atoms reorganize to induce a repeating pattern in the charge density. For decades, researchers have debated whether this ordered state is caused by the spontaneous pairing of electrons and holes—forming excitons—or by a more conventional lattice-driven mechanism. In this study, we determine that excitons are not required to drive the charge-density wave transition in TiSe2.

To probe the origin of the charge-density wave, we study how ultrathin TiSe2 layers respond to different electronic environments. We grow monolayers of TiSe2 on two distinct substrates: metallic graphite and insulating boron nitride. The metallic substrate screens electron-hole interactions, which should weaken or eliminate exciton formation, while the insulating substrate leaves these interactions largely intact. Using a combination of detailed electronic structure measurements and theoretical modeling, we observe that this change in screening significantly alters the electronic states of the TiSe2 layer. Despite this, the charge-density wave remains equally robust on both substrates, even when exciton formation should be suppressed.

This finding demonstrates that lattice effects alone can mediate the charge-density wave in TiSe2, not requiring exciton formation. More broadly, our work provides a general framework for testing how excitons contribute to ordered phases in other materials proposed to host “excitonic insulator” behavior. It also suggests new possibilities for tuning the quantum properties of 2D materials through dielectric screening, offering a versatile approach for both fundamental studies and future device applications.

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References (84)

  1. H. Cercellier, C. Monney, F. Clerc, C. Battaglia, L. Despont, M. G. Garnier, H. Beck, P. Aebi, L. Patthey, H. Berger, and L. Forró, Evidence for an excitonic insulator phase in 1T−TiSe2, Phys. Rev. Lett. 99, 146403 (2007).
  2. C. Monney, E. F. Schwier, M. G. Garnier, N. Mariotti, C. Didiot, H. Beck, P. Aebi, H. Cercellier, J. Marcus, C. Battaglia, H. Berger, and A. N. Titov, Temperature-dependent photoemission on 1T−TiSe2: Interpretation within the exciton condensate phase model, Phys. Rev. B 81, 155104 (2010).
  3. M. D. Watson, O. J. Clark, F. Mazzola, I. Marković, V. Sunko, T. K. Kim, K. Rossnagel, and P. D. C. King, Orbital- and kz-selective hybridization of Se 4p and Ti 3d states in the charge density wave phase of TiSe2, Phys. Rev. Lett. 122, 076404 (2019).
  4. D. Pashov, R. E. Larsen, M. D. Watson, S. Acharya, and M. van Schilfgaarde, TiSe2 is a band insulator created by lattice fluctuations, not an excitonic insulator, npj Comput. Mater. 11, 152 (2025).
  5. D. Jérome, T. M. Rice, and W. Kohn, Excitonic insulator, Phys. Rev. 158, 462 (1967).
  6. W. Kohn, Excitonic phases, Phys. Rev. Lett. 19, 439 (1967).
  7. F. J. Di Salvo, D. E. Moncton, and J. V. Waszczak, Electronic properties and superlattice formation in the semimetal TiSe2, Phys. Rev. B 14, 4321 (1976).
  8. J. A. Wilson, Concerning the semimetallic characters of TiS2 and TiSe2, Solid State Commun. 22, 551 (1977).
  9. T. Pillo, J. Hayoz, H. Berger, F. Lévy, L. Schlapbach, and P. Aebi, Photoemission of bands above the Fermi level: The excitonic insulator phase transition in 1T−TiSe2, Phys. Rev. B 61, 16213 (2000).
  10. H. P. Hughes, Structural distortion in TiSe2 and related materials-a possible Jahn-Teller effect?, J. Phys. C 10, L319 (1977).
  11. K. Rossnagel, L. Kipp, and M. Skibowski, Charge-density-wave phase transition in 1T−TiSe2: Excitonic insulator versus band-type Jahn-Teller mechanism, Phys. Rev. B 65, 235101 (2002).
  12. A. Wegner, J. Zhao, J. Li, J. Yang, A. A. Anikin, G. Karapetrov, K. Esfarjani, D. Louca, and U. Chatterjee, Evidence for pseudo-Jahn-Teller distortions in the charge density wave phase of 1t−TiSe2, Phys. Rev. B 101, 195145 (2020).
