Dramatic Plasmon Response to the Charge-Density-Wave Gap Development in $1T\text{\ensuremath{-}}{\mathrm{TiSe}}_{2}$

Dramatic Plasmon Response to the Charge-Density-Wave Gap Development in $1 T − {TiSe}_{2}$

Zijian Lin, Cuixiang Wang, A. Balassis, J. P. Echeverry, A. S. Vasenko, V. M. Silkin, E. V. Chulkov, Youguo Shi, Jiandi Zhang, Jiandong Guo, and Xuetao Zhu

Phys. Rev. Lett. 129, 187601 – Published 24 October 2022

Abstract

$1 T − {TiSe}_{2}$ is one of the most studied charge density wave (CDW) systems, not only because of its peculiar properties related to the CDW transition, but also due to its status as a promising candidate of exciton insulator signaled by the proposed plasmon softening at the CDW wave vector. Using high-resolution electron energy loss spectroscopy, we report a systematic study of the temperature-dependent plasmon behaviors of $1 T − {TiSe}_{2}$ . We unambiguously resolve the plasmon from phonon modes, revealing the existence of Landau damping to the plasmon at finite momentums, which does not support the plasmon softening picture for exciton condensation. Moreover, we discover that the plasmon lifetime at zero momentum responds dramatically to the band gap evolution associated with the CDW transition. The interband transitions near the Fermi energy in the normal phase are demonstrated to serve as a strong damping channel of plasmons, while such a channel in the CDW phase is suppressed due to the CDW gap opening, which results in the dramatic tunability of the plasmon in semimetals or small-gap semiconductors.

Received 30 December 2021
Revised 20 April 2022
Accepted 29 September 2022

DOI:https://doi.org/10.1103/PhysRevLett.129.187601

Physics Subject Headings (PhySH)

Charge density waves Excitons Phonons Plasmons

Surfaces Transition metal dichalcogenides

High-resolution electron energy loss spectroscopy Time-dependent DFT

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zijian Lin^1,2,*, Cuixiang Wang ^1,2,*, A. Balassis³, J. P. Echeverry ⁴, A. S. Vasenko^5,6, V. M. Silkin^7,8,9, E. V. Chulkov^7,8,5, Youguo Shi^1,10, Jiandi Zhang¹, Jiandong Guo^1,2,10,†, and Xuetao Zhu ^1,2,10,‡

¹Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
³Department of Physics and Engineering Physics, Fordham University, 441 East Fordham Road, Bronx, New York 10458, USA
⁴Universidad de Ibagué Carrera 22 Calle 67 B, Av. Ambalá Ibagué Tolima 730007, Colombia
⁵HSE University, 101000 Moscow, Russia
⁶I. E. Tamm Department of Theoretical Physics, P. N. Lebedev Physical Institute, Russian Academy of Sciences, 119991 Moscow, Russia
⁷Donostia International Physics Center (DIPC), 20018 San Sebastián/Donostia, Basque Country, Spain
⁸Departamento de Polímeros y Materiales Avanzados: Física, Química y Tecnología, Facultad de Ciencias Químicas, Universidad del País Vasco UPV/EHU, Apartado 1072, 20080 San Sebastián/Donostia, Basque Country, Spain
⁹IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Basque Country, Spain
¹⁰Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China

^*These authors contributed equally to this work.
^†jdguo@iphy.ac.cn
^‡xtzhu@iphy.ac.cn

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Vol. 129, Iss. 18 — 28 October 2022

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Figure 1
Schematics of the band structure in $1 T − {TiSe}_{2}$ . (a) Band structure in the normal phase. The red and blue lines represent the valence and conduction bands, respectively. The fluctuating band is represented by the gray shadow. The dashed lines indicate the Fermi level. (b) Band structure in the CDW phase. Black lines represent the folding bands due to the distortion.
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Figure 2
Temperature ( $T$ )-dependent HREELS results in $1 T − {TiSe}_{2}$ . (a)–(d) $E - q_{/ /}$ mappings of HREELS at 300, 175, 115, and 35 K, respectively. At the $\bar{Γ}$ point, the plasmon is labeled by $P$ . Dashed-line rectangles show the typical unchanged phonon dispersions close to the plasmon. The momenta are represented in the form of $(q, 0)$ and $(q, q)$ along $\bar{Γ} − \bar{M}$ and $\bar{Γ} − \bar{K}$ directions with the reciprocal lattice unit (r.l.u.) as the unit. The color scale corresponds to the logarithmic intensity. The positive and negative energy ranges represent the Stokes and anti-Stokes scatterings, respectively. (e)–(h) Second differential images of (a)–(d), respectively. The red triangles are the surface phonon dispersions calculated by the slab method. The size of the triangles indicates the spectral weight of the surface amplitude of phonons. White dashed-line rectangles are the same as the dashed-line rectangles in (a)–(d). (i) Stack of the energy distribution curves (EDCs) at the $\bar{Γ}$ point at different temperatures. The triangles and dashed lines are guides to the eyes of phonons and the plasmon, respectively. (j) Stack of the EDCs at 115 K at different $q$ ’s. The intensities of EDCs at $q = 0.01$ , 0.02, and 0.03 r.l.u. is multiplied by 0.03, 0.08, and 0.2 for better presentation, respectively. The dashed-line rectangle is the same as the dashed-line rectangles in (a)–(d).
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Figure 3
Theoretical SPE in $1 T − {TiSe}_{2}$ . (a) and (b) Calculated loss function mappings of the normal and CDW state, respectively. The gray shadowed areas centered at thick white dashed lines are the calculated SPE regions. The green color mappings in loss functions are plasmons. Thin dashed lines highlight calculated critical momenta $q_{c}$ .
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Figure 4
Temperature-dependent plasmon features in $1 T − {TiSe}_{2}$ . (a) Temperature dependence of the dimensionless lifetime parameter $τ_{pl}$ of the plasmon and the CDW gap $E_{g}$ in Ref. [60]. The dashed line highlights the $T_{c}$ . (b) Temperature dependence of the plasmon energy $E_{pl}$ and the square root of the carrier concentration $n^{1 / 2}$ in Ref. [61], respectively. (c) Temperature dependence of the multiplication of the effective carrier mass $m^{*}$ and the high-frequency dielectric constant $ε_{\infty}$ . The unit of the vertical axis ( $m_{e}$ ) is the mass of free electrons. (d) Temperature dependence of the plasmon dispersion below $q_{c}$ .
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Figure 5
Loss functions simulated by a Drude-Lorentz model. (a)–(e) Loss functions $Im [- ε (q, E)^{- 1}]$ with different CDW gaps $E_{g} = 200$ , 100, 50, 50, and 50 meV and interband damping parameters $Γ_{CDW} = 100$ , 100, 100, 300 meV, and 1 eV, respectively. The yellow, red, and blue lines highlight the input parameters: energies of a partly screened plasmon, the intraband transitions, and the interband transitions across the CDW gap, respectively. Inset: the line shape of the loss function at $q = 0$ . The labels on the horizontal and vertical axes are Energy (meV) and Loss Function, respectively.
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Physical Review Letters

Dramatic Plasmon Response to the Charge-Density-Wave Gap Development in 1T−TiSe2

Zijian Lin, Cuixiang Wang, A. Balassis, J. P. Echeverry, A. S. Vasenko, V. M. Silkin, E. V. Chulkov, Youguo Shi, Jiandi Zhang, Jiandong Guo, and Xuetao Zhu

Phys. Rev. Lett. 129, 187601 – Published 24 October 2022

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Dramatic Plasmon Response to the Charge-Density-Wave Gap Development in $1 T − {TiSe}_{2}$