Transient three-dimensional structural dynamics in $1T\ensuremath{-}\mathrm{TaS}{\mathrm{e}}_{2}$

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Transient three-dimensional structural dynamics in $1 T - TaS e_{2}$

Shaozheng Ji, Oscar Grånäs, Kai Rossnagel, and Jonas Weissenrieder

Phys. Rev. B 101, 094303 – Published 5 March 2020

Abstract

We report on thermal and optically driven transitions between the commensurate (C) and incommensurate (IC) charge-density wave (CDW) phases of $1 T - TaS e_{2}$ . Optical excitation results in suppression of the C-CDW on a subpicosecond timescale. The optically driven C to IC transition involves a short-lived (∼1 ps) unreconstructed phase. Nucleation of an IC phase stacking order is observed already at ∼4 ps following photoexcitation. The short timescales involved in establishing the stacking order implies that the nucleation of the IC phase is influenced by the local geometry of the adjacent layers such that the stacking direction of the C phase determines the stacking direction of the IC phase. From this follows that the nucleation of the IC-CDW is inherently three dimensional (3D). We observe the activation of a coherent shear mode in the optically driven transitions to the transiently stabilized unreconstructed phase. The activation mechanism starts with a rapid lifting of the periodic lattice distortions (PLD) of the Ta sublattice which results in formation of local transient velocity disparities in the Se sublattice. The local differences in Se-phonon amplitudes result in noncompensated shear forces between the layers. This is an example of a multistep coherent launching mechanism. The energy of the optically excited electronic state dissipates energy into modes of the PLD through strong electron-phonon coupling. The rapid suppression of the PLD launches the third step, a coherent vibrational shear mode with low dissipation. The results highlight the importance in considering the 3D nature of the CDWs in the analysis of both structure and dynamics in transition-metal dichalcogenides.

Received 22 October 2019
Revised 30 December 2019
Accepted 19 February 2020

DOI:https://doi.org/10.1103/PhysRevB.101.094303

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. Funded by Bibsam.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Charge density waves Dynamical phase transitions Electronic structure First-principles calculations Ultrafast phenomena

Transmission electron microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Shaozheng Ji ¹, Oscar Grånäs ², Kai Rossnagel ^3,4, and Jonas Weissenrieder ^1,*

¹Materials and Nano Physics, School of Engineering Sciences, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden
²Materials Theory, Department of Physics and Astronomy, Uppsala University, 751 20 Uppsala, Sweden
³Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
⁴Ruprecht-Haensel-Labor, Deutsches Elektronen-Synchrotron DESY, D-22607 Hamburg, Germany

^*jonas@kth.se

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Vol. 101, Iss. 9 — 1 March 2020

