Dynamics of topological defects after photoinduced melting of a charge density wave

Letter

Dynamics of topological defects after photoinduced melting of a charge density wave

Andrei E. Tarkhov, A. V. Rozhkov, and Boris V. Fine

Phys. Rev. B 106, L121109 – Published 20 September 2022

Abstract

Charge-density-wave order in a solid can be temporarily “melted” by a strong laser pulse. Here, we use the discrete Gross-Pitaevskii equation on a cubic lattice to simulate the recovery of the CDW long-range phase coherence following such a pulse. Our simulations indicate that the recovery process is dramatically slowed down by the three-dimensional topological defects—CDW dislocations—created as a result of strongly nonequilibrium heating and cooling of the system. Overall, the simulated CDW recovery was found to be remarkably reminiscent of a recent pump-probe experiment in ${LaTe}_{3}$ .

Received 8 March 2022
Revised 2 August 2022
Accepted 1 September 2022

DOI:https://doi.org/10.1103/PhysRevB.106.L121109

Physics Subject Headings (PhySH)

Anharmonic lattice dynamics Charge density waves Crystal defects Dynamical phase transitions Lattice dynamics Topological defects Topological phase transition Ultrafast phenomena

Bose-Einstein condensates Transition metal dichalcogenides

Photoexcitation Ultrafast pump-probe spectroscopy

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & OpticalNonlinear DynamicsStatistical Physics & Thermodynamics

Authors & Affiliations

Andrei E. Tarkhov ^1,*, A. V. Rozhkov ², and Boris V. Fine^3,†

¹Division of Genetics, Department of Medicine, Brigham and Women's Hospital and Harvard Medical School, Boston, Massachusetts 02115, USA
²Institute for Theoretical and Applied Electrodynamics, Russian Academy of Sciences, Moscow 125412, Russia
³Institute for Theoretical Physics, University of Leipzig, Brüderstr. 16, 04103 Leipzig, Germany

^*atarkhov@bwh.harvard.edu
^†boris.fine@uni-leipzig.de

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Issue

Vol. 106, Iss. 12 — 15 September 2022

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Images

Figure 1
Sketch of the mapping of a CDW dislocation $u cos [q_{CDW} r_{m} + ϕ (r_{m})]$ onto a vortex of the DGPE $U (1)$ lattice variables $u exp [i ϕ (r_{m})]$ . (a) 2D slice of the CDW dislocation (left) vs 2D slice of the DGPE vortex (right). (b) Three-dimensional representations of a vortex loop: CDW (left) vs DGPE lattice (middle) vs vorticity of the DGPE lattice defined in the text (right).
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Figure 2
(a) Time evolution of experimentally measured 2D-integrated intensity of the CDW electron diffraction peak after photoexcitation, for several laser photoexcitation densities (from Ref. [18]). (b) Numerically calculated 2D-integrated intensity $I_{2} \equiv \sum_{k_{x}, k_{y}} {| ψ (k_{x}, k_{y}, 0) |}^{2}$ tracking the ordering in the system [see Eq. (6)] as a function of time for different quench intensities. The color of the curves encodes different quench intensities as indicated on the color bar. Each numerical data point represents the average of 40 quench realizations, and the error bars represent the statistical uncertainty associated with this average. Inset: Variation of the energy density during quenches. The horizontal line marks the critical energy density $ɛ_{c}$ [see Fig. 3] above which the order is destroyed.
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Figure 3
Temperature dependence of various parameters for the 3D DGPE lattice: (a) The equilibrium order parameter $| Ψ_{eq} |^{2}$ and the energy density $ɛ$ , and (b) specific heat $c_{v}$ .
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Figure 4
(a), (b) Snapshots of vorticity for two individual quenches at time $t = 20 J^{- 1}$ : (a) weak quench, (b) strong quench, marked in (c) and (d) by gray and red triangles, respectively [also shown in Fig. 2]. Vorticity $w_{j}$ is depicted by (colored) arrows whose length is proportional to $| w_{j} |$ (see the text). For the visualization purposes, we apply a smoothing filter to $w_{j}$ : At site $j$ we plot $w_{j}$ averaged over 9 sites comprising a cube with side 3 encompassing site $j$ . The arrow color represents the position along one of the lattice axes, as shown by the color bar. In (a) these arrows are visible as mere dots due to the smallness of $| w_{j} |$ . In (b) longer and hence brighter arrows merge into distinctly visible wormlike bundles revealing vortex cores. Vortex lines penetrating the entire system are clearly seen for the stronger quench. (Further snapshots of vorticity for the later times of the stronger quench can be found in the Supplemental Material [32].) (c), (d) Correlation between vorticity and the slowing down of the order recovery for the simulated 3D DGPE lattice. (c) The 2D-integrated intensity $I_{2} (t)$ , same as Fig. 2 but over a longer time interval; (d) the average vorticity $Q_{av} (t)$ . The color coding and the statistical ensemble behind the sampling are used the same as in Fig. 2. (d) Inset: Dependence of the order parameter recovery time $τ_{r}$ on the linear lattice size $V^{1 / 3}$ .
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