Effect of dimensionality and spin-orbit coupling on charge-density-wave transition in 2H-TaSe${}_{2}$

Effect of dimensionality and spin-orbit coupling on charge-density-wave transition in 2H-TaSe $_{2}$

Yizhi Ge and Amy Y. Liu

Phys. Rev. B 86, 104101 – Published 4 September 2012

Abstract

A first-principles investigation of the charge-density-wave (CDW) instability in bulk and single-layer 2H-TaSe $_{2}$ is presented, focusing on the origin of the CDW instability, the role of the interlayer interactions, and the effect of spin-orbit coupling. While interlayer interactions and spin-orbit coupling have a nontrivial effect on the electronic structure and Fermi surface, the CDW instability is predicted to remain robust, with little or no change in the ordering wave vector. This is in contrast to the closely related 2H-NbSe $_{2}$ material, where the CDW wave vector depends on dimensionality. The results are analyzed in terms of the interplay between the momentum dependence of the electron-phonon coupling and that of the electronic response function.

Received 25 June 2012

DOI:https://doi.org/10.1103/PhysRevB.86.104101

Authors & Affiliations

Yizhi Ge and Amy Y. Liu

Department of Physics, Georgetown University, Washington, DC 20057, USA

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Issue

Vol. 86, Iss. 10 — 1 September 2012

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Images

Figure 1
Crystal structure and Brillouin zone of 2H-TaSe $_{2}$ . The large spheres (gray) correspond to Ta atoms and the small spheres (yellow) represent Se atoms. The bulk 2H structure contains two trilayers per unit cell, while the single-layer structure corresponds to an isolated trilayer unit. High-symmetry points in the $q_{z} = 0$ plane of the hexagonal Brillouin zone are labeled, as well as a triplet of ordering vectors $Q_{cdw}$ .Reuse & Permissions
Figure 2
Phonon dispersion of 2H-TaSe $_{2}$ . (a) Bulk results are shown for three cases: scalar relativistic (SR) dispersion curves at two electronic temperatures and fully relativistic (FR) results along $Γ$ - $M$ for the unstable acoustic branch. (b) Single-layer dispersion curves are plotted for both scalar relativistic and fully relativistic calculations. Negative values indicate imaginary frequencies. The inset in (a) shows the $q_{z}$ dispersion of the soft branch along the line that projects onto the CDW ordering vector.Reuse & Permissions
Figure 3
Calculated electronic band structure of (a) bulk and (b) single-layer 2H-TaSe $_{2}$ . The Fermi level is set to zero. Solid lines show the spin-orbit-split fully relativistic Ta $d$ bands. The fully relativistic bulk bands were calculated at the experimental value of the $c$ lattice constant.Reuse & Permissions
Figure 4
Calculated Fermi surfaces arising from Ta $d$ bands in 2H-TaSe $_{2}$ . (a) Bulk Fermi surface in the scalar-relativistic approximation. (b) Bulk Fermi surface calculated fully relativistically, showing spin-orbit splitting of bands in the $k_{z} = π / 2$ plane. (c) Single-layer Fermi surface in the scalar-relativistic approximation. (d) Single-layer Fermi surface calculated fully relativistically, with new sheets appearing as a result of the spin-orbit interaction. The $Γ$ point lies at the corners of the zone shown. The $K$ -centered sheets have strong $d_{x y} / d_{x^{2} - y^{2}}$ character (red), particularly near the $Γ$ - $K$ lines, while the $Γ$ -centered sheets have weak $d_{x y} / d_{x^{2} - y^{2}}$ character (blue).Reuse & Permissions
Figure 5
Wave-vector dependence of electron-phonon coupling and electronic susceptibility in bulk and single-layer 2H-TaSe $_{2}$ . Panels (a), (c), and (e) show $λ_{q ν}$ and for the soft acoustic branch in the SR bulk ( $σ = 0.02$ Ry), the SR single layer ( $σ = 0.03$ Ry), and the FR single layer ( $σ = 0.2$ Ry), respectively. Black denotes $λ_{q ν} = 0$ , while white represents the maximum value, which is different in each case. Panels (b), (d), and (f) show the real part of the susceptibility $χ_{q}^{'}$ per formula unit calculated for the SR bulk, the SR single layer, and the FR bulk, respectively, using a common gray scale. Arrows indicate $Q_{cdw}$ .Reuse & Permissions

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