Introduction

Layered transition-metal dichalcogenides (TMDs) have been extensively studied in recent years because of their potential as electronic materials for future devices. Their intriguing characters of the electronic structures such as the valley degeneracy1 and spin-valley-layer locking2,3,4, provide added value for valley- and spintronic applications. While some of them even exhibit superconductivity and charge density waves originating from the electron-phonon and electron-electron interactions due to their low electronic dimensionality (e.g. in NbSe25,6), most of the studies have been focused on Mo and W compounds due to their semi-conducting properties and close to ideal 2 dimensionality7,8,9,10,11.

Very recently, layered ReS2 and ReSe2 began to draw attention as their layer-layer interactions are much weaker than other layered TMDs12. More interestingly, ReS2 and ReSe2 have one-dimensional (1D) characters in their structure as well as optical and electrical properties due to the formation of Re chain structure stemming from the distortion in the 1T structural phase12,13,14. High-resolution transmission electron microscopy and electron diffraction studies reveal distorted 1T structure with Re chain formation12. Such structure distortion is directly related to the high anisotropy in the Raman response from in-plane lattice vibrations14,15,16,17,18,19. It also affects optical properties, e.g., anisotropic character in optical absorption or photoluminescence comes from that of excitons20,21,22,23,24. Electrical conductivity is also found to be much higher along the chain direction than the direction perpendicular to the chain13,25,26.

As the above-mentioned intriguing 1D properties are determined by the characteristics of hole and electron band dispersions, electronic structure studies by angle resolved photoemission spectroscopy (ARPES) are naturally desired. Especially, the effective mass is a fundamental parameter that can be obtained from the energy and momentum dispersion relationship and governs the electrical and optical properties such as mobility, conductivity, light absorption and photoluminescence. In fact, a couple of ARPES studies on ReS2 and ReSe2 have been reported and the results indicate an in-plane anisotropy in the hole band dispersion as expected from the chain structures in ReS227,28,29 and in ReSe230. However, obtaining very high-quality data needed to determine the effective mass for all directions turned out to be challenging. For example, the photon energy dependence of the valence band dispersion for ReS2 appears to be very different among the reported results27,29. In addition, direct comparison between measured valence band dispersions of ReS2 and ReSe2, for which lattice parameters are quite different31, are difficult because the data were taken in different Brillouin zones for ReS2 and ReSe229,30.

In order to resolve aforementioned issues, we have performed systematic ARPES studies on ReS2 and ReSe2. 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 studies29,30,32. (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 ReSe2 may be located at non-high-symmetric momentum point30,33. (2) The \({k}_{z}\) dispersion of ReSe2 is much smaller than that of published quasiparticle band structure within the LDA + GdW approximation32. (3) The effective hole masses along and perpendicular to the chain direction are quite different from the reported experimental and theoretical values29,30,34.

Results and Discussion

Valence band maximum of ReSe2 and ReS2

ReS2 and ReSe2 are layered materials in which the van der Waals interaction between layers is extremely weak, even weaker than other TMDs12. The crystal structure for both ReS2 and ReSe2 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 characteristics14,15,16,17,18,19,20,21,22,23,24,25,26.

Figure 1
figure 1

Crystal structure and out-of-plane valence band dispersions. (a) Top and side views of the crystal structure of ReX2 (X = S, Se). It shows distorted 1 T structure with Re chains indicated by black solid lines. (b,c) Intensity plots of ReS2 and ReSe2 ARPES data in the energy and momentum space, respectively. kZ dependent intensities are taken by using different photon energies from 60 eV to 110 eV with 2 eV step. kZ is obtained with inner potentials of 17.8 and 12.4 eV for ReS2 and ReSe2, respectively. \({{\boldsymbol{k}}}_{\parallel }\) and \({{\boldsymbol{k}}}_{\perp }\) are in-plane momentum parallel and perpendicular to the chain, respectively. Red dashed lines are guides to eye for \({{\boldsymbol{k}}}_{{\boldsymbol{z}}}\) dispersion of the top-most valence bands. Insets are 2D constant energy (E = EVBM) intensity map in the momentum-space (as functions of \({{\boldsymbol{k}}}_{\parallel }\) and \({{\boldsymbol{k}}}_{\perp }\)) at the \({{\boldsymbol{k}}}_{{\boldsymbol{z}}}\) = Z-point. Note that there is a single peak at the zero in-plane momentum point (Z-point).

