Na Qin(秦娜)Xian Du(杜憲)Yangyang Lv(呂洋洋)Lu Kang(康璐)Zhongxu Yin(尹中旭)Jingsong Zhou(周景松)Xu Gu(顧旭) Qinqin Zhang(張琴琴) Runzhe Xu(許潤哲) Wenxuan Zhao(趙文軒) Yidian Li(李義典)Shuhua Yao(姚淑華) Yanfeng Chen(陳延峰) Zhongkai Liu(柳仲楷)Lexian Yang(楊樂仙) and Yulin Chen(陳宇林)

1State Key Laboratory of Low Dimensional Quantum Physics,Department of Physics,Tsinghua University,Beijing 100084,China

2National Laboratory of Solid State Microstructures,Department of Materials Science and Engineering,Nanjing University,Nanjing 210093,China

3School of Physical Science and Technology,ShanghaiTech University and CAS-Shanghai Science Research Center,Shanghai 201210,China

4ShanghaiTech Laboratory for Topological Physics,Shanghai 200031,China

5Frontier Science Center for Quantum Information,Beijing 100084,China

6Department of Physics,Clarendon Laboratory,University of Oxford,Parks Road,Oxford OX1 3PU,UK

Keywords: transition metal chalcogenides, spin-orbit coupling, electronic structure, angle-resolved photoemission spectroscopy(ARPES)

1. Introduction

Transition metal chalcogenides with quasi-twodimensional crystal structure exhibit various fascinating properties, such as superconductivity, charge-density wave, magnetism, novel topological phase, valleytronics, etc.,[1-14]which provide not only significant scientific implications but also great application potential in the next-generation electronic and spintronic devices. Recently, ternary transition metal chalcogenides (TTMCs) have attracted great attention.Compared with their binary counterparts, TTMCs show improved tunability and complexity, thus promising a rich platform to search for and study new physics,such as the interplay between magnetism and topology, giant anomalous Hall effect,and topological quantum properties.[15-21]

It is well-known that spin-orbit coupling (SOC) plays a pivotal role in the novel properties of quantum materials. It serves as a fundamental tuning parameter to bridge different topological phases;[22-25]it is also essentially related to the large magnetoresistance[26]and magnetocrystalline anisotropy[27]in solid materials; from application perspective, it enables electrical manipulation of spins, which is of significant importance in the newly developed spintronics and valleytronics. Therefore, it is attractive to search for and investigate materials with large SOC.

In this work, using high-resolution angle-resolved photoemission spectroscopy (ARPES) andab initiocalculation,we study the electronic structures of Cu2TlTe2and Cu2TlSe2,newly discovered ternary transition metal chalcogenides. Our calculation shows a semiconductor and semimetal phase in Cu2TlTe2and Cu2TlSe2,respectively,suggesting a tunability of the band gap with Se/Te composition. The band dispersions near the Fermi level(EF)are mainly from p orbitals,that is, 5p orbitals of Te and 4p orbitals of Se. With the help ofab initiocalculation, we identify strong SOC effect that lifts the band degeneracy and opens large energy gaps in the band structure. Moreover, we observe a band folding near theXpoint, suggesting a surface reconstruction or surface chargedensity wave. Our study provides insights into the SOC and electronic structure of TTMC materials Cu2TlX2, which may be an interesting and useful platform to search and study novel physics,particularly in their ultrathin films.

2. Methods

High-quality Cu2TlX2crystals were synthesized using Bridgeman method.[28]ARPES measurements were performed at beam line I05 of the Diamond Light Source(DLS,proposal No. SI20683-1),beam line 13U of the National Synchrotron Radiation Laboratory (NSRL), and Tsinghua University. Scienta R4000 (DA30) analyzer was used at DLS(NSRL). Measurements at Tsinghua University were performed using DA30L analyzer and VUV5050 helium lamp.Samples were cleaved and measured under ultrahigh vacuum better than 1×10-10mbar. The overall energy and angular resolutions were 15 meV and 0.2°, respectively.First-principles band structure calculations of Cu2TlX2(X=Se,Te) were performed using QUANTUM ESPRESSO code package[29]with a plane wave basis. The pseudopotentials suggested by Standard Solid State Pseudopotentials (SSSP)Precision v1.1[30]were chosen for all elements. The exchange and correlation energy was considered under Perdew-Burke-Ernzerhof(PBE)type generalized gradient approximation (GGA).[31]Both lattice constants and fractional atomic coordinates were set to the experimental values. The cutoff energy for the plane-wave basis was set to 560 eV in all calculations, which was sufficient to converge the total energy for a givenk-point sampling. AΓ-centered Monkhorst-Packk-point mesh of 16×16×16 (15×15×15) with a spacing of 0.15 °A-1was adopted for Cu2TlSe2(Cu2TlTe2) to get a self-consistent charge density. Both the conditions of excluding and including spin-orbit coupling were considered in the self-consistent calculations. The electronic minimization algorithm used for self-consistent calculations was a blocked Davidson algorithm. Surface-projected band structures were calculated with the WANNIERTOOLS package,[32]based on the tight-binding type Hamiltonian constructed from maximally localized Wannier functions (MLWF) supplied by the Wannier90 code,[33]by projecting theab initioconstructed(Kohn-Sham) Bloch states into the atomic-orbital like Wannier functions starting from a 9×9×9 uniformkgrid.

