Experimental Realization of Type-II Dirac Fermions in a ${\mathrm{PdTe}}_2$ Superconductor

A Dirac fermion in a topological Dirac semimetal is a quadruple-degenerate quasiparticle state with a relativistic linear dispersion. Breaking either time-reversal or inversion symmetry turns this system into a Weyl semimetal that hosts double-degenerate Weyl fermion states with opposite chiralities. These two kinds of quasiparticles, although described by a relativistic Dirac equation, do not necessarily obey Lorentz invariance, allowing the existence of so-called type-II fermions. The recent theoretical discovery of type-II Weyl fermions evokes the prediction of type-II Dirac fermions in ${\mathrm{PtSe}}_2$-type transition metal dichalcogenides, expecting experimental confirmation. Here, we report an experimental realization of type-II Dirac fermions in ${\mathrm{PdTe}}_2$ by angle-resolved photoemission spectroscopy combined with ab initio band calculations. Our experimental finding shows the first example that has both superconductivity and type-II Dirac fermions, which turns the topological material research into a new phase.

Figure 1

ARPES-measured electronic structure of ${\mathrm{PdTe}}_2$. (a) Bulk and (001) surface Brillouin zones for a hcp structure. (b) Calculated bulk band structure along the $K\text{−}\mathrm{\Gamma }\text{−}M$ symmetric line by the DFT method. The blue dotted box is the region of ARPES measurement. (c) Constant energy maps measured at energies ranging from 0 ($E_F$) to $-1.90\mathrm{eV}$ using $\hslash \omega =36.0\mathrm{eV}$, which corresponds to $k_z=3.0c*$ ($c*=2\pi /c$). The red hexagons are BZs. (d) Corresponding isoenergy contours by DFT calculations. The upper half of the topmost contour is a $k_z$-integrated Fermi surface map from $-0.5c*$ to $0.5c*$, and the others are for $k_z=0$. (e),(f) ARPES image (left) and calculated surface band structure (right) in the $\overline{\mathrm{\Gamma }}\text{−}\overline{K}/\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ direction. The surface states (SS) and the surface Dirac cone (SD) show strong surface character (red color) in the calculations.

Figure 2

Photon energy dependence and circular dichroism of the ARPES data. (a) ARPES image of ${\mathrm{PdTe}}_2$ along the $A\text{−}\mathrm{\Gamma }\text{−}A$ line measured with varying photon energy from 55 to 103 eV. The thin dotted curves are calculated bulk bands along the same line. (b) ARPES image along the $D\text{−}S$ line ($k_z=3.6c*$) obtained by summing two ARPES images using circular light with opposite polarization. The dotted curves are calculated bulk bands along the same line. (c) Normalized circular dichroic ARPES image along the $D\text{−}S$ line. A noticeable difference is observed in dichroic reversal between the D-II region (dotted circle) and the SD region (dotted square).

Figure 3

Type-II Dirac fermion in ${\mathrm{PdTe}}_2$ evidenced by ARPES. (a),(b),(c),(d) ARPES images along the $k_y$ direction at $k_z=2.54c*$ ($\mathrm{\Delta }k=-0.06c*$), 2.61c* (D-II), $2.68c*$ ($\mathrm{\Delta }k=0.08c*$), and $2.75c*$ ($\mathrm{\Delta }k=0.15c*$). The red dashed lines are the calculated bands at the corresponding $k_z$ value. (b’,c’,d’) ARPES images measured in the next BZ at $k_z=3.61c*$ (D-II), $3.32c*$ ($\mathrm{\Delta }k=0.08c*$), $3.26c*$ ($\mathrm{\Delta }k=0.14c*$). In (c’), the calculated bands are for $\mathrm{\Delta }k=0.02c*$. (e) Calculated bands along the $A\text{−}\mathrm{\Gamma }$ line and schematic type-II Dirac cone. The vertical lines denote the measuring $k_z$ point of the ARPES images in (a)–(d’).