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Figure 1
(a) Illustration of superstructure and stacking arrangement in $1 T - TaS e_{2}$ . The periodic lattice displacements form a 13-Ta atom Star of David cluster (illustrated by solid bonds). The a and b vectors indicate the C-CDW unit cell and the a′ and b′ vectors the IC-CDW unit cell. Blue dashed triangles indicate the threefold symmetric stacking displacements. Se atoms are color coded according to their $c$ -axis coordinate (in fractions of $c$ ) as listed in the lower part of (a). The Se atoms at the center of a Star of David cluster are at highest (most protruding, red-shaded areas) positions. The buckling of the Se layer results in a $2 a_{0}$ translation vector as the Star of David center on an adjacent layer will locate above positions where Se atoms are at the lowest positions (blue-shaded areas). (b) Stacking arrangement along the $c_{0}$ direction for two adjacent layers of the C-CDW phase. Only Se atoms between the Ta layers are included. Projections of the commensurate phase at (c) [001] and (f) [102] zone axis (as indexed by the unreconstructed phase) and the corresponding experimental diffraction patterns in (d) and (g), respectively. The simulated diffraction patterns along [001] (e) and [102] (h) are in excellent agreement with the experimental result. At the [102] zone axis, one (out of three) stacking shift direction is placed in bright Bragg diffraction condition.
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Figure 2
Diffraction patterns collected along the [102] zone axis of the C-CDW phase at 423 K (a) and of the IC-CDW phase at 503 K (b). Enlarged diffraction patterns of the areas indicated by the red-dashed circles in (a) and (b) are shown in (e) and (f). (g) shows the subtracted (f)−(e) diffraction pattern. (c) The intensity of $q_{C}^{1}$ and $q_{I C}^{1}$ as a function of temperature, across the C-IC transition, and (d) the temperature-resolved intensities of $q_{I C}^{1}$ and $q_{I C}^{2}$ at temperatures close to the transition.
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Figure 3
(a), (b) Time dependence of the diffraction intensity of the satellite clusters of the commensurate and incommensurate phases. The legends of the traces ( $q_{C}^{1}, q_{C}^{2}, q_{I C}^{1}$ , and $q_{I C}^{2}$ ) are indicated in the diffraction patterns to the left, where the top panel shows the C-CDW before time zero, the middle panel the IC-CDW phase after time zero, and the lower panel the difference pattern for the two phases. The laser pump fluences in (a) and (b) were 1.4 and 2.5 $mJ / c m^{2}$ , respectively.
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Figure 4
Time-resolved diffraction patterns illustrating the change in superstructure satellite spot intensity and position following 515-nm excitation at 2.5- $mJ / c m^{2}$ fluence. Collected at the [102] zone axis.
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Figure 5
Temporal traces of average Bragg diffraction spots intensity in $1 T - TaS e_{2}$ at increasing laser pulse fluence: (a) 1.3 $mJ / c m^{2}$ , (b) 2.0 $mJ / c m^{2}$ , and (c) 2.4 $mJ / c m^{2}$ . A softening of the shear phonon is observed with extracted frequencies at 0.43, 0.36, and 0.30 THz, respectively. A phase transition to IC-CDW is observed for the fluencies in (b) and (c), while the fluence in (a) results in a relaxation to the C-CDW from the transiently unreconstructed state.
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Figure 6
Time decomposition of the events leading to the launching of the shear mode. The optical pump immediately initiates a suppression of the PLD in the Ta sublattice, as shown in (a). After melting, there are remnant effects of the Se-layer bond oscillations in terms of a difference in velocity for Se atoms situated at different locations within the C-CDW unit cell. On the right-hand side of panel (a), the Ta–Se bonds are color coded according to bond-compression/elongation with respect to the $1 T$ -unreconstructed state Ta–Se bond, a compression of 5% or more is colored blue, and an elongation of similar magnitude is colored red. At the edge of the Star of David cluster the bond-length disparity between Ta and Se atoms is large, as indicated by the red-shaded region on the right-hand side of panel (a), where a strong bond compression and bond elongation to the same Se atom is seen. Panel (b) shows how locations with high Se velocities are related for the stacking sequence of the calculation. Similar to panel (a), the bonds are colored with respect to the deviation to the unreconstructed-state bond length. The arrows indicate the direction of the forces. Panel (c) shows a schematic view of the potential-energy surface and the dependence on the coordinates $Q_{s}$ and $Q_{c}$ . When $Q_{c} = 1$ , the energy is decreased by launching the shear mode. The PLD that is present in the C-CDW phase pins the starting position to be roughly $Q_{c} = 1$ (depending on the phase of the lattice vibrations in the system).
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Physical Review B

covering condensed matter and materials physics

Transient three-dimensional structural dynamics in $1 T - TaS e_{2}$

Shaozheng Ji, Oscar Grånäs, Kai Rossnagel, and Jonas Weissenrieder

Phys. Rev. B 101, 094303 – Published 5 March 2020

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Physical Review B

covering condensed matter and materials physics

Transient three-dimensional structural dynamics in 1T−TaSe2

Shaozheng Ji, Oscar Grånäs, Kai Rossnagel, and Jonas Weissenrieder

Phys. Rev. B 101, 094303 – Published 5 March 2020

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Transient three-dimensional structural dynamics in $1 T - TaS e_{2}$