Hyperbolicity in two-dimensional transition metal ditellurides induced by electronic bands nesting

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Hyperbolicity in two-dimensional transition metal ditellurides induced by electronic bands nesting

Hongwei Wang and Tony Low

Phys. Rev. B 102, 241104(R) – Published 4 December 2020

Abstract

Naturally occurring hyperbolic plasmonic media is rare, and was only recently observed in the $1 T^{'}$ phase of ${WTe}_{2}$ . We elucidate on the physical origin of this strong infrared hyperbolic response, and attribute it to band-nested anisotropic interband transitions. Such a phenomenon does not occur in general anisotropic materials, at least not in their pristine state. However, band-nested anisotropic interband transitions can in principle be induced via proper electronic band nesting. We illustrate this principle and demonstrate a topological elliptic-to-hyperbolic transition in ${MoTe}_{2}$ via strain engineering, which is otherwise nonhyperbolic.

Received 14 May 2020
Accepted 9 October 2020

DOI:https://doi.org/10.1103/PhysRevB.102.241104

Physics Subject Headings (PhySH)

Optical conductivity Plasmonics Plasmons

Band structure methods

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Hongwei Wang and Tony Low^*

Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA

^*tlow@umn.edu

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Issue

Vol. 102, Iss. 24 — 15 December 2020

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Images

Figure 1
(a)–(c) Schematic illustration showing the crystal structures of (a) monolayer, (b) bilayer, and (c) trilayer ${WTe}_{2}$ . The dark green and yellow balls represent the W and Te atoms. (d)–(f) Real parts of the dielectric functions for (d) monolayer, (e) bilayer, and (f) trilayer ${WTe}_{2}$ materials. (g)–(i) Similar to panels (d)–(f) but for the imaginary part instead. The spectral region of in-plane hyperbolicity associated with intraband transition is enlarged and displayed in the insets of panels (a)–(c). The energy range of in-plane hyperbolicity originated from interband transition only is marked with a green background.
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Figure 2
(a) Imaginary parts of the in-plane dielectric functions for monolayer ${WTe}_{2}$ . (b) Two-dimensional band structure along the paths associated with in-plane high-symmetry $k$ points for monolayer ${WTe}_{2}$ . (c) $E_{v}$ (blue) and $E_{c}$ (green) as a function of the $k$ mesh. The energy difference between $E_{v}$ and $E_{c}$ is shown at the bottom contour projection, with the color bar displayed on the right. The lower and upper energy boundaries for the second prominent peak [marked with the green shadow in panel (a)] in the imaginary part of the dielectric function along the $x$ direction are plotted with two red contour lines in panel (c). The $\vec{k}$ -space area sandwiched by two red contour lines is defined as $A_{nest}$ .
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Figure 3
(a), (b) The projected band structures of monolayer ${WTe}_{2}$ with (a) the $p_{z^{'}}$ orbital on the Te atom and (b) the $d_{z^{' 2}}$ orbital on the W atom. The wave functions of $E_{v}$ and $E_{c}$ for a momentum along the high-symmetry $Γ − Y$ line, corresponding to the band-nesting region, are plotted on the bottom. The Te- $p_{z^{'}}$ and W- $d_{z^{' 2}}$ Wannier orbitals are displayed for comparison.
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Figure 4
(a) The contour plot of the energy difference between $E_{v}$ and $E_{c}$ for unstrained monolayer ${MoTe}_{2}$ . (b) Real and (c) imaginary parts of the dielectric functions for unstrained monolayer ${MoTe}_{2}$ . (d)–(f) Similar to panels (a)–(c) but for 2% strained monolayer ${MoTe}_{2}$ . The two iso-value lines in each contour plot represent the upper- and lower-energy limits of the shaded green region in the imaginary parts of dielectric functions. (g) $E_{v}$ and (h) $E_{c}$ corresponding to the band-nesting region for unstained (blue color) and strained (orange color) monolayer ${MoTe}_{2}$ . The contour lines in the $E_{v}$ and $E_{c}$ energy profiles range from $- 0.6$ to 0.0 eV and 0.0 to 0.6 eV, respectively, with an energy interval of 0.2 eV. (i) The partial charge densities for the unstained monolayer ${MoTe}_{2}$ contributed from electronic states in the band-nesting region. The isosurface value is $0.006 e / Å^{3}$ .
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