3. Results and discussion

Copper based ternary TTMCs Cu2TlX2(X= Se,Te)crystallize into a layered tetragonal ThCr2Si2-type structure with alternatively stacking Cu2X2and Tl layers, as shown in Fig. 1(a). Figure 1(b) shows the three-dimensional Brillouin zone of Cu2TlX2and its surface projection with highsymmetry points indicated. Our resistivity measurements in Fig.1(c)show prototypical metallic behaviors that can be well understood within Fermi-liquid theory.[28]We observe sharp peaks in single crystal x-ray diffraction measurements, suggesting a lattice constant ofc= 14.03 °A and 15.21 °A for Cu2TlSe2and Cu2TlTe2,respectively.

Although the materials are quasi-two dimensional, our photon-energy dependent Fermi surface (FS) measurements on Cu2TlTe2in Fig.2(a)show resolvable variation. Using an inner potential of 13 eV,we can determine the high symmetry points alongkz, as shown in Figs. 2(a) and 2(b). We observe a strong dispersion between-0.95 eV and-0.5 eV alongΓ Z[white dashed line in Fig.2(b)], suggesting an important role of interlayer coupling in the electronic structure of Cu2TlTe2.TheΓandZpoints can be approached by 122 eV and 102 eV photons, respectively. Figures 2(c) and 2(d) show the evolution of the constant energy contour with binding energy on theΓ ΣXandZΣ1Y1planes, respectively. The measured Fermi surface consists of a four-fold symmetric hole pocket near theˉΓpoint, an electron pocket around the ˉMpoint, and a small hole pocket around the ˉXpoint,which evolves into a complex texture at high binding energies. The FS and constant energy contours at different binding energies are perfectly reproduced by ourab initiocalculation as shown in Fig.2(e).

Fig.1.(a)Crystal structure of Cu2TlX2(X=Se,Te).(b)Three-dimensional Brillouin zone of Cu2TlX2 and its surface projection with high-symmetry points indicated. (c) Resistivity of Cu2TlX2 as a function of temperature.(d)Single-crystal x-ray diffraction data of Cu2TlSe2 and Cu2TlTe2.

Figure 3 shows the band structure of Cu2TlTe2along high symmetry directions. We observe anisotropic dispersions alongΓ ΣandΓ X[Figs. 3(a)-3(c)]. NearEF, there exist mainly two bands,αandβcrossingEF. Theαband is nearly flat near theΓpoint, which may contribute high density of states nearEF. Theβband,on the other hand,shows a linear dispersion in a large energy range,as shown in Figs.3(b)and 3(c).The Fermi velocity of theβband is about 4.8 eV·°A alongΣX, about 60%of that of graphene.[16]The linear dispersion of theβband may contribute to the unsaturated magnetoresistance in Cu2TlTe2at high magnetic field.[28]The band structure of Cu2TlTe2is nicely reproduced by our calculation with SOC included [Figs. 3(d) and 3(e)], in which theαandβbands are shown by the blue and red curves,respectively. We emphasize that thekzdispersion observed in Fig. 2(b) is also captured by ourab initiocalculation.

Fig.2. (a)Fermi surface of Cu2TlTe2 in the Γ ΣZ plane obtained by photon-energy dependent measurements. (b)The kz-dispersion along Γ Z. (c),(d)Evolution of the constant-energy-contours with binding energy on(c)Γ ΣX and(d)ZΣ1Y1 planes,respectively. (e)Calculated constant-energycontours of Cu2TlTe2. Data were taken at 10 K.

Fig. 3. (a)-(c) ARPES measured band dispersions of Cu2TlTe2 along high symmetry directions. (d), (e) Band structures obtained by ab initio calculation with(d)and without(e)spin-orbit coupling(SOC).The red arrows indicate the band gaps induced by SOC.The red and blue circles indicate the band crossings with small energy gap. Data were taken with 122 eV photons at 10 K.

By comparing our experiment with the calculations with and without SOC,we notice that the flat band nearΓis actually induced by the strong SOC in the system. Moreover,the SOC induces a band gap as large as 399(174)meV along theΓ X(Γ Σ) direction [red arrows in Fig. 3(e)], in good agreement with our experiment[red arrows in Figs.3(a)and 3(b)],suggesting strong SOC effect modulating the band structure of Cu2TlTe2. The SOC also lifts the band degeneracy alongΓ Z,inducing a band splitting as large as 380 meV.

