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ABSTRACT Monolayer MX2 (M = Mo, W; X = S, Se) has recently been drawn much attention due to their application possibility as well as the novel valley physics. On the other hand, it is also

important to understand the electronic structures of bulk MX2 for material applications since it is very challenging to grow large size uniform and sustainable monolayer MX2. We performed

angle-resolved photoemission spectroscopy and tight binding calculations to investigate the electronic structures of bulk 2H-MX2. We could extract all the important electronic band

parameters for bulk 2H-MX2, including the band gap, direct band gap size at K (-K) point and spin splitting size. Upon comparing the parameters for bulk 2H-MX2 (our work) with mono- and

multi-layer MX2 (published), we found that stacked layers, substrates for thin films, and carrier concentration significantly affect the parameters, especially the band gap size. The origin

of such effect is discussed in terms of the screening effect. SIMILAR CONTENT BEING VIEWED BY OTHERS FIRST-PRINCIPLES PREDICTION OF HIGH CARRIER MOBILITY FOR Β-PHASE MX2N4 (M = MO, W; X = 

SI, GE) MONOLAYERS Article Open access 29 September 2024 DIRECT IDENTIFICATION OF MOTT HUBBARD BAND PATTERN BEYOND CHARGE DENSITY WAVE SUPERLATTICE IN MONOLAYER 1T-NBSE2 Article Open access

30 March 2021 UNUSUALLY LARGE EXCITON BINDING ENERGY IN MULTILAYERED 2H-MOTE2 Article Open access 16 March 2022 INTRODUCTION The successful exfoliation of graphene1,2,3 is important on its

own right but also has triggered the intensive/extensive research on similar two-dimensional layered materials4,5. Transition metal dichalcogenides (TMDs) such as NbSe2 and MoS2 have strong

in-plane covalent and weak out-of-plane van der Waals bonds. Such bonding character reduces the dimensionality from 3D to 2D and allows us to obtain monolayer systems by the exfoliation

method. Monolayer TMDs often exhibit qualitatively different electronic properties compared to the bulk6,7,8. Among the TMDs, the group 6 TMDs, MX2 (M = Mo, W; X = S, Se), exhibit

interesting electronic properties such as indirect (bulk) to direct (monolayer) band gap transition6,7, valley degeneracy9 and spin-orbit interaction (SOI) induced spin band splitting at the

K and -K points of the hexagonal Brillouin zone10. Exploiting these fundamental electronic properties, the valley degeneracy could be lifted by using circularly polarized

light11,12,13,14,15 and valley Hall effect was observed in monolayer MX216,17,18. These raised the notion of the valleytronics19,20,21,22,23,24,25. These low energy electronic properties of

monolayer MX2 are found to be explained within a minimal model, the so-called massive Dirac fermion model9. The model has only three independent parameters: the effective hopping (_t_), band

gap without SOI (_Δ_), and spin band splitting (2λ). The details of the model are described in section 2.1. The electronic structure of monolayer MX2 has been measured by angle-resolved

photoemission spectroscopy (ARPES), which has confirmed the direct band gap and the spin band splitting at the K and -K points7,26,27,28,29,30,31. More importantly, band parameters could be

extracted from the ARPES data7,26,27,28,29,30,31,32,33,34. The extracted values of _Δ_ and 2_λ_ are 1.465 and 0.15 eV for the epitaxial monolayer MoS2 on Au(111), and 1.67 and 0.18 eV for

monolayer MoSe2 grown on bilayer graphene7,29. 2_λ_ of monolayer WS2 grown on Au(111) has been recently measured and found to be 0.42 eV30. These results show that the massive Dirac fermion

parameters for monolayer MX2 can be affected not only by the chemical composition but also by other factors such as the substrate and the carrier concentration of the system29,30,31,34. For

the MX2 based electronic devices, it is natural to start with multi-layer MX2 films which are closer to bulk rather than monolayer since it is difficult to grow high-quality monolayer-MX2 in

wafer scale. Then, the information on the electronic structure of bulk MX2 is also important as stacked layers affect the electronic structure. Moreover, it is interesting to see how the

electronic structure of monolayer MX2 evolves as it is stacked into the bulk, and also to understand how the massive Dirac fermion model connects to the bulk electronic structure. 2H-MX2 is

the most abundant bulk form of MX2 in which in-plane polarization of the MX2 monolayers are antiparallel to that of the nearest neighbor layers, resulting in unit-cell doubling. Previous

ARPES studies have shown that the valence band maximum (VBM) is located at the in-plane Γ-point in various bulk 2H-MX32,33,34. As a result, these materials have an indirect band gap7,33.