  13. A. Kogar, M. S. Rak, S. Vig, A. A. Husain, F. Flicker, Y. I. Joe, L. Venema, G. J. MacDougall, T. C. Chiang, E. Fradkin, J. van Wezel, and P. Abbamonte, Signatures of exciton condensation in a transition metal dichalcogenide, Science 358, 1314 (2017).
  14. Z. Lin, C. Wang, A. Balassis, J. P. Echeverry, A. S. Vasenko, V. M. Silkin, E. V. Chulkov, Y. Shi, J. Zhang, J. Guo, and X. Zhu, Dramatic plasmon response to the charge-density-wave gap development in 1T−TiSe2, Phys. Rev. Lett. 129, 187601 (2022).
  15. T. Rohwer, S. Hellmann, M. Wiesenmayer, C. Sohrt, A. Stange, B. Slomski, A. Carr, Y. Liu, L. M. Avila, M. Kalläne et al., Collapse of long-range charge order tracked by time-resolved photoemission at high momenta, Nature (London) 471, 490 (2011).
  16. M. Porer, U. Leierseder, J.-M. Ménard, H. Dachraoui, L. Mouchliadis, I. Perakis, U. Heinzmann, J. Demsar, K. Rossnagel, and R. Huber, Non-thermal separation of electronic and structural orders in a persisting charge density wave, Nat. Mater. 13, 857 (2014).
  17. C. Monney, M. Puppin, C. W. Nicholson, M. Hoesch, R. T. Chapman, E. Springate, H. Berger, A. Magrez, C. Cacho, R. Ernstorfer, and M. Wolf, Revealing the role of electrons and phonons in the ultrafast recovery of charge density wave correlations in 1T−TiSe2, Phys. Rev. B 94, 165165 (2016).
  18. F. Kurtz, T. N. Dauwe, S. V. Yalunin, G. Storeck, J. G. Horstmann, H. Böckmann, and C. Ropers, Non-thermal phonon dynamics and a quenched exciton condensate probed by surface-sensitive electron diffraction, Nat. Mater. 23, 890 (2024).
  19. Z. Ye, T. Cao, K. O’Brien, H. Zhu, X. Yin, Y. Wang, S. G. Louie, and X. Zhang, Probing excitonic dark states in single-layer tungsten disulphide, Nature (London) 513, 214 (2014).
  20. A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2, Phys. Rev. Lett. 113, 076802 (2014).
  21. M. Ugeda, A. Bradley, S.-F. Shi, F. Da Jornada, Y. Zhang, D. Qiu, S.-K. Mo, Z. Hussain, Z.-X. Shen, F. Wang, S. Louie, and M. Crommie, Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor, Nat. Mater. 13, 1091 (2014).
  22. P. Goli, J. Khan, D. Wickramaratne, R. K. Lake, and A. A. Balandin, Charge density waves in exfoliated films of van der Waals materials: Evolution of Raman spectrum in TiSe2, Nano Lett. 12, 5941 (2012).
  23. L. J. Li, W. J. Zhao, B. Liu, T. H. Ren, G. Eda, and K. P. Loh, Enhancing charge-density-wave order in 1T−TiSe2 nanosheet by encapsulation with hexagonal boron nitride, Appl. Phys. Lett. 109, 141902 (2016).
  24. P. Chen, Y.-H. Chan, M.-H. Wong, X.-Y. Fang, M. Y. Chou, S.-K. Mo, Z. Hussain, A.-V. Fedorov, and T.-C. Chiang, Dimensional effects on the charge density waves in ultrathin films of TiSe2, Nano Lett. 16, 6331 (2016).
  25. K. Sugawara, Y. Nakata, R. Shimizu, P. Han, T. Hitosugi, T. Sato, and T. Takahashi, Unconventional charge-density-wave transition in monolayer 1T−TiSe2, ACS Nano 10, 1341 (2016).
  26. M. D. Watson, A. Rajan, T. Antonelli, K. Underwood, I. Marković, F. Mazzola, O. J. Clark, G.-R. Siemann, D. Biswas, A. Hunter, S. Jandura, J. Reichstetter, M. McLaren, P. L. Fèvre, G. Vinai, and P. D. C. King, Strong-coupling charge density wave in monolayer TiSe2, 2D Mater. 8, 015004 (2020).
