Experimental evidence for type-II Dirac semimetal in ${\mathrm{PtSe}}_2$

While a monolayer ${\mathrm{PtSe}}_2$ film is a semiconductor with interesting spin structure, bulk ${\mathrm{PtSe}}_2$ crystal has been predicted to be a topological Dirac semimetal that can host a new type of Lorentz-violating Dirac fermions. Despite the intriguing predictions, experimental progress on the electronic structure of bulk ${\mathrm{PtSe}}_2$ has been hindered due to the lack of large, high-quality single-crystal samples. Here we report the growth and characterization of high-quality ${\mathrm{PtSe}}_2$ single crystals and reveal the electronic structure to provide direct evidence for the existence of three-dimensional type-II Dirac fermions. A comparison of the crystal, vibrational, and electronic structure to a related compound, ${\mathrm{PtTe}}_2$, is also discussed. Our work provides an important platform for exploring the novel quantum phenomena associated with type-II Dirac fermions in the $1T-{\mathrm{PtSe}}_2$ class of transition-metal dichalcogenides.

Figure 1

Crystal structure and Brillouin zone of ${\mathrm{PtSe}}_2$ (${\mathrm{PtTe}}_2$). (a) Schematic drawing of type-I and type-II Dirac fermions. (b) Top and (c) side views of the crystal structure of ${\mathrm{PtSe}}_2$ (${\mathrm{PtTe}}_2$). Green balls are Se (Te) atoms, and blue balls are Pt atoms. The unit cell is indicated by black dashed lines. (d) BZ of bulk and the projected surface BZs of a (001) surface. The blue dots indicate the high-symmetry points of the BZ, and the red dots highlight the 3D Dirac point positions.

Figure 2

Characterization of ${\mathrm{PtSe}}_2$ compared to ${\mathrm{PtTe}}_2$. X-ray diffraction patterns of (a) ${\mathrm{PtSe}}_2$ and (b) ${\mathrm{PtTe}}_2$ measured at room temperature. The inset shows a picture of the few-millimeter-size single crystal. LEED pattern of (c) ${\mathrm{PtSe}}_2$ and (d) ${\mathrm{PtTe}}_2$. Temperature-dependent resistivity of (e) ${\mathrm{PtSe}}_2$ and (f) ${\mathrm{PtTe}}_2$. Raman spectrum of (g) ${\mathrm{PtSe}}_2$ and (h) ${\mathrm{PtTe}}_2$ measured at room temperature. The inset illustrates vibrational modes in ${\mathrm{PtSe}}_2$ or ${\mathrm{PtTe}}_2$ with the same color code used in Fig. 1. Arrows guide the vibration directions.

Figure 3

Band structure of a type-II Dirac cone in ${\mathrm{PtSe}}_2$ and ${\mathrm{PtTe}}_2$. ${\mathrm{PtSe}}_2$ band dispersions along the (a) $\mathrm{\Gamma }-K$ and (b) $\mathrm{\Gamma }-M$ directions at a photon energy of 23.5 eV ($k_z=0.37c^{*}$). (c) $k_z$ dispersions of ${\mathrm{PtSe}}_2$ measured at $k_{\parallel }=0$. Red dashed lines are calculated dispersions for comparison. ${\mathrm{PtTe}}_2$ band dispersions along the (e) $\mathrm{\Gamma }-K$ and (f) $\mathrm{\Gamma }-M$ directions at a photon energy of 22 eV ($k_z=0.35c^{*}$). (g) $k_z$ dispersions of ${\mathrm{PtTe}}_2$ measured at $k_{\parallel }=0$. Calculated band dispersion of (d) ${\mathrm{PtSe}}_2$ and (h) ${\mathrm{PtTe}}_2$ along the in-plane direction $S-D-T$ and out-of-plane direction $A-\mathrm{\Gamma }-A$ through the Dirac point $D$.

Figure 4

(a)–(l) Comparison of linear dispersion in the $k_x$ direction at different $k_z$ for ${\mathrm{PtSe}}_2$.

Figure 5

Electronic structures of ${\mathrm{PtSe}}_2$ and ${\mathrm{PtTe}}_2$. (a)–(e) Intensity maps at constant energies from $E_F$ to $-1.2$ eV for ${\mathrm{PtSe}}_2$ at a photon energy of 21 eV ($k_z=0.29{\mathrm{c}}^{*}$). The black dashed line indicates the surface BZ; the locations of two momentum cuts are marked by blue dashed lines. (f) and (g) High-symmetry direction cuts 1 and 2 in (a), respectively. (h)–(l) Intensity maps at constant energies from $E_F$ to $-1.2$ eV for ${\mathrm{PtTe}}_2$ at a photon energy of 21.2 eV ($k_z=0.3c^{*}$). The locations of two momentum cuts are marked by blue dashed lines. (m) and (n) High-symmetry direction cuts 3 and 4 in (h), respectively.

Figure 6

Modulation of the electronic structures under chemical doping. (a) Calculated band dispersion of ${\mathrm{IrTe}}_2$ along high-symmetry directions, resolving the tilted Dirac node above the Fermi level. (b) Calculated band dispersion of ${\mathrm{Pt}}_{0.5}{\mathrm{Ir}}_{0.5}{\mathrm{Te}}_2$ along high-symmetry directions. The gray arrow indicates the tilted Dirac cone.