Spin band splitting has also been observed31. However, it has not been systematically studied in regards to the material dependent band-gap, including the direct band gap at the in-plane K

point in bulk 2H-MX2 (M = Mo, W; X = S, Se). For example, the direct band gap at the in-plane K point has been investigated only for 2H-WSe234. It is therefore desired to systematically

investigate electronic structures of 2H-MX2. We performed ARPES experiments to investigate all the important electronic band parameters of bulk 2H-MoS2, MoSe2, WS2 and WSe2 including band

gap, direct band gap at K-point and spin splitting. We also carried out tight binding calculations to interpret our ARPES data and to provide a simple understanding of electronic structure

evolution from monolayer to bulk 2H-MX2. We could successfully extract all the parameters of bulk 2H-MX2 from the ARPES data. Upon comparing the parameters of bulk 2H-MX2 with those of

previously studied MX2 thin films, including monolayer, we found that the direct band gap at the K point is significantly affected by the number of layers and doped electron density, while

other parameters such as spin splitting size does not change appreciably. We will discuss the underlying physics behind the behavior of the parameters. RESULTS AND DISCUSSIONS TIGHT BINDING

CALCULATIONS FOR ELECTRONIC STRUCTURE EVOLUTION FROM MONOLAYER TO BULK 2H-MX2 Low energy electronic structure of monolayer MX2 is well described by the massive Dirac fermion model. We will

try to show that the band dispersion of bulk MX2 near the in-plane K point can be also described within the model. Note that while the inversion symmetry is restored in the bulk and thus the

valley physics is removed, the characteristics of the monolayer such as the spin band splitting remains in the dispersion at the K point. Figure 1 is a schematic sketch of the massive Dirac

fermion model. Two cases are illustrated in the figure, one without SOI and the other with SOI. The Hamiltonian of the massive Dirac fermion model including SOI reads where _a_ is the

lattice constant, _t_ the effective hopping parameter, _τ_ the valley index, the Pauli matrices for the basis functions, _Δ_ the direct band gap size without SOI, 2_λ_ the SOI induced spin

band splitting size, and the Pauli matrix for spin (see ref. 9 for more details). Note that there are only three free parameters in this model, _Δ_, 2_λ_, and _t_. We performed tight binding

calculations with a focus on how the electronic structure at the in-plane K and Γ points evolves from monolayer MX2 to bulk MX2. Our calculations show that band dispersion along _k__z_ at

the in-plane K point is zero and can still be described by the band dispersion of the massive Dirac fermion parameters, whereas band dispersion along _k__z_ at the in-plane Γ point is strong

enough to induce direct to indirect band-gap transition. As noted above, only the dispersion of the model can be used for the 2H-MX2, since the broken inversion symmetry of monolayer is

recovered in bulk 2H-MX2. Spin states are, for instance, degenerate in bulk 2H-MX2. The evolution of the dispersion relations from the monolayer to the bulk system at the Γ and K point are

studied by investigating how the eigenstates in different layers become mixed together as a result of the stacking. Details are in Supplementary Material (SM) and only the main results are

given. Here, we neglect the SOI which does not affect the _k__z_ dependences of the energy spectra due to its on-site character. Then, we obtain the energy spectra along _k__z_ as at the

in-plane Γ point, and at the in-plane K point. The subscripts VB and CB represent the valence and conduction bands, respectively. _∈_Γ_,VB_ and _∈_K_,VB_ are energies at Γ and K point for