  27. T. Antonelli, A. Rajan, M. D. Watson, S. Soltani, J. Houghton, G.-R. Siemann, A. Zivanovic, C. Bigi, B. Edwards, and P. D. King, Controlling the charge density wave transition in single-layer TiTe2x Se2(1−x) alloys by band gap engineering, Nano Lett. 24, 215 (2023).
  28. S. Kolekar, M. Bonilla, Y. Ma, H. Coy Diaz, and M. Batzill, Layer- and substrate-dependent charge density wave criticality in 1T−TiSe2, 2D Mater. 5, 015006 (2018).
  29. S. Kolekar, M. Bonilla, H. Coy Diaz, M. Hashimoto, D. Lu, and M. Batzill, Controlling the charge density wave transition in monolayer TiSe2: Substrate and doping effects, Adv. Quantum Technol. 1, 1800070 (2018).
  30. N. Ohba, K. Miwa, N. Nagasako, and A. Fukumoto, First-principles study on structural, dielectric, and dynamical properties for three BN polytypes, Phys. Rev. B 63, 115207 (2001).
  31. A. Laturia, M. L. Van de Put, and W. G. Vandenberghe, Dielectric properties of hexagonal boron nitride and transition metal dichalcogenides: From monolayer to bulk, npj 2D Mater. Appl. 2, 6 (2018).
  32. A. Pierret, D. Mele, H. Graef, J. Palomo, T. Taniguchi, K. Watanabe, Y. Li, B. Toury, C. Journet, P. Steyer, V. Garnier, A. Loiseau, J.-M. Berroir, E. Bocquillon, G. Fève, C. Voisin, E. Baudin, M. Rosticher, and B. Plaçais, Dielectric permittivity, conductivity and breakdown field of hexagonal boron nitride, Mater. Res. Express 9, 065901 (2022).
  33. Y. Kang, D. Jeon, and T. Kim, Local mapping of the thickness-dependent dielectric constant of MoS2, J. Phys. Chem. C 125, 3611 (2021).
  34. L. J. Li, E. C. T. O’Farrell, K. P. Loh, G. Eda, B. Özyilmaz, and A. H. Castro Neto, Controlling many-body states by the electric-field effect in a two-dimensional material, Nature (London) 529, 185 (2016).
  35. P. Chen, Y.-H. Chan, X.-Y. Fang, Y. Zhang, M. Y. Chou, S.-K. Mo, Z. Hussain, A.-V. Fedorov, and T.-C. Chiang, Charge density wave transition in single-layer titanium diselenide, Nat. Commun. 6, 8943 (2015).
  36. A. Rajan, K. Underwood, F. Mazzola, and P. D. C. King, Morphology control of epitaxial monolayer transition metal dichalcogenides, Phys. Rev. Mater. 4, 014003 (2020).
  37. B. Seredyński, R. Bożek, J. Suffczyński, J. Piwowar, J. Sadowski, and W. Pacuski, Molecular beam epitaxy growth of MoTe2 on hexagonal boron nitride, J. Cryst. Growth 596, 126806 (2022).
  38. D. Fu, X. Zhao, Y.-Y. Zhang, L. Li, H. Xu, A.-R. Jang, S. I. Yoon, P. Song, S. M. Poh, T. Ren, Z. Ding, W. Fu, T. J. Shin, H. S. Shin, S. T. Pantelides, W. Zhou, and K. P. Loh, Molecular beam epitaxy of highly crystalline monolayer molybdenum disulfide on hexagonal boron nitride, J. Am. Chem. Soc. 139, 9392 (2017).
  39. W. Pacuski, M. Grzeszczyk, K. Nogajewski, A. Bogucki, K. Oreszczuk, J. Kucharek, K. E. Połczyńska, B. Seredyński, A. Rodek, R. Bożek, T. Taniguchi, K. Watanabe, S. Kret, J. Sadowski, T. Kazimierczuk, M. Potemski, and P. Kossacki, Narrow excitonic lines and large-scale homogeneity of transition-metal dichalcogenide monolayers grown by molecular beam epitaxy on hexagonal boron nitride, Nano Lett. 20, 3058 (2020).
  40. H. Henck, D. Pierucci, G. Fugallo, J. Avila, G. Cassabois, Y. J. Dappe, M. G. Silly, C. Chen, B. Gil, M. Gatti, F. Sottile, F. Sirotti, M. C. Asensio, and A. Ouerghi, Direct observation of the band structure in bulk hexagonal boron nitride, Phys. Rev. B 95, 085410 (2017).
