Strong One-Dimensional Characteristics of Hole-Carriers in ReS2 and ReSe2

Each plane of layered ReS2 and ReSe2 materials has 1D chain structure, from which intriguing properties such as 1D character of the exciton states and linearly polarized photoluminescence originate. However, systematic studies on the 1D character of charge carriers have not been done yet. Here, we report on systematic and comparative studies on the energy-momentum dispersion relationships of layered transition metal dichalcogenides ReS2 and ReSe2 by angle resolved photoemission. We found that the valence band maximum or the minimum energy for holes is located at the high symmetric Z-point for both materials. However, the out-of-plane (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${k}_{z}$$\end{document}kz) dispersion for ReSe2 (20 meV) is found to be much smaller than that of ReS2 (150 meV). We observe that the effective mass of the hole carriers along the direction perpendicular to the chain is about 4 times larger than that along the chain direction for both ReS2 and ReSe2. Remarkably, the experimentally measured hole effective mass is about twice heavier than that from first principles calculation for ReS2 although the in-plane anisotropy values from the experiment and calculations are comparable. These observation indicate that bulk ReS2 and ReSe2 are unique semiconducting transition metal dichalcogenides having strong one-dimensional characters.

www.nature.com/scientificreports www.nature.com/scientificreports/ valence band dispersion for ReS 2 appears to be very different among the reported results 27,29 . In addition, direct comparison between measured valence band dispersions of ReS 2 and ReSe 2 , for which lattice parameters are quite different 31 , are difficult because the data were taken in different Brillouin zones for ReS 2 and ReSe 2 29,30 .
In order to resolve aforementioned issues, we have performed systematic ARPES studies on ReS 2 and ReSe 2 . Our goal is to take data for the entire momentum space which is good enough to do quantitative analysis and obtain in-plane anisotropy in the effective hole mass for the two materials for a comparative study. Our data show a striking difference from what were reported in previous experimental and theoretical studies 29,30,32 . (1) The valence band maximum (VBM) is located at the Z-point for both systems, while it was reported in a previous ARPES study reported that VBM of ReSe 2 may be located at non-high-symmetric momentum point 30,33 . (2) The k z dispersion of ReSe 2 is much smaller than that of published quasiparticle band structure within the LDA + GdW approximation 32 . (3) The effective hole masses along and perpendicular to the chain direction are quite different from the reported experimental and theoretical values 29,30,34 .