the corresponding bands of monolayer MX2. Constants _D_Γ and _D_K are described in SM. One can note that the width of this VB at the in-plane Γ point is 2_D_Γ which is evaluated to be

approximately 0.86 eV for MoS2 from the tight binding parameters and the lattice constants in refs 35, 36, 37. This is comparable with the experimental result. As shown in the above results,

two high symmetry points Γ and K of the monolayer MX2 show completely different responses to the stacking. The VB at the Γ point gains strong dispersions along _k__z_ while the VB and CB at

the K point are almost dispersionless and experience only small shifts (_D__K_ ≈ 0.0263 eV). This distinction originates from the difference in the orbital compositions between them and the

three-fold rotational symmetry of the system. At the Γ point, the eigenstates mainly consist of the out-of-plane orbitals such as orbitals at M atoms and _p_z orbitals at X atoms. As a

result, the overlap integrals between them in different layers are expected to be large compared to the in-plane orbitals. Also, it is impossible to have the phase cancellation related to

the factor at the Γ point (_K_⊥ = 0) so that there is no chance to remove the dispersion along _k__z_ direction. This is why we have strong dispersions in the VB along _k__z_ at the in-plane

Γ point. On the other hand, the eigenstates on the CB at the in-plane Γ point consist of _p__x_ and _p__y_ orbitals at X atoms and their dispersions along _k__z_ direction induced by

stacking are relatively weak. At the K point, on the contrary, both the conduction and valence electrons only have the in-plane orbital components (_p__x_ and _p__y_) in X atoms. Although

there are out-of-plane orbitals in M atoms, they give next order terms when layers are stacked since the M-M or M-X distances between neighboring layers are quite far compared to the X-X

distance. This in-plane character of the constituent orbitals immediately makes us to expect smaller dispersions for the VB and CB along _k__z_ direction at the in-plane K point than that of

the VB at the in-plane Γ point. However, we have shown that even these small dispersions are suppressed and the band spectra along _k__z_ direction becomes almost flat due to the

graphene-like phase cancellation among the nearest neighboring hopping processes stemming from the C3 symmetry of the system38. ARPES MEASUREMENTS ON BULK 2H-MX2 We first performed

photon-energy dependent ARPES to obtain the _k__z_ dispersion of the electronic band. Figure 2(a) shows the ARPES data taken with incident photon energies between 50 and 100 eV near the

in-plane Γ point. Black dashed lines indicate band dispersions expected from Eq. (2). The data is in good agreement with the calculation results and show strong _k__z_ dispersions. The

breadth in the ARPES data in the energy direction is due to the finite escape depth of the ARPES process (finite _k__z_ resolution). _k__z_ dispersions in MoS2, MoSe2, and WS2 near the

in-plane Γ point are as strong as that in WSe2 [Fig. 2(b–d)]. On the other hand, photon-energy dependent ARPES data show no _k__z_ dispersion near the in-plane K point as seen in Fig.

2(b–e), consistent with our calculation results in Eq. (3). Dashed lines in Fig. 2(b–e) are guides to eye and are straight (that is, no _k__z_ dispersion). Since the energy of the band at a

specific in-plane momentum is the same regardless of _k__z_, ARPES spectra near the K point are very sharp in comparison to the Γ point data, both in the energy and in-plane momentum

directions. This fact can be seen in Fig. 2(b–e) as well as in Fig. 3(a–d). In order to extract the electronic band parameters, we need ARPES data along the in-plane Γ to K direction (see

Fig. 3). 2_λ_ of MoS2, MoSe2, WS2, and WSe2 can be clearly observed in the data shown in Fig. 3(a–d). 2λ is drastically increased as the transition metal changes from Mo to W since 2_λ_

mostly relies on the atomic spin-orbit coupling of the transition metal atom. In order to observe the direct band gap at the K point and the indirect band gap, it is necessary to see the

bottom of the CB. The problem is that the states are not occupied and thus cannot be observed by ARPES. One way to circumvent the problem is to populate the CB bottom by potassium (K)

dosing7,29,31. K has very low electron affinity and, when dosed on the sample surface, provides electrons. ARPES experiments after K evaporation reveal the conduction band minimum (CBM) from