  41. R. J. Koch, J. Katoch, S. Moser, D. Schwarz, R. K. Kawakami, A. Bostwick, E. Rotenberg, C. Jozwiak, and S. Ulstrup, Electronic structure of exfoliated and epitaxial hexagonal boron nitride, Phys. Rev. Mater. 2, 074006 (2018).
  42. A. Rajan, S. Buchberger, B. Edwards, A. Zivanovic, N. Kushwaha, C. Bigi, Y. Nanao, B. K. Saika, O. R. Armitage, P. Wahl, P. Couture, and P. D. C. King, Epitaxial growth of large-area monolayers and van der waals heterostructures of transition-metal chalcogenides via assisted nucleation, Adv. Mater. 36, 2402254 (2024).
  43. See Supplemental Material at http://link.aps.org/supplemental/10.1103/9trc-9865 for additional materials characterisation, ARPES data and fitting, and calculations of band renormalisation and nonlocal screening effects.
  44. I. C. Gerber and X. Marie, Dependence of band structure and exciton properties of encapsulated WSe2 monolayers on the hBn-layer thickness, Phys. Rev. B 98, 245126 (2018).
  45. K. F. Berggren and B. E. Sernelius, Band-gap narrowing in heavily doped many-valley semiconductors, Phys. Rev. B 24, 1971 (1981).
  46. B. Bennett, R. Soref, and J. Del Alamo, Carrier-induced change in refractive index of InP, GaAs and InGaAsP, IEEE J. Quantum Electron. 26, 113 (1990).
  47. A. Steinhoff, M. Rösner, F. Jahnke, T. O. Wehling, and C. Gies, Influence of excited carriers on the optical and electronic properties of MoS2, Nano Lett. 14, 3743 (2014).
  48. A. Chernikov, A. M. van der Zande, H. M. Hill, A. F. Rigosi, A. Velauthapillai, J. Hone, and T. F. Heinz, Electrical tuning of exciton binding energies in monolayer WS2, Phys. Rev. Lett. 115, 126802 (2015).
  49. S. Gao and L. Yang, Renormalization of the quasiparticle band gap in doped two-dimensional materials from many-body calculations, Phys. Rev. B 96, 155410 (2017).
  50. D. Erben, A. Steinhoff, C. Gies, G. Schönhoff, T. O. Wehling, and F. Jahnke, Excitation-induced transition to indirect band gaps in atomically thin transition-metal dichalcogenide semiconductors, Phys. Rev. B 98, 035434 (2018).
  51. Z. Qiu, M. Trushin, H. Fang, I. Verzhbitskiy, S. Gao, E. Laksono, M. Yang, P. Lyu, J. Li, J. Su, M. Telychko, K. Watanabe, T. Taniguchi, J. Wu, A. H. C. Neto, L. Yang, G. Eda, S. Adam, and J. Lu, Giant gate-tunable bandgap renormalization and excitonic effects in a 2D semiconductor, Sci. Adv. 5, eaaw2347 (2019).
  52. C. Sahoo, Y. i. t. Veld, A. J. H. Jones, Z. Jiang, G. Lupi, P. E. Majchrzak, K. Hsieh, K. Watanabe, T. Taniguchi, P. Hofmann, J. A. Miwa, Y. P. Chen, M. Rösner, and S. Ulstrup, Quasiparticle gap renormalization driven by internal and external screening in WS2 device, Phys. Rev. Lett. 135, 056401 (2025).
  53. A. Schobert, J. Berges, E. G. C. P. Van Loon, M. A. Sentef, S. Brener, M. Rossi, and T. O. Wehling, Ab initio electron-lattice downfolding: Potential energy landscapes, anharmonicity, and molecular dynamics in charge density wave materials, SciPost Phys. 16, 046 (2024).
  54. M. Rösner, C. Steinke, M. Lorke, C. Gies, F. Jahnke, and T. O. Wehling, Two-dimensional heterojunctions from nonlocal manipulations of the interactions, Nano Lett. 16, 2322 (2016).