Results and Discussion
Valence band maximum of ReSe 2 and Res 2 . ReS 2 and ReSe 2 are layered materials in which the van der Waals interaction between layers is extremely weak, even weaker than other TMDs 12 . The crystal structure for both ReS 2 and ReSe 2 is the so-called distorted 1T structure. Re atoms show a hexagonal network but the structure is distorted to have chain structures as indicated by black lines in Fig. 1(a). The 1D chain structure makes these materials unique among TMDs in that optical and electrical properties carry 1D characteristics [14][15][16][17][18][19][20][21][22][23][24][25][26] .
The inner potential can be estimated from the k z dispersion of electronic band ( Fig. 1(b) and (c)) with the reciprocal lattice vector c*. Based on the results of reported X-ray diffraction measurements 31 , the reciprocal lattice vector c* is calculated to be 1.032 Å −1 (0.984 Å −1 ) for ReS 2 (ReSe 2 ). The inner potential is estimated to be V 0 = 17.8 and 12.4 eV for ReS 2 and ReSe 2 . These estimated values are similar to those of other TMDs 35,36 .
ARPES experiments are performed on ReS 2 and ReSe 2 to obtain the energy-and-momentum dispersion of the hole carriers. ARPES intensities as a function of the energy referenced to the valence band maximum (E VBM ) are mapped along two momentum directions, parallel to chain (k ) and perpendicular to the layer (k z ) ( Fig. 1(b,c)). While several band dispersions are observed within the energy range, the top-most valence band is of interest as it determines the low energy properties of the materials such as electrical conductivity. Due to the layered structure, the top-most bands of ReS 2 and ReSe 2 show relatively weak dispersions along k z than along in-plane momentum. Interestingly, we observed as shown in Fig. 1 that the k z dispersion of ReSe 2 (about 20 meV) is even weaker compared to that of ReS 2 (about 150 meV) which is known as a material with very weak inter-layer interaction 12 . Therefore, our results show an evidence for even smaller interaction between layers in ReSe 2 .
Our photon energy dependence data reveal that VBM is located at Z for both ReS 2 and ReSe 2 as indicated by the red dashed lines in Fig. 1(b,c). While previous ARPES studies also showed that VBM of ReS 2 is located at Z, VBM of ReSe 2 has been under debate. Hart et al. reported that the k z for VBM of ReSe 2 is the same as the Z-point but the in-plane momentum was reported to be non-zero 30  . One of them is at Z and the other is away from Z. But their experiment could not decide which is global VBM, since data quality is not good enough. The global VBM of ReSe 2 can be decided to be located at Z due to high quality data. Please refer to the supplementary materials for more details. In fact, we find that ReSe 2 result about VBM is consistent with a recent theoretical prediction as well 32 . www.nature.com/scientificreports www.nature.com/scientificreports/ Directional dependence of effective hole masses in ReS 2 and Rese 2 . In order to investigate the effective mass of the hole carrier, we analyze ARPES data obtained in the in-plane momentum space that includes the Z-point. As shown in Fig. 2(a,c), constant energy maps of ARPES intensities of ReS 2 and ReSe 2 at E-E VBM = − 0.2 eV show two-fold symmetry and strong anisotropic band contours which are not closed along the direction perpendicular to the chain. These observations indicate much smaller band dispersion along the direction perpendicular to the chain. The top-most band dispersions, which we are interested in, along the chain are much stronger than those along the other for both ReS 2 and ReSe 2 . For quantitative analysis, we try to fit the band dispersions with a quadratic function for which the effective mass is a free parameter 32 . The dotted lines in Fig. 2(b,d) indicate the fit functions. So, obtained effective masses along the direction perpendicular to the chain (4.63 m e for ReS 2 and 4.14 m e for ReSe 2 ) are much heavier than the effective masses along chain (1.08 m e for ReS 2 and 1.13 m e for ReSe 2 ). That is, the effective mass along the chain is about 4 times lighter than that perpendicular to the chain for both ReS 2 and ReSe 2 . This in-plane anisotropy value in the effective hole mass is the largest among semiconducting TMDs 37,38 .
The valence band dispersion can also be analyzed for different theta angle and corresponding effective hole mass can be obtained. Shown in Fig. 3(a,b) are ARPES data along in-plane momentum set by the θ angle defined in Fig. 2(a). The data are subsequently analyzed and the corresponding effective hole mass is obtained for a www.nature.com/scientificreports www.nature.com/scientificreports/ systematic study of direction dependence. We notice the top-most band can be fitted well with a quadratic function indicated by dotted lines, which makes us confident in our analysis. The extracted effective mass from the quadratic function is plotted in polar coordinate as a function of the theta angle in Fig. 3(c). The plot clearly shows two-fold symmetry and strong in-plane anisotropy of the effective hole mass for both ReS 2 (red) and ReSe 2 (blue). There is an important point to discuss in comparison with the results of first principles calculations on ReS 2 . The experimentally observed effective mass is about twice larger than that from the first principles calculations. The effective mass from the first principles calculations is 2.4 m e along the direction perpendicular to the chain and 0.8 m e along the chain 27 . The electron-electron and electron-phonon interactions or atomic spin-orbit coupling of Re atom which were not considered in the calculation may play a crucial role in the clear enhancement of the effective hole mass.

Conclusions
In this study, we performed systematic ARPES studies of ReS 2 and ReSe 2 to reveal the energy-momentum dispersion relationships of the top most valence bands. We found that ReSe 2 have much smaller k z dispersion than ReS 2 , indicating the more 2D-like feature in ReSe 2 than in ReS 2 . We systematically investigated in-plane directional dependence of the effective hole masses of ReS 2 and ReSe 2 . The effective masses show strong anisotropy, about 4 times lighter along the chain than the direction perpendicular to the chain. In-plane anisotropy of the hole effective masses in ReS 2 and ReSe 2 is larger than that in black phosphorus which also shows anisotropic electrical and optical properties 39,40 . Therefore, ReS 2 and ReSe 2 are quasi 1D materials in terms of the low energy hole carrier dynamics, which makes ReS 2 and ReSe 2 promising bulk materials for 1D semiconducting electronics. The effective mass of ReS 2 observed by ARPES is found to be significantly enhanced compared to that from first principles calculations. Electron-electron and electron-phonon interactions or atomic spin-orbit coupling of Re atom may be attributed to the mass enhancement 41 . The quasi 1D character of the hole carriers as well as possibility of the electron-electron and electron-phonon interactions may lead to charge density wave order if enough amount of hole carriers are doped into ReS 2 and ReSe 2 42 .

Methods
ARpes measurement. We performed ARPES experiments at the beamline 4.0.3.2 (MERLIN) of the Advanced Light Source at the Lawrence Berkeley National Laboratory equipped with VG-Scienta R8000 electron analyzer. All samples are cleaved in-situ and data were taken at 200 K to avoid the charging effect in a vacuum better than 6 × 10 −11 Torr. with linearly polarized light. For the k z dependence experiment, photon energies between 60 and 110 eV with 2 eV energy step were used. The total energy resolution was better than 20 meV with a momentum resolution of 0.004 Å −1 .