which we can determine _Δ_ [Fig. 3(e–h)]. The energy of the CBM is determined from the onset of the photoemission intensity, as indicated by dashed lines near the Fermi energy at the K

point for MoS2 and MoSe2 [Fig. 3(e,f)] and at the Σ point for WS2 and WSe2 [Fig. 3(g,h)]. A local CBM for the K point for WS2 and WSe2 is also observed as indicated by dashed lines. The CBM

is found to be located at the K point in MoS2 and MoSe2, while it is located at the Σ point in WS2 and WSe2. We note that the CBM of monolayer WS2 and WSe2 is located at the Σ point instead

of K point. This is because the _k__z_ dispersion at the Σ point for WS2 and WSe2 causes the CBM at the Σ point to be located even lower than that at the K point. The effective hopping

integral, _t_, can also be estimated by fitting the band dispersion with the band dispersion of the massive Dirac fermion model. _t_ is linearly proportional to the slope of band dispersion

at off K point, which is for example _k_|| = 0.5 (2 π/a) in Fig. 3. Therefore, _t_ in WS2 and WSe2 is clearly greater than that in MoS2 and MoSe2, and so is the mobility when electrons or

holes are doped into these systems. The extracted _t_ values for MoS2, MoSe2, WS2, and WSe2 are given in Table 1. Here, we assume that the CB dispersion which cannot be measured is

mirror-symmetric with the VB dispersion. This is not an unreasonable assumption considering the band calculation results36. All the parameters of 2H-MX2 (this work) and the known parameters

of mono- and multi-layer MX2 are summarized in Table 1. We show in the first column the doped electron density by potassium dosing since doped electron density can affect some of parameters,

especially _Δ_34. In the second through fourth columns, the three fundamental parameters of the model are summarized. In the last two columns, other interesting parameters, which are direct

band gap at K point (_Δ_–_λ_) and indirect band gap, are also summarized. Comparing the fundamental parameters of 2H-MX2 and monolayer MX2, we notice that spin band splitting (2_λ_) is

about 20 meV larger in 2H-MX2. This is consistent with the results of optical experiments39. We also find that the doped electron density does not affect the size of the spin band splitting

(Fig. 3). On the other hand, the story for _Δ_ is different from that of the spin band splitting (2_λ_). Unlike the spin band splitting, _Δ_ is affected by various factors such as the

density of doped electrons. In order to measure _Δ_ or direct band gap (_Δ_–_λ_) by ARPES, it is necessary to introduce electrons into MX2 to populate the CBM. The measured value of _Δ_–_λ_

by ARPES in such a way is clearly smaller than that measured by STM on undoped MX2 even though there is some variation in the reported STM values40,41,42. The observed trend is attributed to

the fact that the doped electrons enhance the screening and thus reduce the size of the direct band gap7,40,43. Likewise, it is expected that stacked layers or metallic substrates for thin

film play a similar role in the screening effect and thus affect the band gap size. The effects on the band gap reduction from stacked layers and bilayer graphene substrate appear to be

similar since the band gaps for 2H-MoSe2 and 1ML MoSe2/bilayer graphene measured by ARPES are almost the same7. On the other hand, the effect from Au substrate must be much larger,

considering the fact that 1ML MoS2/Au(111) has significantly reduced band gap compared to 2H-MoS229. However, we note that quantitative estimation of the band gap reduction from stacking or

metallic substrates is not possible without the band gap size of a free-standing MX2 monolayer. CONCLUSIONS In the theoretical part, we found that the band dispersion along the _k__z_

direction at the in-plane K and -K points vanishes in bulk 2H-MX2 due to the graphene-like phase cancellation. Therefore, the electronic band dispersions near the in-plane K and -K points in

bulk 2H-MX2 are well described by the massive Dirac fermion model. In the experimental part, we confirmed the vanishing _k__z_ dispersion at the in-plane K and -K points in bulk 2H-MoS2,

