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. 2017 Aug 15;8(1):257.
doi: 10.1038/s41467-017-00280-6.

Lorentz-violating type-II Dirac fermions in transition metal dichalcogenide PtTe2

Mingzhe Yan  1 , Huaqing Huang  1 , Kenan Zhang  1 , Eryin Wang  1 , Wei Yao  1 , Ke Deng  1 , Guoliang Wan  1 , Hongyun Zhang  1 , Masashi Arita  2 , Haitao Yang  1   3 , Zhe Sun  4 , Hong Yao  5   6 , Yang Wu  7 , Shoushan Fan  1   3   6 , Wenhui Duan  8   9 , Shuyun Zhou  10   11
Affiliations

Lorentz-violating type-II Dirac fermions in transition metal dichalcogenide PtTe2

Mingzhe Yan et al. Nat Commun. .

Abstract

Topological semimetals have recently attracted extensive research interests as host materials to condensed matter physics counterparts of Dirac and Weyl fermions originally proposed in high energy physics. Although Lorentz invariance is required in high energy physics, it is not necessarily obeyed in condensed matter physics, and thus Lorentz-violating type-II Weyl/Dirac fermions could be realized in topological semimetals. The recent realization of type-II Weyl fermions raises the question whether their spin-degenerate counterpart-type-II Dirac fermions-can be experimentally realized too. Here, we report the experimental evidence of type-II Dirac fermions in bulk stoichiometric PtTe2 single crystal. Angle-resolved photoemission spectroscopy measurements and first-principles calculations reveal a pair of strongly tilted Dirac cones along the Γ-A direction, confirming PtTe2 as a type-II Dirac semimetal. Our results provide opportunities for investigating novel quantum phenomena (e.g., anisotropic magneto-transport) and topological phase transition.Whether the spin-degenerate counterpart of Lorentz-violating Weyl fermions, the Dirac fermions, can be realized remains as an open question. Here, Yan et al. report experimental evidence of such type-II Dirac fermions in bulk PtTe2 single crystal with a pair of strongly tilted Dirac cones.

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Conflict of interest statement

The authors declare no competing financial interests.

Figures

Fig. 1
Fig. 1
Characterization of type-II Dirac semimetal PtTe2. a, b Schematic drawing of type-I and type-II Dirac fermions. c, d Side and top views of PtTe2 crystal structure. Green balls are Pt atoms and red balls are Te atoms. The unit cell is indicated by black dashed line. e Bulk and projected surface Brillouin zone onto (001) plane. Red dots (labeled as D) mark the positions of 3D Dirac points. f Raman spectrum measured at room temperature. g XRD of PtTe2 measured at room temperature. The inset shows the picture of one single crystal with a few mm size. h LEED pattern taken at beam energy of 70 eV
Fig. 2
Fig. 2
The electronic structure of PtTe2. a, b Band dispersions along the Γ-M (a) and Γ-K (b) direction at photon energy of 22 eV. Red and gray arrow indicate the bulk Dirac cone and the surface state Dirac cone respectively. c, d Calculated band dispersion along the Γ-M (c) and Γ-K (d) directions using Wannier function. e Measured Fermi surface map at photon energy of 21.2 eV. Black dashed line indicates surface Brillouin zone. f Calculated Fermi surface map. g, h Three-dimensional E–k x–k y plots of the bulk Dirac cone around the Γ point g and the surface state Dirac cone h
Fig. 3
Fig. 3
Evidence of type-II Dirac fermions in PtTe2. a–e Dispersions along the M-Γ-K direction measured at 17, 19, 21, 22, and 24 eV respectively. The corresponding k z values in the reduced BZ are labeled in each panel. f–j Comparison of EDC-curvature with calculated dispersions from first-principles calculations (red dashed lines). Surface states are highlighted by yellow and gray dashed line respectively. k In-plane Dirac cone along the M-Γ-K direction measured at 22 eV. l MDCs for the data shown in k. Red and gray markers are guides for the peak positions of inner and outer bands. m Measured dispersion at k || = 0. Red broken lines are calculated dispersions for comparison. n Three-dimensional map E–k x–k z at k y = 0, blue and red arrows indicate hole and electron pockets. The k z values are calculated in extended Brillouin Zone. o Illustration for the evolution of hole pocket (blue) and electron pocket (red) with binding energy
Fig. 4
Fig. 4
Theoretical calculation of type-II Dirac cone in PtTe2. a Calculated band dispersion along the in-plane direction S-D-T and out-of-plane direction A-D-Γ-D-A through the Dirac point. b Three-dimensional plot of the electron and hole pockets at the Dirac point energy. The electron and hole pockets touch at the Dirac point D. c–e Contours of electron and hole pockets at −20, 0, + 20 meV around the Dirac point energy in the k x–k z plane. The electron and hole pockets touch at E D and clearly separated at E D ± 20 meV
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