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Observation of monolayer valence band spin-orbit effect and induced quantum well states (QWS) in MoX2

Transition metal dichalcogenides have attracted much attention recently due to their potential applications in spintronics and photonics as a result of the indirect to direct band gap transition and the emergence of the spin-valley coupling phenomenon upon moving from the bulk to monolayer limit. Here, we report high-resolution angle-resolved photoemission spectroscopy on MoSe2 (molybdenum diselenide) single crystals and monolayer films of MoS2 grown on Highly Ordered Pyrolytic Graphite substrate. Our experimental results, for the first time, resolve the two distinct bands at the Brillouin zone corner of the bulk MoSe2, and provide evidence for the critically important spin-orbit split bands of the monolayer MoS2. Moreover, by depositing potassium on cleaved surfaces of these materials, the process through which quantum well states form on the surfaces of transition metal dichalcogenides is systematically imaged. We present a theoretical model to account for the observed spin-orbit splitting and the rich spectrum of the quantum well states observed in our experiments. Our findings taken together provide important insights into future applications of transition metal dichalcogenides in nanoelectronics, spintronics, and photonics devices as they critically depend on the spin-orbit physics of these materials.


3
In the recent years, with the discovery of two-dimensional states in graphene [1][2][3] and topological insulator surfaces [4][5][6], there has been an outburst of research activities to understand the physical properties of materials featuring two-dimensional (2D) states and their applications to optoelectronics and spintronics. One family of 2D materials that has recently attracted much attention is transition metal dichalcogenides (TMDCs) such as monolayers and few-layers of MX 2 (M = Mo, W and X = S, Se) [7,8]. These materials are easy to cleave, exfoliate, and fabricate [9,10], and have band gaps comparable in size to that of silicon (1.1 eV -1.4 eV in bulk and 1.5 eV -1.9 eV in monolayers) with the predicted property of transitioning from an indirect to a direct one upon reduction in size from bulk to monolayer [7,[11][12][13][14][15][16], making them suitable for potential use in electronics applications such as thin film transistors. Furthermore, it has been predicted that the exotic spinvalley coupling phenomena occurs in monolayers of TMDCs, thus making them appropriate for spintronics and valleytronics devices [17][18][19][20]. Nevertheless, even though many recent studies have examined the possibility of using transition metal dichalcogenides in singlelayer transistors [21][22][23][24], and have investigated their optical properties and potential use in optoelectronics [15,16,19,[25][26][27], surprisingly there have only been a few experimental works on uncovering the electronic band structures of the bulk, few-layers, and monolayers of these materials and their modification under external effects such as doping, surface deposition, or heterostructuring. The few existing momentum-resolved spectroscopic studies on these materials also lack the resolution and depth to highlight the important features of their band structures [28][29][30][31][32]. For instance, only recently using micro-ARPES the evolution of the valence band at the corner of the Brillouin zone (BZ) from higher to lower binding energies upon reducing the number of layers to monolayer has been demonstrated [32].
The interest in monolayers of the MX 2 series lies in the emergence of the direct band gap as a consequence of the disappearance of van der Waals interlayer interactions in the monolayer limit [7,16], as well as the valence band strong spin-orbit splitting due to the loss of inversion symmetry [7,17,18,32]. However, since films of TMDCs on typical substrates such as Si/SiO 2 grow in very small flakes of ∼ 10 µm × 10 µm and are usually composed of islands of variable thicknesses next to each other, tracking these two properties in a momentum-resolved fashion has proven to be challenging. Furthermore, the splitting of the valence band top into two distinct degenerate bands in the bulk limit due to both strong spin-orbit coupling and interlayer hopping [33] could be of interest and has not been resolved 4 to date. Moreover, until very recently MoS 2 has experimentally gotten the most attention amongst various members of the TMDCs family such as MoSe 2 , WS 2 , and WSe 2 . This is despite the fact that the stronger spin-orbit coupling of the later compounds make them more attractive for spintronics applications.
Thus, in this work we utilize angle-resolved photoemission spectroscopy (ARPES) to directly map the electronic band structure of bulk MoSe 2 across the entire BZ. We then study the evolution of its band structure upon in-situ surface deposition with an alkali metal (potassium). Our results demonstrate the formation of a nearly free 2D electron gas (2DEG) within the potassium overlayers confined to the surface of MoSe 2 in the form of quantum well states (QWSs). This quantum confinement of potassium layers could potentially enhance the optoelectronics performance of bulk and thin films of the TMDCs and be utilized in optoelectronics applications of these materials. Moreover, we resolve the band structure of a monolayer of MoS 2 grown on Highly Ordered Pyrolytic Graphite (HOPG) substrate using the chemical vapor deposition (CVD) growth method and find evidence suggesting the existence of the split valence band induced by strong spin-orbit coupling and broken inversion symmetry. We compare our ARPES results with first-principles theoretical calculations to gain microscopic insights on the electron behavior in these materials which is critically important for optimizing their potential performance in device settings.