2H-MoSe2, 2H-WS2 and 2H-WSe2. All the fundamental band parameters could be extracted for bulk 2H-MoS2, 2H-MoSe2, 2H-WS2 and 2H-WSe2. Most importantly, the direct band gap at the K point

(_Δ_–_λ_) shows significant variation depending on the doped electron density, the number of stacking layers and the substrates. The direct band gap variation can be attributed to reduction

of the direct band gap due to the enhanced screening. Our work provides useful information on the electronic band dispersions of 2H-, monolayer and multi-layer MX2 and suggests a way to

manipulate the band gap of MX2. METHODS ARPES data were obtained at the beam line 4.0.3.2 (MERLIN) of the Advanced Light Source equipped with a VG-SCIENTA R8000 analyzer. The total energy

resolution was better than 20 meV. Four high quality single crystal samples were purchased from 2D Semiconductors and HQGraphene. All the data were taken under 40 K in a base pressure better

than 4 × 10−11 Torr. For the photon energy dependence, we used the photon energy between 50 and 100 eV. Alkali Metal Dispensers from SAES Getters were used for potassium evaporation

experiments and evaporation was conducted _in situ_ with the samples at the measurement position. ADDITIONAL INFORMATION HOW TO CITE THIS ARTICLE: Kim, B. S. _et al._ Determination of the

band parameters of bulk 2H-MX2 (M = Mo, W; X = S, Se) by angle-resolved photoemission spectroscopy. _Sci. Rep._ 6, 36389; doi: 10.1038/srep36389 (2016). PUBLISHER’S NOTE: Springer Nature

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nonlinear band gap renormalization in two-dimensional semiconductors. Phys. Rev. Lett. 114, 063001 (2015). Article  ADS  CAS  Google Scholar  Download references ACKNOWLEDGEMENTS We thank

Yeongkwan Kim, Jonathan D. Denlinger, Jongkeun Jung, and Soohyun Cho for assistance in the experiments. We also thank Wonshik Kyung for helpful discussions. This work was supported by the

Incheon National University Research Grant in 2013. B.S.K. and C.K. were supported by IBS-R009-G2, Korea. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Center for Correlated Electron

Systems, Institute for Basic Science, Seoul, 08826, Korea Beom Seo Kim & Changyoung Kim * Department of Physics and Astronomy, Seoul National University, Seoul, 08826, Korea Beom Seo Kim

 & Changyoung Kim * Department of Physics, Incheon National University, Incheon, 22012, Korea Beom Seo Kim & Seung Ryong Park * Max-Planck-Institut für Physik komplexer System,

Dresden, 01187, Germany Jun-Won Rhim * Department of Physics, Pohang University of Science and Technology, Pohang, 37673, Korea Beomyoung Kim * Advanced Light Source, Lawrence Berkeley

National Laboratory, Berkeley, CA 94720, USA Beomyoung Kim Authors * Beom Seo Kim View author publications You can also search for this author inPubMed Google Scholar * Jun-Won Rhim View

author publications You can also search for this author inPubMed Google Scholar * Beomyoung Kim View author publications You can also search for this author inPubMed Google Scholar *

Changyoung Kim View author publications You can also search for this author inPubMed Google Scholar * Seung Ryong Park View author publications You can also search for this author inPubMed 

Google Scholar CONTRIBUTIONS B.S.K. and S.R.P. conceived this project. B.S.K. and B.K. performed angle resolved photoemission spectroscopy measurements. J.-W.R. performed tight binding

calculation. B.S.K., J.-W.R., C.K. and S.R.P. prepared the manuscript. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial interests. ELECTRONIC SUPPLEMENTARY

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ABOUT THIS ARTICLE CITE THIS ARTICLE Kim, B., Rhim, JW., Kim, B. _et al._ Determination of the band parameters of bulk 2H-MX2 (M = Mo, W; X = S, Se) by angle-resolved photoemission

spectroscopy. _Sci Rep_ 6, 36389 (2016). https://doi.org/10.1038/srep36389 Download citation * Received: 28 May 2016 * Accepted: 12 October 2016 * Published: 02 November 2016 * DOI:

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