  55. A. Raja, A. Chaves, J. Yu, G. Arefe, H. M. Hill, A. F. Rigosi, T. C. Berkelbach, P. Nagler, C. Schüller, T. Korn, C. Nuckolls, J. Hone, L. E. Brus, T. F. Heinz, D. R. Reichman, and A. Chernikov, Coulomb engineering of the bandgap and excitons in two-dimensional materials, Nat. Commun. 8, 15251 (2017).
  56. E. G. C. P. van Loon, M. Schüler, D. Springer, G. Sangiovanni, J. M. Tomczak, and T. O. Wehling, Coulomb engineering of two-dimensional Mott materials, npj 2D Mater. Appl. 7, 47 (2023).
  57. C. Chen, X. Chen, W. Tang, Z. Li, S. Wang, S. Ding, Z. Kang, C. Jozwiak, A. Bostwick, E. Rotenberg, M. Hashimoto, D. Lu, J. P. C. Ruff, S. G. Louie, R. J. Birgeneau, Y. Chen, Y. Wang, and Y. He, Role of electron-phonon coupling in excitonic insulator candidate Ta2NiSe5, Phys. Rev. Res. 5, 043089 (2023).
  58. K. F. Mak, K. He, C. Lee, G. H. Lee, J. Hone, T. F. Heinz, and J. Shan, Tightly bound trions in monolayer MoS2, Nat. Mater. 12, 207 (2013).
  59. 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).
  60. T. N. Lin, S. R. M. Santiago, S. P. Caigas, C. T. Yuan, T. Y. Lin, J. L. Shen, and Y. F. Chen, Many-body effects in doped WS2 monolayer quantum disks at room temperature, npj 2D Mater. Appl. 3, 46 (2019).
  61. Z. Torbatian and D. Novko, Plasmon excitations across the charge-density-wave transition in single-layer TiSe2, J. Phys. Chem. Lett. 15, 6045 (2024).
  62. J. Berges, N. Girotto, T. Wehling, N. Marzari, and S. Poncé, Phonon self-energy corrections: To screen, or not to screen, Phys. Rev. X 13, 041009 (2023).
  63. E. G. C. P. van Loon, M. Rösner, M. I. Katsnelson, and T. O. Wehling, Random phase approximation for gapped systems: Role of vertex corrections and applicability of the constrained random phase approximation, Phys. Rev. B 104, 045134 (2021).
  64. L. Waldecker, A. Raja, M. Rösner, C. Steinke, A. Bostwick, R. J. Koch, C. Jozwiak, T. Taniguchi, K. Watanabe, E. Rotenberg, T. O. Wehling, and T. F. Heinz, Rigid band shifts in two-dimensional semiconductors through external dielectric screening, Phys. Rev. Lett. 123, 206403 (2019).
  65. Y. Lin, X. Ling, L. Yu, S. Huang, A. L. Hsu, Y.-H. Lee, J. Kong, M. S. Dresselhaus, and T. Palacios, Dielectric screening of excitons and trions in single-layer MoS2, Nano Lett. 14, 5569 (2014).
  66. S. Fragkos, H. Orio, N. G. Erhardt, A. Jabed, S. Sasi, Q. Courtade, M. Masilamani, M. Ünzelmann, F. Diekmann, B. Hildebrand et al., Electron-phonon-dominated charge-density-wave fluctuations in TiSe2 accessed by ultrafast nonequilibrium dynamics, arXiv:2507.12430.
  67. Y. Wakisaka, T. Sudayama, K. Takubo, T. Mizokawa, M. Arita, H. Namatame, M. Taniguchi, N. Katayama, M. Nohara, and H. Takagi, Excitonic insulator state in Ta2NiSe5 probed by photoemission spectroscopy, Phys. Rev. Lett. 103, 026402 (2009).
  68. Y. F. Lu, H. Kono, T. I. Larkin, A. W. Rost, T. Takayama, A. V. Boris, B. Keimer, and H. Takagi, Zero-gap semiconductor to excitonic insulator transition in Ta2NiSe5, Nat. Commun. 8, 14408 (2017).
  69. Y. Jia et al., Evidence for a monolayer excitonic insulator, Nat. Phys. 18, 87 (2022).
  70. B. Sun, W. Zhao, T. Palomaki, Z. Fei, E. Runburg, P. Malinowski, X. Huang, J. Cenker, Y.-T. Cui, J.-H. Chu, X. Xu, S. S. Ataei, D. Varsano, M. Palummo, E. Molinari, M. Rontani, and D. H. Cobden, Evidence for equilibrium exciton condensation in monolayer WTe2, Nat. Phys. 18, 94 (2022).
