Experimental evidence of type-II Dirac fermions in PtSe2

TL;DR

This paper provides experimental evidence for the existence of three-dimensional type-II Dirac fermions in high-quality PtSe2 crystals, highlighting its potential for exploring novel quantum phenomena in topological semimetals.

Contribution

It presents direct experimental evidence of type-II Dirac fermions in PtSe2, a significant step in understanding topological semimetals with Lorentz invariance breaking.

Findings

Evidence of 3D type-II Dirac fermions in PtSe2

Comparison of electronic structures between PtSe2 and PtTe2

Identification of PtSe2 as a platform for quantum phenomena exploration

Abstract

Topological semimetals have attracted extensive research interests for realizing condensed matter physics counterparts of three-dimensional Dirac and Weyl fermions, which were originally introduced in high energy physics. Recently it has been proposed that type-II Dirac semimetal can host a new type of Dirac fermions which break Lorentz invariance and therefore does not have counterpart in high energy physics. Here we report the electronic structure of high quality PtSe$_2$ crystals 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 sister compound PtTe$_2$ is also discussed. Our work provides an important platform for exploring the novel quantum phenomena in the PtSe$_2$ class of type-II Dirac semimetals.

Figures

Full text

I I. INTRODUCTION

Dirac and Weyl fermions were originally introduced in high energy physics Weyl (1929). Their counterparts in condensed matter physics have been realized in three-dimensional (3D) Dirac and Weyl semimetals. Such topological semimetals exhibit a rich variety of novel phenomena, such as negative magnetoresistance (MR) Xiong et al. (2015); Liang et al. (2014); Huang et al. (2015), chiral magnetic effects Zyuzin and Burkov (2012), and quantum anomalous Hall effect Liu et al. (2015a). Dirac and Weyl semimetals can be classified into type-I and type-II, depending on whether the Lorentz invariance is preserved or not. For type-I Dirac Liu et al. (2014); Neupane et al. (2014) and Weyl semimetals Weng et al. (2015); Lv et al. (2015); Xu et al. (2015a) which obey Lorentz invariance, massless Dirac fermions with linear dispersions are expected at the Dirac or Weyl points. Type-II Dirac and Weyl fermions Soluyanov et al. (2015) emerge at the topologically protected touching points of electron and hole pockets, and they show highly tilted Dirac cones along certain momentum direction (see schematics in Fig. 1(a)), thereby breaking the Lorentz invariance Deng et al. (2016); Chang et al. (2016); Huang et al. (2016a). The anisotropic electronic structure can also lead to anisotropic MR, and negative MR is expected only along directions where the cones are not tilted enough to break the Lorentz invariance Soluyanov et al. (2015); Zyuzin and Tiwari (2016); Fei et al. (2016). Type-II Dirac semimetal can be tuned to a Weyl semimetal or topological crystalline insulator when the crystal symmetry or time reversal symmetry is broken Burkov and Balents (2011); Halász and Balents (2012), and therefore they are ideal candidates for investigating topological phase transitions and potential device applications.

Recently, PtTe2 has been reported to be a Lorentz violating type-II Dirac semimetal Yan et al. (2016). Its sister compound PtSe2 has also been predicted to be a type-II Dirac semimetal Huang et al. (2016b). Although monolayer PtSe2 film has been shown to exhibit interesting electronic properties Wang et al. (2015) and helical spin texture with spin-layer locking Yao et al. (2017), so far research in bulk PtSe2 crystals has been limited due to the lack of high quality single crystals. Here we report the growth and characterization of high quality PtSe2 single crystal, and provide direct experimental evidence for type-II Dirac fermions from angle-resolved photoemission spectroscopy (ARPES). A comparison of PtSe2 with PtTe2 in crystal, vibrational and electronic structure is also discussed.

II II. METHODS

Although high quality PtTe2 single crystals can be directly synthesized by a self-flux method as reported previously Yan et al. (2016), PtSe2 single crystals cannot be grown using the same method. Instead, we need to use chemical vapor transport (CVT). Precursor of polycrystalline PtSe2 was synthesized by directly heating the stoichiometric mixture of high-purity Pt granules (99.9%, Alfa Aesar) and Se ingot (99.99%, Alfa Aesar) at 1,173 K in a vacuum-sealed silica ampoule for 3 days. The polycrystalline PtSe2 was then recrystallized by the CVT method using SeBr4 (99%, Aladdin, with a concentration of $\leq$2.7 mg/ml) as the transporting agent. The growth rate is much slower than PtTe2. After 3 weeks, PtSe2 single crystals of a few millimeters in size with shiny surfaces can be obtained.

