Large change of interlayer vibrational coupling with stacking in ${\mathrm{Mo}}_{1\ensuremath{-}x}{\mathrm{W}}_{x}{\mathrm{Te}}_{2}$

Large change of interlayer vibrational coupling with stacking in ${Mo}_{1 - x} W_{x} {Te}_{2}$

John A. Schneeloch, Yu Tao, Jaime A. Fernandez-Baca, Guangyong Xu, and Despina Louca

Phys. Rev. B 105, 014102 – Published 7 January 2022

Abstract

Stacking variations in quasi-two-dimensional materials can have an important influence on material properties, such as changing the topology of the band structure. Unfortunately, the weakness of van der Waals (vdW) interactions makes it difficult to compute the stacking dependence of properties, and even in a material as simple as graphite the stacking energetics remain unclear. ${Mo}_{1 - x} W_{x} {Te}_{2}$ is a material in which three differently stacked phases are conveniently accessible by temperature changes: $1 T^{'}, T_{d}^{*}$ , and the reported Weyl semimetal phase $T_{d}$ . The transitions proceed via layer sliding, and the corresponding interlayer shear mode (ISM) is relevant not just for the stacking energetics but also for understanding the relationship between Weyl physics and structural changes. However, the interlayer interactions of ${Mo}_{1 - x} W_{x} {Te}_{2}$ are not well understood, with wide variation in computed properties. We report inelastic neutron scattering of the ISM in a ${Mo}_{0.91} W_{0.09} {Te}_{2}$ crystal. The ISM energies are generally consistent with the linear chain model, as expected given the weak interlayer interaction, though there are some discrepancies from predicted intensities. However, the interlayer force constants $K_{x}$ in the $T_{d}^{*}$ and $1 T^{'}$ phases are substantially weaker than that of $T_{d}$ at 75(3) and 83(3)%, respectively. Considering that the relative positioning of atoms in neighboring layers is approximately the same regardless of overall stacking, our results suggest that longer-range influences, such as stacking-induced electronic band-structure changes, may be responsible for the substantial change in the interlayer vibrational coupling and thus the $C_{55}$ elastic constant. These findings should elucidate the stacking energetics of ${Mo}_{1 - x} W_{x} {Te}_{2}$ and other vdW layered materials.

Received 21 October 2021
Accepted 20 December 2021

DOI:https://doi.org/10.1103/PhysRevB.105.014102

Physics Subject Headings (PhySH)

Phonons Structural phase transition

Weyl semimetal

Inelastic neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

John A. Schneeloch ¹, Yu Tao¹, Jaime A. Fernandez-Baca², Guangyong Xu³, and Despina Louca^1,*

¹Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA
²Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
³NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20877, USA

^*Corresponding author: louca@virginia.edu

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Vol. 105, Iss. 1 — 1 January 2022

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Figure 1
(a) Crystal structure of ${Mo}_{1 - x} W_{x} {Te}_{2}$ , with A/B stacking options displayed. (b) Diagram of interlayer interaction energy as a function of relative displacement of neighboring layers along the $a$ axis. (c) A depiction of the dispersion along $(2, 0, L)$ for the $a$ -axis ISM based on the LCM for a four-layer unit cell (i.e., $T_{d}^{*}$ ). One subbranch of the LCM dispersion is made bold. The sets of blue circles, red squares, and green triangles each mark a particular vibrational mode on the LCM curve and are accompanied by diagrams of the polarization of the interlayer vibrations, depicting the relative phases (...,1,1,1,1,...), $(. . ., 1, - i, - 1, i, . . .)$ , and $(. . ., 1, - 1, 1, - 1, . . .)$ , respectively.
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Figure 2
Calculated inelastic neutron-scattering intensity for each phase as determined by the LCM, setting $T = 270 K$ and $ℏ ω_{m}$ to the values for each phase listed in Table 2. Intensity convoluted with an energy FWHM of 0.3 meV. The left (right) shows the intensity for the $T_{d}^{*} / 1 T^{'}$ twin fractions derived from elastic scans taken on the SPINS (CTAX) instrument. The blue and pink bars denote scans taken on CTAX and SPINS, respectively. The letters refer to the data sets in Fig. 3.
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Figure 3
(a–h) Scans of INS intensity vs $ℏ ω$ taken on (a–d) CTAX and (e–h) SPINS, as labeled in Fig. 2. Blue and magenta curves are resolution-convoluted $S (Q, ω)$ calculations. For the blue curves, intensity, twin fraction, and $ℏ ω_{m}$ were allowed to vary. For magenta curves, intensities in (b–d) and (f–h) were constrained by the LCM and fitted intensities of (a) and (e), twin fractions were set to values consistent with elastic $(2, 0, L)$ scans, and $ℏ ω_{m}$ was set to the average values for each phase listed in Table 2. Dashed lines are background. Gray points are data not included in fit. See Supplemental Material [35] for additional fitting details. Error bars represent a standard deviation of statistical uncertainty.
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Figure 4
Comparison of the LCM with ${Mo}_{0.91} W_{0.09} {Te}_{2}$ neutron-scattering data. The data points are $ℏ ω_{m} sin (\frac{π}{2} q)$ plotted against $q$ , where $q$ is the LCM wave vector corresponding to the branch that dominates the contribution to the intensity, and $ℏ ω_{m}$ (see Table 1) are the averages of the values obtained from fits. The LCM curves are $ℏ ω = ℏ ω_{m} sin \frac{π}{2} q$ for each phase, with $ℏ ω_{m}$ given by the values in Table 2. The side curves show changes in the LCM curve by a standard deviation in $ℏ ω_{m}$ . The inset shows the center region in more detail. Error bars denote a standard deviation of statistical uncertainty.
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Physical Review B

covering condensed matter and materials physics

Large change of interlayer vibrational coupling with stacking in ${Mo}_{1 - x} W_{x} {Te}_{2}$

John A. Schneeloch, Yu Tao, Jaime A. Fernandez-Baca, Guangyong Xu, and Despina Louca

Phys. Rev. B 105, 014102 – Published 7 January 2022

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Physical Review B

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Large change of interlayer vibrational coupling with stacking in Mo1−xWxTe2

John A. Schneeloch, Yu Tao, Jaime A. Fernandez-Baca, Guangyong Xu, and Despina Louca

Phys. Rev. B 105, 014102 – Published 7 January 2022

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Large change of interlayer vibrational coupling with stacking in ${Mo}_{1 - x} W_{x} {Te}_{2}$