- Open Access
Many-body signatures of dimensional reduction in quasi-one-dimensional
Phys. Rev. B 114, 225125 – Published 14 October, 2026
DOI: https://doi.org/10.1103/vfpp-dm6l
Abstract
The electronic and optical properties of quasi-one-dimensional transition-metal trichalcogenides remain largely unexplored beyond the mean-field approximation, and it is not clear how they evolve as the crystal is thinned. By performing first-principles many-body perturbation theory calculations, we determine the quasiparticle band structures and the polarization-resolved optical response of in the bulk, bilayer, and monolayer limits, using a hierarchy of methods (hybrid DFT, , and the Bethe-Salpeter equation). We find that all three systems are indirect-gap semiconductors with a quasidirect character, the direct-indirect splitting being and nearly independent of both the level of theory and the dimensionality. The mean-field gaps are almost insensitive to thickness, whereas the quasiparticle corrections increase the gap by from bulk to monolayer. The effective exact-exchange fraction reproducing the gap scales as , increasing from to , so that no single hybrid functional describes the full dimensional series. The optical onset blueshifts monotonically () and the near-edge absorption is strongly dichroic. A change in light polarization does not simply shift the excitonic resonance (); it also reorganizes the underlying excitonic wave function, selecting distinct band channels and -space regions. A real-space, participation-ratio analysis resolves moderately delocalized, Wannier-Mott-like excitons templated along the covalent chains. They are predominantly sulfur-derived (75%–88% of the density on sulfur for the chain-polarized bulk states), which identifies them as ( disulfide excitations rather than charge-transfer states, while in the bilayer the electron delocalizes across both layers, the real-space imprint of interlayer screening. These results provide a consistent reference for the quasiparticle and excitonic energy scales of from the bulk to the few-layer limit.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (48)
- J. Dai, M. Li, and X. C. Zeng, Group IVB transition metal trichalcogenides: A new class of 2D layered materials beyond graphene, WIREs Comput. Mol. Sci. 6, 211 (2016).
- Y. Jin, X. Li, and J. Yang, Single layer of (, Zr; , Se, Te): A new platform for nano-electronics and optics, Phys. Chem. Chem. Phys. 17, 18665 (2015).
- S. Furuseth, L. Brattås, A. Kjekshus, A. F. Andresen, and P. Fischer, On the crystal structures of , and , Acta Chem. Scand. A 29, 623 (1975).
- W. Schairer and M. W. Shafer, Growth and optical absorption spectra of the layer-type trichalcogenides and , Phys. Status Solidi (A) 17, 181 (1973).
- K. Osada, S. Bae, M. Tanaka, H. Raebiger, K. Shudo, and T. Suzuki, Phonon properties of few-layer crystals of quasi-one-dimensional and , J. Phys. Chem. C 120, 4653 (2016).
- M. Campetella, G. Marini, J. S. Zhou, and M. Calandra, Electron-phonon driven charge density wave in CuTe, Phys. Rev. B 108, 024304 (2023).
- H. Yi, S. J. Gilbert, A. Lipatov, A. Sinitskii, J. Avila, J. Abourahma, T. Komesu, M. C. Asensio, and P. A. Dowben, The electronic band structure of quasi-one-dimensional van der Waals semiconductors: The effective hole mass of compared to , J. Phys.: Condens. Matter 32, 29LT01 (2020).
- D. Pacilé, M. Papagno, M. Lavagnini, H. Berger, L. Degiorgi, and M. Grioni, Photoemission and optical studies of , and , Phys. Rev. B 76, 155406 (2007).
- S. Kurita, J. L. Staehli, M. Guzzi, and F. Lévy, Optical properties of and , Physica B + C 105, 169 (1981).
- S. Kurita, M. Tanaka, and F. Lévy, Optical spectra near the band edge of and , Phys. Rev. B 48, 1356 (1993).