The band structures were carried out using density functional theory (DFT) as implemented in the Vienna ab initio simulation package Kresse and Furthmüller (1996). We employ the Perdew-Burke-Ernzerhof–type generalized gradient approximation Perdew et al. (1996) and the projector augmented wave (PAW) method PE (1994). A plane wave basis set with a default energy cutoff and an $18\times 18\times 11$ k-point mesh were used. Spin-orbit coupling (SOC) is included self-consistently within the DFT calculation.

ARPES measurements were taken at BL13U of Hefei National Synchrotron Radiation Laboratory, BL9A of Hiroshima Synchrotron Radiation Center under the proposal No.15-A-26 and our home laboratory. The crystals were cleaved in-situ and measured at a temperature of T$\approx$20 K in vacuum with a base pressure better than 1$\times$10*-10* Torr.

III III. RESULTS

As its isostructural counterpart PtTe2, PtSe2 crystallizes in the centrosymmetric CdI2-type structure with space group P$\overline{3}$m1 (No. 164) and point group D3d (-3m). The structure can be regarded as the hexagonal close-packed Se atoms where Pt atoms occupy the octahedral sites in alternative Se layers. The adjacent unoccupied Se layers are held together by weak van der Waals interactions, which emphasize the 2D nature. The top and side views of the crystal structure of PtSe2 (PtTe2) are shown in Fig. 1(b,c). The hexagonal bulk and projected surface Brillouin zones (BZs) are shown in Fig. 1(d) where high-symmetry points and Dirac points are also indicated.

Figure 2 shows the characterization of the PtSe2 single crystals as compared to PtTe2. Figure 2(a,b) shows the X-ray diffraction (XRD) patterns. Sharp (00l) diffraction peaks are observed. The larger diffraction angles for corresponding (00l) peaks of PtSe2 as compared to those of PtTe2 suggests that PtSe2 has a smaller layer separation. The extracted out-of-plane lattice constants are c = 5.07 $\pm$ 0.01 $\AA$ for PtSe2 and c = 5.21 $\pm$ 0.01 $\AA$ for PtTe2. The in-plane lattice constants are a = b = 3.727 $\AA$ for PtSe2 and a = b = 4.0242 $\AA$ for PtTe2 Kliche (1985). Figure 2(c,d) shows the low energy electron diffraction (LEED) pattern of the PtSe2 and PtTe2 single crystals after cleaving in ultra-high vacuum chamber. Sharp diffraction spots with hexagonal symmetry are observed on the entire sample surface, indicating the high quality, homogeneous single crystals. Figure 2(e,f) shows the temperature dependent resistivity of PtSe2 and PtTe2. A metallic behavior is observed in both samples from 380 K to 5 K with a high residual resistance ratio (RRR) of 184 for PtSe2 and 29 for PtTe2. The large interlayer spacing of PtSe2 leads to changes in the lattice vibrations. The Raman spectrum in Fig. 2(g) shows the Eg and A1g modes at $\sim$ 175 cm*-1* and 205 cm*-1* respectively for PtSe2, which are at much larger energies compared to 110 cm*-1* and 157 cm*-1* in PtTe2 (Fig. 2(h)). The Eg mode involves the in-plane vibration with the upper and the bottom Se atoms moving in opposite directions, and the A1g mode corresponds to the out-of-plane vibration of Se atoms. The blue shift of the Raman modes in PtSe2 indicates a stronger interaction than PtTe2 O’Brien et al. (2016), which is in good agreement with the smaller layer separation.

The most important characteristic of a type-II Dirac semimetal is the tilted 3D Dirac cone in the band structure. To reveal the 3D Dirac cone, we measure the dispersions around k*∥* =0 at different kz values using different photon energies. A conical dispersion is observed along the in-plane directions parallel to the $\Gamma$-K (Fig. 3(a)) and $\Gamma$-M (Fig. 3(b)) directions at kz = 0.37 c∗ (c${}^{*}=2\pi/c$) of the reduced BZ. Along the out-of-plane direction (Fig. 3(c)), the dispersion shows a highly tilted Dirac cone crossing at the same kz value. The band dispersions of PtSe2 are overall similar to those of PtTe2 (Fig. 3(e-h)) Yan et al. (2016), except that the Dirac points are at slightly different energies (-1.48 eV compared to -0.86 eV) and at different kz values (0.37 c∗ compared to 0.35 c∗). These differences are attributed to the different lattice constants. In addition, compared to PtTe2 where the intensity is suppressed at the crossing point showing a gap-like fetaure, PtSe2 shows a 3D Dirac cone without any signature of gap opening at the Dirac point. The anisotropic 3D Dirac cones with the Dirac cone highly tilted along the kz direction provides direct evidence that it is a type-II Dirac semimetal.