Figure 4 shows the band structure of Cu2TlSe2. Overall, the band structure of Cu2TlSe2is very similar to that of Cu2TlTe2. The Fermi surface is likewise mainly contributed by theαandβbands [Fig. 4(a)]. The flat band nearEFas in Cu2TlTe2is not observed since it locates slightly aboveEF, and such difference may be due to the non-stoichiometry of Cu2TlTe2.[28]However, we observe another flat band near 500 meV belowEFusing 21.2 eV photons [Figs. 4(b) and 4(c)]. The Fermi velocity of theβband along ˉΣˉXis about 2 eV·°A, much smaller than that in Cu2TlTe2. The band gap along ˉ?！[red arrows in Figs. 4(c) and 4(f)] and the band splitting alongΓ Zinduced by SOC are also much smaller than those in Cu2TlTe2, suggesting a stronger SOC effect in Cu2TlTe2. The measured band structure of Cu2TlSe2and calculations along high symmetry directions are shown in Figs. 4(b)-4(f). Although the flat band near-500 meV is not in the calculation along high symmetry points, it can be reproduced by the calculation at akzposition betweenΓandZ, since the band below theαband shows an electron (hole)like dispersion alongΓ Σ(ZΣ1) in the calculation [Fig. 4(f)].Indeed,thekzvalue corresponding to 21.2 eV photons is estimated to be near the middle ofΓandZin the Brillouin zone.

From the calculations in Figs.3(e)and 4(f),we note that Cu2TlSe2is a semiconductor with indirect band gap of about 226 meV, in contrast to the semi-metallic band structure of Cu2TlTe2, suggesting a tunability of the band gap by Se/Te composition in the Cu2TlX2materials. We further conducted orbital-projectedab-initiocalculation as shown in Fig.5. The band dispersions nearEFare mainly contributed by the 4p/5p orbital of the Se/Te atoms. Therefore, the change of Se/Te composition can efficiently tune the band gap of Cu2TlX2. It is worth noting that both of our Cu2TlX2samples are p-doped with the valence bands crossingEF. Further electron doping or the synthesis of intrinsic samples are required to establish the tunability of the band gap.

In both Cu2TlTe2and Cu2TlSe2, there exist band crossings that are nearly gapless alongΓ Σ[red and blue circles in Figs. 3(d), 3(e), 4(e) and 4(f)]. According to our calculation,the hybridization gaps near these band crossings are less than 10 meV in Cu2TlTe2and less than 5 meV in Cu2TlSe2,which are immune to the SOC[red and blue circles in Figs.3(d),3(e),4(e)and 4(f)]. In Cu2TlSe2,we observe a Dirac-like band dispersion nearEF, consistent with our calculation [red circles in Figs. 4(b) and 4(f)]. It is likely that, with lighter atoms in the system, for example, in Cu2TlS2, a nearly gapless Dirac fermion can exist nearEF.

Fig.4. (a)Measured(left)and calculated(right)Fermi surface of Cu2TlSe2. (b)-(d)ARPES measured band dispersions of Cu2TlSe2 along high symmetry directions. (e),(f)Band structure obtained by ab initio calculation with(e)and without(f)SOC.The red arrows indicate the band gaps induced by SOC.The red and blue circles indicate the band crossings with small energy gap. Data were collected with 21.2 eV photons delivered by a helium lamp at 68 K.

Fig.5.Orbital-projected band structure calculations of Cu2TlX2 without SOC,in which the point size indicates the weight of the orbital contributions to band dispersions. (a),(b)Cu d and Te p states in Cu2TlTe2. (c),(d)Cu d and Se p states in Cu2TlSe2.

Fig.6. (a)Fermi surface of Cu2TlTe2 measured with 80 eV photon energy.(b) Band dispersion of Cu2TlTe2 along ΣX, which is indicated by red line in (a), showing band folding from the Σ point to the X point. Data were collected at 10 K.

Noticeably, in the Fermi surface and band dispersion alongΣXof Cu2TlTe2, we observe band folding fromΣtoX(Figs. 6(a) and 6(b)) using photon energy of 80 eV that is more surface-sensitive. The band folding fromΣtoΓis also resolvable in Fig.3(a),which complicates the band dispersion nearΓin Fig.3(a).Such band folding suggests a 2-fold reconstruction of the crystal structure. Since we do not observe any anomaly in temperature dependent resistivity measurements,the observed band folding is likely due to a surface reconstruction or surface charge-density wave,which requires further experimental investigations.

4. Summary

To sum up, we systematically measure the electronic structure of Cu2TlX2using high-resolution ARPES.The transition from a semiconductor in Cu2TlSe2to a semimetal in Cu2TlTe2, as indicated by ourab initiocalculation, suggests a tunability of the electronic structure and physical property of the materials with Se/Te composition. With the help ofab initiocalculation, we identify strong SOC effect in the band structure of Cu2TlTe2, which opens a band gap and lifts the band degeneracy alongΓ Z. We propose that a massless Dirac fermion may exist nearEFin the sibling Cu2TlX2crystal,i.e.,Cu2TlS2if it is successfully synthesized. Our results are helpful to understand the electronic properties of Cu2TlX2, and also provide a material platform to search for SOC-related physics.

Acknowledgments

This study was supported by the National Natural Science Foundation of China(Grant No.11774190). We thank for access to DLS beamline I05 and NSRL beamline 13U with help from S.W.Jung,C.Cacho,S.T.Cui,and Z.Sun.