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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 measurements31, the reciprocal lattice vector c* is calculated to be 1.032 Å−1 (0.984 Å−1) for ReS2 (ReSe2). The inner potential is estimated to be V0 = 17.8 and 12.4 eV for ReS2 and ReSe2. These estimated values are similar to those of other TMDs35,36.

ARPES experiments are performed on ReS2 and ReSe2 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 (EVBM) are mapped along two momentum directions, parallel to chain (\({k}_{\parallel }\)) 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 ReS2 and ReSe2 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 ReSe2 (about 20 meV) is even weaker compared to that of ReS2 (about 150 meV) which is known as a material with very weak inter-layer interaction12. Therefore, our results show an evidence for even smaller interaction between layers in ReSe2.

Our photon energy dependence data reveal that VBM is located at Z for both ReS2 and ReSe2 as indicated by the red dashed lines in Fig. 1(b,c). While previous ARPES studies also showed that VBM of ReS2 is located at Z, VBM of ReSe2 has been under debate. Hart et al. reported that the \({k}_{z}\) for VBM of ReSe2 is the same as the Z-point but the in-plane momentum was reported to be non-zero30. More recently, Eickholt et al. reported two VBM of ReSe233. 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 ReSe2 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 ReSe2 result about VBM is consistent with a recent theoretical prediction as well32.

Directional dependence of effective hole masses in ReS2 and ReSe2

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 ReS2 and ReSe2 at E-EVBM = − 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 ReS2 and ReSe2. For quantitative analysis, we try to fit the band dispersions with a quadratic function for which the effective mass is a free parameter32. 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 me for ReS2 and 4.14 me for ReSe2) are much heavier than the effective masses along chain (1.08 me for ReS2 and 1.13 me for ReSe2). That is, the effective mass along the chain is about 4 times lighter than that perpendicular to the chain for both ReS2 and ReSe2. This in-plane anisotropy value in the effective hole mass is the largest among semiconducting TMDs37,38.

Figure 2
figure 2

In-plane valence band dispersions near the valence band maximum. Constant energy (E-EVBM = − 0.2 eV) ARPES maps of ReS2 (a) and ReSe2 (c). The photon energy used for the experiment was 70 eV for ReS2 and 68 eV for ReSe2. For these photon energies, \({{\boldsymbol{k}}}_{{\boldsymbol{z}}}\) = Z point (white dot) where VBM is located is included in the data. Red solid and dashed lines in (a,c) indicate the direction parallel and perpendicular to the Re chain direction, respectively. θ is defined as the relative angle from the direction along the chain as shown in the figure. The honey comb structured line indicates the projected Brillouin zone boundary. (b,d) High symmetric cuts along (θ = 0°) and perpendicular (θ = 90°) to the Re chain. The dotted lines in (b,d) are quadratic fit to the top-most bands. The effective masses of hole carriers of ReX2 extracted from the fitting functions are shown in the figures.

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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 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 ReS2 (red) and ReSe2 (blue). There is an important point to discuss in comparison with the results of first principles calculations on ReS2. 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 me along the direction perpendicular to the chain and 0.8 me along the chain27. 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.

Figure 3
figure 3

Anisotropic effective hole masses. ARPES cut data along the in-plane momentum defined by the angle θ (see Fig. 2(a) for definition) for (a) ReS2 and (b) ReSe2. All the data sets are centered around the Z-point at which VBM is located. The dotted lines indicate a quadratic function fitting the dispersions of the top-most bands. The effective mass from the quadratic fit function for each angle can be extracted and is plotted for ReS2 and ReSe2 in (c). Arrows indicate crystallographic orientation of ReX2.

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Conclusions

In this study, we performed systematic ARPES studies of ReS2 and ReSe2 to reveal the energy-momentum dispersion relationships of the top most valence bands. We found that ReSe2 have much smaller \({k}_{z}\,\)dispersion than ReS2, indicating the more 2D-like feature in ReSe2 than in ReS2. We systematically investigated in-plane directional dependence of the effective hole masses of ReS2 and ReSe2. 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 ReS2 and ReSe2 is larger than that in black phosphorus which also shows anisotropic electrical and optical properties39,40. Therefore, ReS2 and ReSe2 are quasi 1D materials in terms of the low energy hole carrier dynamics, which makes ReS2 and ReSe2 promising bulk materials for 1D semiconducting electronics. The effective mass of ReS2 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 enhancement41. 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 ReS2 and ReSe242.

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 kz 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.