Vibrational and dielectric properties of the bulk transition metal dichalcogenides

Nicholas A. Pike, Antoine Dewandre, Benoit Van Troeye, Xavier Gonze, and Matthieu J. Verstraete

Phys. Rev. Materials 2, 063608 – Published 28 June 2018

Abstract

Interest in the bulk transition metal dichalcogenides for their electronic, photovoltaic, and optical properties has grown and led to their use in many technological applications. We present a systematic investigation of their interlinked vibrational and dielectric properties using density functional theory and density functional perturbation theory, studying the effects of the spin-orbit interaction and of the long-range $e^{-} - e^{-}$ correlation as part of our investigation. This study confirms that the spin-orbit interaction plays a small role in these physical properties, while the direct contribution of dispersion corrections is of crucial importance in the description of the interatomic force constants. Here, our analysis of the structural and vibrational properties, including the Raman spectra, compare well to experimental measurement. Three materials with different point groups are showcased, and data trends on the full set of 15 existing hexagonal, trigonal, and triclinic materials are demonstrated. This overall picture will enable the modeling of devices composed of these materials for novel applications.

Received 6 April 2018

DOI:https://doi.org/10.1103/PhysRevMaterials.2.063608

Physics Subject Headings (PhySH)

Dielectric properties Elasticity Electronic structure

Transition metal dichalcogenides

Density functional theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Nicholas A. Pike^1,2,*, Antoine Dewandre², Benoit Van Troeye³, Xavier Gonze³, and Matthieu J. Verstraete²

¹Centre for Materials Science and Nanotechnology, University of Oslo, NO-0349 Oslo, Norway
²Nanomat/Q-Mat/CESAM, Université de Liège & European Theoretical Spectroscopy Facility, B-4000 Liège, Belgium
³Université Catholique de Louvain, Institute of Condensed Matter and Nanosciences (IMCN) & European Theoretical Spectroscopy Facility, B-1348 Louvain-la-Neuve, Belgium

^*Nicholas.pike@ulg.ac.be

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Vol. 2, Iss. 6 — June 2018

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Images

Figure 1
The top and side view of a (a) h-TMD, (b) t-TMD, and (c) a tc-TMD. Here the transition metal atoms are shown in blue and the chalcogen atoms are in red. In each case, a coordinate system is used such that the $x$ and $y$ axes lie in the plane of atoms and the $z$ axis lies perpendicular to the plane. Additionally, the corresponding high-symmetry paths [33] in momentum space used in our band structure calculations for (d) the h- and t-TMDs and (e) the tc-TMDs are given.
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Figure 2
Mode- and momentum-dependent Grüneisen parameters of ${MoTe}_{2}$ . Top: acoustic and lattice Grüneisen parameters; Middle and bottom: intralayer Grüneisen parameters. The high-symmetry path is from Ref. [33].
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Figure 3
(a) Raman spectra for ${MoTe}_{2}$ with three different polarizations corresponding to a DFT-D3/DFT-D3 calculation in which the Raman signals relate to our calculation (in black) of the $Γ$ point phonons in (b). (b) Calculated phonon band structure of ${MoTe}_{2}$ along a path of high-symmetry points in $q$ space. The red lines correspond to a DFT-D3/DFT calculation, and the black lines correspond to a DFT-D3/DFT-D3 calculation in which the DFT-D3 scheme is used during both the DFT and DFPT calculation. (c) Phonon density of states corresponding to the same color scheme as in (b). Experimental data points correspond to the measurements in Ref. [46]. The high-symmetry path comes from Ref. [33].
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Figure 4
(a)–(f) A comparison between our DFT and experiments for some of the principal vibrational and dielectric properties. Symbols (colors) represent different symmetry classes: h-TMDs (black), t-TMDs (blue), and tc-TMDs (red). (a) In-plane lattice parameter, (b) out-of-plane lattice parameter, (c) indirect energy gap, (d) static dielectric constant, (e) absolute value of the in-plane Born effective charge on the transition metal atom, and (f) Debye temperature. Points correspond to cases where both calculated and experimental data were found. The light-gray wedge represents an error of $\pm 5 %$ . The overall agreement is very good, but the electronic gap is quite scattered, for reasons described in the text, whereas the dielectric constant is well reproduced. In (g)–(l) we show trends in our calculated data with respect to the atomic number of the metal ion or atomic mass per formula unit (f.u.). Lines are linear fits to the available data. For comparison, we plot half the out-of-plane lattice parameter for the hexagonal compounds in (b) and (h), and in (a) and (g) we plot half the in-plane lattice parameter for the triclinic compounds.
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Figure 5
Kohn-Sham electronic band structures of the three example compounds plotted along a high-symmetry path in $k$ space [33]. In each case, the calculated Fermi energy is shifted to the zero of energy, as indicated by the light-blue line.
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Figure 6
Raman spectra, phonon band structure, and phonon density of states for our three example compounds plotted along a high-symmetry path in $q$ space. Raman spectra are plotted for nonsymmetric polarizations, experimental neutron scattering data from Ref. [125], and experimental Raman and infrared data at $Γ$ from Refs. [45, 46, 128, 136].
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