- L. Thole, A. B. Kalefa, C. Belke, S. Locmelis, L. Bockhorn, P. Behrens, and R. J. Haug, Long-persistent photoconductivity in transistor structures made from thin -films, ACS Appl. Electron. Mater. 5, 6286 (2023).
- A. S. Rosyadi, Y.-X. Lin, Y.-H. Peng, and C.-H. Ho, Axially-polarized excitonic series and anisotropic van der Waals stacked heterojunction in a quasi-1D layered transition-metal trichalcogenide, Adv. Sci. 11, 2406781 (2024).
- B. Mortazavi, F. Shojaei, M. Yagmurcukardes, M. Makaremi, and X. Zhuang, A theoretical investigation on the physical properties of zirconium trichalcogenides, and monolayers, Energies 15, 5479 (2022).
- M. Abdulsalam and D. P. Joubert, Optical spectrum and excitons in bulk and monolayer (, Hf; , Se), Physica Status Solidi (B) 253, 705 (2016).
- A. Pant, E. Torun, B. Chen, S. Bhat, X. Fan, K. Wu, D. P. Wright, F. M. Peeters, E. Soignard, H. Sahin, and S. Tongay, Strong dichroic emission in the pseudo one dimensional material , Nanoscale 8, 16259 (2016).
- R. Ahammed, A. Rawat, N. Jena, Dimple, and A. De Sarkar, and /MXY (M = Mo, W; X, Y = S, Se, Te; ) type-II van der Waals hetero-bilayers: Prospective candidates in 2D excitonic solar cells, Appl. Surf. Sci. 499, 143894 (2020).
- Y. Wang, C. Du, P. Li, Y. Yang, Y. Xiao, T. Ge, X. Jiang, Y. Liu, H. Gao, K. Li, and W. Wang, Photodetectors based on heterostructures ACS Appl. Mater. Interfaces 16, 29049 (2024).
- R. Dovesi, A. Erba, R. Orlando, C. M. Zicovich-Wilson, B. Civalleri, L. Maschio, M. Rérat, S. Casassa, J. Baima, S. Salustro, and B. Kirtman, Quantum-mechanical condensed matter simulations with crystal, WIREs Comput. Mol. Sci. 8, e1360 (2018).
- A. Erba, J. K. Desmarais, S. Casassa, B. Civalleri, L. Donà, I. J. Bush, B. Searle, L. Maschio, L. Edith-Daga, A. Cossard, C. Ribaldone, E. Ascrizzi, N. L. Marana, J.-P. Flament, and B. Kirtman, crystal23: A program for computational solid state physics and chemistry, J. Chem. Theory Comput. 19, 6891 (2023).
- C. Adamo and V. Barone, Toward reliable density functional methods without adjustable parameters: The PBE0 model, J. Chem. Phys. 110, 6158 (1999).
- S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132, 154104 (2010).
- M. F. Peintinger, D. V. Oliveira, and T. Bredow, Consistent Gaussian basis sets of triple-zeta valence with polarization quality for solid-state calculations, J. Comput. Chem. 34, 451 (2013).
- J. Laun, D. V. Oliveira, and T. Bredow, Consistent Gaussian basis sets of double- and triple-zeta valence with polarization quality of the fifth period for solid-state calculations, J. Comput. Chem. 39, 1285 (2018).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/vfpp-dm6l for computational parameters and convergence tests, optimized structures, projected densities of states, real- and reciprocal-space exciton analyses, and assessments of dispersion and spin-orbit effects, which also includes Ref. [3].
- G. Ambrogio, J. K. Desmarais, and A. Erba, Efficient hybrid density functional calculations for solids with a local basis set, Phys. Rev. Mater. 10, 073803 (2026).
- M. Campetella, J. Baima, N. M. Nguyen, L. Maschio, F. Mauri, and M. Calandra, Hybrid-functional electronic structure of multilayer graphene, Phys. Rev. B 101, 165437 (2020).