The type-II Dirac fermions in PtSe2 is also supported by first-principles calcualtions and symmetry analysis. The 3D Dirac cone corresponds to the band crossing along the in-plane S-D-T momentum path in calculated band structure in Fig. 3(d). The Dirac cone is strongly tilted along the $\Gamma$-A direction, but not along the in-plane S-D-T path, which is the characteristic feature of the type-II Dirac fermions. The bulk Dirac cone of PtSe2 is formed by two valence bands with Se-p orbitals labeled S1 and S2 in Fig. 3(d) (highlighted by red color), while that of PtTe2 is formed by two valence bands of Te-p orbitals, labeled as T1 and T2 in Fig. 3(h). As each band is doubly degenerate, the isolated symmetry-protected band crossing is four-fold degenerate. Group theory analysis shows that these two bands belong to different irreducible representations. More importantly, the C3 rotational symmetry about the c axis prohibits hybridization between them and protects the 3D Dirac fermions. In addition to the 3D Dirac cone, there also exists conical Z2 surface states which are induced by the band inversion. The deep topological surface states are revealed in the ARPES data in Fig. 3(a,b) (pointed by green arrows), and they connect the gapped bulk bands S3 and S4 with opposite parities in Fig. 3(d). Similar type-II Dirac cone and deep topological surfaces also exist in PtTe2 (Fig. 3(e-g)).

Figure 4 shows a comparison of the electronic structure between PtSe2 and PtTe2 to reveal their difference. Figure 4(a-e) and (h-l) show the evolution of the constant energy maps from EF to -1.2 eV. The Fermi surface map of PtSe2 shows three small elliptical pockets around the $\Gamma$ point (denoted as $\alpha$ in Fig. 4(a)) and six pockets located at the mid-point between the $\Gamma$ and M points, which are from the bottom of the $\beta$ band (Fig. 4(g)). Below -0.4 eV, there is an additional pocket emerging at the $\Gamma$ point (Fig. 4(c)), and this pocket evolves into the 3D Dirac point at kz = 0.37 c∗ discussed above. The Fermi surface map of PtTe2 features a small triangular pocket (denoted as $\gamma$) and six small circles (denoted as $\delta$ ) with alternating brightness located near the mid-point between $\Gamma$ and M. The dispersions along the $\Gamma$-K and $\Gamma$-M directions are shown in Fig. 4(f, g) for PtSe2 and (m, n)for PtTe2. The corresponding bands which contribute to $\alpha$, $\beta$ in (a), and $\gamma$, $\delta$ in (h) Fermi surface sheets are noted. Similar band structure can been found in PdTe2 Liu et al. (2015b); Noh et al. (2016). One major difference in the surface topology of PtSe2 and PtTe2 is that the band at the mid-point between $\Gamma$ and M shows a gapped Dirac cone in PtTe2 , while there is only a small electron pocket in PtSe2. These gapped Dirac cones are nontrivial surface states due to the extra band inversion for the top two bands at the $\Gamma$ point in PtTe2 (Fig. 3(h)). Such band inversion does not occue in PtSe2, leading to different surface states.

IV IV. CONCLUSIONS

To summarize, by performing a systematic study of PtSe2 single crystals, we provide the experimental evidence for type-II Dirac fermions in PtSe2. The difference in the lattice constant, vibrational modes and electronic structure is also presented. Our work paves the way for studying a number of similar type-II Dirac materials in the PtSe2 class of transition metal dichalcogenides. This family of TMDs provide a platform for investigating novel electronic structures and topologic phase transition like doping-driven Lifshitz transition Soluyanov et al. (2015); Xu et al. (2015b) in the near future.

V ACKNOWLEDGMENTS

This work is supported by the National Natural Science Foundation of China (Grant No. 11427903 and 11334006), Ministry of Science and Technology of China (Grant No. 2015CB921001, 2016YFA0301001 and 2016YFA0301004).