3D Dirac Plasmons in the Type-II Dirac Semimetal ${\mathrm{PtTe}}_2$

Transition-metal dichalcogenides showing type-II Dirac fermions are emerging as innovative materials for nanoelectronics. However, their excitation spectrum is mostly unexplored yet. By means of high-resolution electron energy loss spectroscopy and density functional theory, here, we identify the collective excitations of type-II Dirac fermions (3D Dirac plasmons) in ${\mathrm{PtTe}}_2$ single crystals. The observed plasmon energy in the long-wavelength limit is $\sim 0.5\mathrm{eV}$, which makes ${\mathrm{PtTe}}_2$ suitable for near-infrared optoelectronic applications. We also demonstrate that interband transitions between the two Dirac bands in ${\mathrm{PtTe}}_2$ give rise to additional excitations at $\sim 1$ and $\sim 1.4\mathrm{eV}$. Our results are crucial to bringing to fruition type-II Dirac semimetals in optoelectronics.

Figure 1

(a) The LEED pattern of (0001)-oriented ${\mathrm{PtTe}}_2$ single crystals, acquired at a primary electron beam energy of 74 eV. (b) Brillouin zone of ${\mathrm{PtTe}}_2$. The two Dirac points are located on the $A-\mathrm{\Gamma }-A^{\prime }$ line at $\pm D$. (c) and (d) show the side and top views of the crystal structure, respectively. The purple and yellow balls denote the Pt and Te atoms, respectively. (e) The band structure of ${\mathrm{PtTe}}_2$, showing the two Dirac points tilted in opposite directions, located on the $A-\mathrm{\Gamma }-A^{\prime }$ axis. The dispersion around each of the Dirac points is isotropic in the horizontal SDT plane (parallel to the experimental $\mathrm{\Gamma }KM$ plane) and anisotropic and “tilted” along the $\mathrm{\Gamma }-A$ direction. A magnification of the band structure around one of the Dirac points, along with the fit of the low-energy dispersion [see Eq. (1)], is shown in panels (f) for the isotropic SDT direction [marked by the green circle in (e)], and along the $\mathrm{\Gamma }-A^{\prime }$ direction in (g) [marked by the orange circle in (e)].

Figure 2

(a) Wave-vector-resolved HREELS spectra, acquired for $E_p=6\mathrm{eV}$ as a function of the scattering angle. The corresponding value of the wave vector along the $\mathrm{\Gamma }-K$ direction (or along ${\widehat{q}}_x$ with $\theta =\pi /2$ and $\varphi =0$, as indicated in the inset) is reported on the right. All HREELS experiments have been carried out at room temperature. (b) The experimentally measured Dirac-plasmon dispersion is indicated with green circles, along with the theoretically calculated loss function for ${\mathrm{PtTe}}_2$ [see Eq. (2)], in the $\mathrm{\Gamma }-K$ direction (with $\theta =\pi /2$ and $\varphi =0$). The green bars indicate the experimental inaccuracy in determining $q$ (see Sec. S3 in the SM [22] for its evaluation). The ${\mathcal{E}}_{\text{Loss}}$ is calculated using the low-energy tilted and anisotropic Dirac Hamiltonian in Eq. (1). The yellow (red) region bounded by the black lines indicates the absence (presence) of single-particle excitations in the $\omega -q$ plane. The plasmon enters the interband single-particle excitation regime for $q>0.17{\AA }^{-1}$ and becomes increasingly damped.

Figure 3

(a) Ab initio loss function for the selected case of $q=0.026{\AA }^{-1}$ along the $\mathrm{\Gamma }-K$ direction. The colored region enclosed by the green curve shows a fit with three Gaussian line shapes to the DFT-based loss function (in black circles). (b) HREELS spectrum recorded for a higher value of impinging energy ($E_p=11\mathrm{eV}$), enabling the observation of three well-separated spectral components. In both theoretical and experimental loss functions, background has been subtracted.

Figure 4

The direct transitions between the two bands hosting Dirac Fermions, for $\mu =-E_D=0.76\mathrm{eV}$ above the Dirac points, shaded by pink in panel (a), give rise to the joint density of states (JDOS) shown in (b). The JDOS under the pink curve in (b) can be resolved as a sum of two Gaussians of roughly equal strength, with one of them centered around $\sim 1\mathrm{eV}$ and the other around $\sim 1.5\mathrm{eV}$. The two JDOS peaks are consistent with the additional peaks resolved in the excitation spectrum experimentally probed by HREELS with higher impinging energies [see Fig. 3].