- M. Campetella, A. Perfetto, and I. Ciofini, Quantifying partial hole-particle distance at the excited state: A revised version of the DCT index, Chem. Phys. Lett. 714, 81 (2019).
- H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
- T. Yanai, D. P. Tew, and N. C. Handy, A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP), Chem. Phys. Lett. 393, 51 (2004).
- J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys. 118, 8207 (2003).
- J. Heyd, G. E. Scuseria, and M. Ernzerhof, Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)] J. Chem. Phys. 124, 219906 (2006).
- A. V. Krukau, O. A. Vydrov, A. F. Izmaylov, and G. E. Scuseria, Influence of the exchange screening parameter on the performance of screened hybrid functionals, J. Chem. Phys. 125, 224106 (2006).
- P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, et al., quantum espresso: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
- P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A. Dal Corso, S. de Gironcoli, P. Delugas, R. A. DiStasio Jr, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, et al., Advanced capabilities for materials modelling with Quantum espresso, J. Phys.: Condens. Matter 29, 465901 (2017).
- P. Giannozzi, O. Baseggio, P. Bonfà, D. Brunato, R. Car, I. Carnimeo, C. Cavazzoni, S. de Gironcoli, P. Delugas, F. Ferrari Ruffino, A. Ferretti, N. Marzari, I. Timrov, A. Urru, and S. Baroni, quantum espresso toward the exascale, J. Chem. Phys. 152, 154105 (2020).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- M. J. van Setten, M. Giantomassi, E. Bousquet, M. J. Verstraete, D. R. Hamann, X. Gonze, and G.-M. Rignanese, The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table, Comput. Phys. Commun. 226, 39 (2018).
- T. Sohier, M. Calandra, and F. Mauri, Density functional perturbation theory for gated two-dimensional heterostructures: Theoretical developments and application to flexural phonons in graphene, Phys. Rev. B 96, 075448 (2017).
- J. Deslippe, G. Samsonidze, D. A. Strubbe, M. Jain, M. L. Cohen, and S. G. Louie, BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures, Comput. Phys. Commun. 183, 1269 (2012).
- M. S. Hybertsen and S. G. Louie, Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies, Phys. Rev. B 34, 5390 (1986).
- S. Ismail-Beigi, Truncation of periodic image interactions for confined systems, Phys. Rev. B 73, 233103 (2006).
- F. Fuchs, J. Furthmüller, F. Bechstedt, M. Shishkin, and G. Kresse, Quasiparticle band structure based on a generalized Kohn-Sham scheme, Phys. Rev. B 76, 115109 (2007).
- M. Shishkin and G. Kresse, Self-consistent calculations for semiconductors and insulators, Phys. Rev. B 75, 235102 (2007).
- M. Li, J. Dai, and X. C. Zeng, Tuning the electronic properties of transition-metal trichalcogenides via tensile strain, Nanoscale 7, 15385 (2015).
- F. Chen, G. Liu, Z. Xiao, H. Zhou, L. Fei, S. Wan, X. Liao, J. Yuan, and Y. Zhou, Quasi-one-dimensional nanoflakes for broadband and polarized photodetection with high tuning flexibility, ACS Appl. Mater. Interfaces 15, 16999 (2023).
- X. Wang, K. Wu, M. Blei, Y. Wang, L. Pan, K. Zhao, C. Shan, M. Lei, Y. Cui, B. Chen, D. Wright, W. Hu, S. Tongay, and Z. Wei, Highly polarized photoelectrical response in vdW nanoribbons, Adv. Electron. Mater. 5, 1900419 (2019).
- F. Jellinek, R. A. Pollak, and M. W. Shafer, X-ray photoelectron spectra and electronic structure of zirconium trisulfide and triselenide, Mater. Res. Bull. 9, 845 (1974).
- A. S. Davydov, The theory of molecular excitons, Sov. Phys. Usp. 7, 145 (1964).