  71. Y. Song, C. Jia, H. Xiong, B. Wang, Z. Jiang, K. Huang, J. Hwang, Z. Li, C. Hwang, Z. Liu, D. Shen, J. A. Sobota, P. Kirchmann, J. Xue, T. P. Devereaux, S.-K. Mo, Z.-X. Shen, and S. Tang, Signatures of the exciton gas phase and its condensation in monolayer 1T−ZrTe2, Nat. Commun. 14, 1116 (2023).
  72. Q. Gao, Y.-h. Chan, Y. Wang, H. Zhang, P. Jinxu, S. Cui, Y. Yang, Z. Liu, D. Shen, Z. Sun, J. Jiang, T. C. Chiang, and P. Chen, Evidence of high-temperature exciton condensation in a two-dimensional semimetal, Nat. Commun. 14, 994 (2023).
  73. Q. Gao, Y.-h. Chan, P. Jiao, H. Chen, S. Yin, K. Tangprapha, Y. Yang, X. Li, Z. Liu, D. Shen, S. Jiang, and P. Chen, Observation of possible excitonic charge density waves and metal–insulator transitions in atomically thin semimetals, Nat. Phys. 20, 597 (2024).
  74. J. Huang et al., Evidence for an excitonic insulator state in Ta2Pd3Te5, Phys. Rev. X 14, 011046 (2024).
  75. S. Buchberger, Y. in ’t Veld, A. Rajan, P. A. E. Murgatroyd, B. Edwards, B. K. Saika, N. Kushwaha, M. H. Visscher, J. Berges, D. Carbone, J. Osiecki, C. Polley, T. Wehling, and P. D. C. King, Persistence of charge ordering instability to Coulomb engineering in the excitonic insulator candidate TiSe2 (dataset), Dataset, University of St. Andrews Research Portal, 10.17630/45e7aa5c-c165-4869-8fca-35e7154f14f3 (2025).
  76. P. D. C. King, B. Edwards, S. Mo, T. Antonelli, E. A. Morales, L. Hart, and L. Trzaska, Peaks: A python package for analysis of angle-resolved photoemission and related spectroscopies, arXiv:2508.04803.
  77. M. Rösner, E. Şaş𝚤oğlu, C. Friedrich, S. Blügel, and T. O. Wehling, Wannier function approach to realistic Coulomb interactions in layered materials and heterostructures, Phys. Rev. B 92, 085102 (2015).
  78. L. Hedin, New method for calculating the one-particle Green’s function with application to the electron-gas problem, Phys. Rev. 139, A796 (1965).
  79. C. Steinke, T. O. Wehling, and M. Rösner, Coulomb-engineered heterojunctions and dynamical screening in transition metal dichalcogenide monolayers, Phys. Rev. B 102, 115111 (2020).
  80. O. Parcollet, M. Ferrero, T. Ayral, H. Hafermann, I. Krivenko, L. Messio, and P. Seth, TRIQS: A toolbox for research on interacting quantum systems, Comput. Phys. Commun. 196, 398 (2015).
  81. H. U. Strand, N. Wentzell, S. Kaeser, Y. in ’t Veld, D. Simon, A. Hampel, M. Roesner, E. van Loon, O. Parcollet, O. Gingras, P. Dumitrescu, T. Hahn, and M. Zingl, TRIQS/tprf: Version 3.2.1 (2023), 10.5281/zenodo.13652322.
  82. G. Giuliani and G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, Cambridge, England, 2005).
  83. J. Comtet, A. Niguès, V. Kaiser, B. Coasne, L. Bocquet, and A. Siria, Nanoscale capillary freezing of ionic liquids confined between metallic interfaces and the role of electronic screening, Nat. Mater. 16, 634 (2017).
  84. R. Akashi and R. Arita, Development of density-functional theory for a plasmon-assisted superconducting state: Application to lithium under high pressures, Phys. Rev. Lett. 111, 057006 (2013).

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Phys. Rev. X 15, 041028– Published 12 November, 2025
  • Received 30 May 2025
  • Revised 29 August 2025
  • Accepted 9 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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