Unveiling the microscopic dynamics of the charge density wave transition in monolayer $\mathrm{V}{X}_{2}$ ($X=\mathrm{S}$, Te)

Letter

Unveiling the microscopic dynamics of the charge density wave transition in monolayer $V X_{2}$ ( $X = S$ , Te)

Yuxuan Chen, Chao Liang, Jian Yuan, Biao Wang, and Huashan Li

Phys. Rev. B 109, L140105 – Published 25 April 2024

Abstract

Charge density waves (CDWs) in two-dimensional materials have received great attention due to their intriguing properties, yet the microscopic evolution process of CDW transition and its impact on charge transport remain to be fully understood. Herein we employed density-functional theory calculations to ascertain the richness of CDW phases in $V X_{2}$ ( $X = S$ , Te) originated from electron-phonon coupling. Reversible transitions between the normal and CDW phases are directly simulated with ab initio molecular dynamics, indicating that the formation of CDW phase is a rapid nucleation process. The corresponding microscopic dynamic processes involve the formation, flipping, translation, and aggregation of characteristic patterns, which are driven by the soft phonon modes. Modifications of electrical conductivity in CDW phase transition are found to stem from the varying orientation and location distributions of relevant wave functions. The revealed dynamic mechanism opens an opportunity for the control of CDW phase transition that is crucial to its applications in logical circuits and neural networks.

Received 20 November 2023
Revised 18 February 2024
Accepted 25 March 2024

DOI:https://doi.org/10.1103/PhysRevB.109.L140105

Physics Subject Headings (PhySH)

Charge density waves First-principles calculations Phase transitions Spin-phonon coupling

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yuxuan Chen¹, Chao Liang¹, Jian Yuan¹, Biao Wang^1,*, and Huashan Li ^1,2,3,†

¹School of Physics, Sun Yat-Sen University, Guangzhou 510275, China
²Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, School of Physics, Sun Yat-sen University, Guangzhou 510275, China
³School of Materials Science and Engineering, Dongguan University of Technology, Dongguan 523808, China

^*Corresponding author: wangbiao@mail.sysu.edu.cn
^†Corresponding author: lihsh25@mail.sysu.edu.cn

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Vol. 109, Iss. 14 — 1 April 2024

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Figure 1
Electronic and phononic structures of $V S_{2}$ and $VT e_{2}$ . The projected band structure of (a) $V S_{2}$ and (b) $VT e_{2}$ . The electron orbits of V $3 d$ , S $3 p$ , and Te $5 p$ are presented in red, blue, and brown dots, respectively, with the dot size denoting the orbital weight. Atomic structures of $V S_{2}$ and $VT e_{2}$ are shown in the inset. (c) Fermi-nesting function η( $q$ ) and (f) phonon linewidth $γ_{μ}$ ( $q$ ) of $V S_{2}$ and $VT e_{2}$ evaluated to probe the electron-phonon interactions. The $q$ vectors of unstable phonon modes are represented by the purple dashed lines. Phonon dispersions of (d) $V S_{2}$ and (e) $VT e_{2}$ . Harmonic phonon dispersions are represented with gray solid lines, while anharmonic phonon dispersions at different temperatures are displayed with colored dotted lines.
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Figure 2
Analyses of potential CDW phases in $V S_{2}$ and $VT e_{2}$ . Two-dimensional Fermi surfaces of NS: (a) $V S_{2}$ and (b) $VT e_{2}$ on the (001) surface plane, along with the CDW vectors indicated by red arrows. Schematic illustration of the relative atomic motion driven by soft phonon modes associated with the (c) $q_{1}, q_{2}$ , and $q_{3}$ vectors for $V S_{2}$ as well as the (d) $q_{4}, q_{5}$ , and $q_{6}$ vectors for $VT e_{2}$ . Formation energies $Δ E$ of the potential CDW structures in (e) $V S_{2}$ and (h) $VT e_{2}$ . Schematic diagrams of CDW structures with the lowest $Δ E$ : (f) $\sqrt{7} \times \sqrt{3}$ and (g) $9 \times \sqrt{3}$ CDW in $V S_{2}$ ; (i) 4×4 and (j) 8×8 CDW by AIMD in $VT e_{2}$ . Red, blue, and brown spheres denote the V, S, and Te atoms, respectively. The black dashed parallelograms show periodicities of CDW structures. The cutoff lengths for the V–V bonds in $V S_{2}$ and $VT e_{2}$ are 3.11 and 3.44 Å, respectively.
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Figure 3
Schematic illustration of the multicenter bonding and the p-d hybridization in CDW. The atomic structure and corresponding Integrated crystal orbital Hamilton population (ICOHP) in (a) $V S_{2} \sqrt{7} \times \sqrt{3}$ , (b) $V S_{2} 9 \times \sqrt{3}$ CDW, (c) $VT e_{2}$ 4×1, and (d) $VT e_{2}$ 4×4 CDW, respectively. Note that in order to highlight the three-center bonds, the V-V cutoff is shrunk to 3.05 Å in $V S_{2}$ and 3.25 Å in $VT e_{2}$ . The three-center (3c) bonds with high values of ICOBI are highlighted with black dashed boxes.
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Figure 4
Microscopic evolutions of CDW phase transitions revealed by AIMD simulations. The variations of atomic structure during the AIMD cooling and heating processes for (a) $V S_{2}$ and (b) $VT e_{2}$ . (c) The maximum distances of V-V along the $Z$ direction during the AIMD cooling processes as a function of temperature for $V S_{2}$ and $VT e_{2}$ . Custom order parameters as a function of temperature for (d) $V S_{2}$ and (e) $VT e_{2}$ . The red and blue dotted lines represent the AIMD heating and cooling processes, respectively. Each dot represents the average value of adjacent 100 structures during AIMD.
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Figure 5
Schematic illustration of CDW formation and its impact on transport property. Critical structural evolution during the AIMD cooling processes for (a)–(d) $V S_{2}$ and (e)–(h) $VT e_{2}$ . Colored dashed shapes highlight the parts with significant structural changes. Comparison of electric conductivity at 300 K between the CDW and NS phases for (i) $V S_{2}$ and (j) $VT e_{2}$ . Partial charge density distributions of (k) $\sqrt{7} \times \sqrt{3}$ CDW in $V S_{2}$ and (l) 4×4 CDW structures in $VT e_{2}$ within the energy range of ( $E_{F}$ −0.1 eV, $E_{F}$ ). The value of the isosurface is set to $0.003 e Å^{- 3}$ .
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Physical Review B

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Unveiling the microscopic dynamics of the charge density wave transition in monolayer $V X_{2}$ ( $X = S$ , Te)

Yuxuan Chen, Chao Liang, Jian Yuan, Biao Wang, and Huashan Li

Phys. Rev. B 109, L140105 – Published 25 April 2024

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Physical Review B

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Unveiling the microscopic dynamics of the charge density wave transition in monolayer VX2 (X=S, Te)

Yuxuan Chen, Chao Liang, Jian Yuan, Biao Wang, and Huashan Li

Phys. Rev. B 109, L140105 – Published 25 April 2024

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Unveiling the microscopic dynamics of the charge density wave transition in monolayer $V X_{2}$ ( $X = S$ , Te)