Results
Crystal structure of MX 2 . The crystal structure of MX 2 (M = Mo, W and X = S, Se) is a layered structure with layers of M atoms sandwiched between two layers of X atoms.
These layers, which are held together through van der Waals forces, are shifted relative to each other in such a way that M atoms in one layer are placed directly above the X atoms in the neighboring layers [7,8,29]. This crystal structure and the corresponding Brillouin zone are shown in Figs. 1b and 1c, respectively. The center of the BZ is the Γ point, with M points the center of the hexagonal BZ edges, and K points the corners of the hexagon. Γ, M , and K are the projection of these points onto the 2D surface BZ as illustrated in Fig. 1c. X-ray photoemission spectroscopy (XPS) measurements of the single crystals of MoSe 2 used in our studies reveal sharp peaks corresponding to Mo 3s, 3p, and 3d core levels, as well as those of Se 3p and 3d as shown in Fig. 1a, thus indicating the high quality of the studied samples. Moreover, we note the broadening of the valence band close to the Fermi level along the Γ − K high symmetry direction (see Fig. 3c). Performing 2D curvature analysis [34] of the obtained bands, we resolve two split branches of the valence band of MoS 2 along this high symmetry direction (close to the K point) as shown in Fig. 3d. The white dotted lines are guides to the eyes for these two spin-orbit split branches of the valence band. This is consistent with the spin splitting scenario predicted to exist in this material.
Monolayers of TMDCs lack inversion symmetry and are non-centrosymmetric. The in-plane confinement of electron motion and high mass of the elements in these materials result in strong spin-orbit splitting of the valence band. This property makes these materials promising candidates for applications in spintronics devices [7,17,18,20]. Our observation here is the first momentum-resolved experimental evidence for such spin-orbit splitting.
Further spin-resolved ARPES studies are needed to identify the spin configuration of these split bands.
To further demonstrate the orbital property and spin texture of monolayer MoS 2 , we calculate the charge densities and spin expectation values of the lowest two conduction states and the topmost two valence states at K marked in Fig. 1d as C1, C2, V1, and V2, respectively. The charge density plots shown in Fig. 3e indicate that the dominant orbital components are Mo 4d 3z 2 −r 2 and Mo 4d x 2 −y 2 + 4d xy for C1(C2) and V1(V2), respectively.
The calculated spin expectation values of states near K show nearly out-of-plane spin polarization, which can be attributed to an interplay of the pure in-plane electron motion and the inversion symmetry breaking crystal potential. The out-of-plane character of Mo 4d 3z 2 −r 2 explains the negligible spin splitting between the C1 and C2 states.
On the other hand, the calculated energy splitting between V1 and V2 states is 138 meV at K, as a consequence of the prominent in-plane charge density variation of Mo 4d x 2 −y 2 + 7 4d xy orbital, which is in good agreement with previous results from Density Functional Theory calculations [17]. According to the calculated spin expectation values, we deploy a straightforward method to determine the spin orientation of the V1 and V2 states, which are important when considering the selection rule of polarized photon excitations. Viewing monolayer MoS 2 from top, since sulfur atoms sit on the hexagonal lattices it's alway possible to find a primitive vector connecting to adjacent sulfur atoms in the same direction as Γ−K.
Call this vector a and drawing another vector b from the sulfur atom at the origin of a to the nearest Mo atom, the spin orientation of V2 is in the direction of a × b and that of V1 points to the opposite direction.
Observation of QWSs of a nearly free 2DEG by surface deposition. In order to study the effect of alkali metal deposition on the surface of bulk MoSe 2 , we deposit potassium (K) in-situ on cleaved surfaces of crystals of this material, and track the evolution of the band structure spectra as the deposition occurs. Deposition was performed at T = 60 K with an estimated deposition rate of ∼ 0.08 -0.09Åmin −1 . Fig. 4a shows the evolution of the band structure k -E map along the Γ − M direction of the BZ during the deposition process. We observe that the VBM at Γ moves closer to the Fermi level by about 200 meV.
We associate this shift with the formation of a conducting layer on the surface of our sample after potassium deposition. More specifically, the VBM of the MoSe 2 sample is at E B ∼ 1.0 eV, but before deposition is shifted down by about 200 meV due to the electronic charging effect. Next, we observe the formation of new electronic states in the band gap of MoSe 2 , extending from the Fermi level to the valence band (see middle panels in Fig. 4a). Upon the completion of the deposition process these in-gap states are completely formed as shown in the last panel of Fig. 4a and Fig. 4b.
We note the formation of electron-like pockets on the Fermi surface after the completion of the deposition process. These pockets appear right at the K points of the BZ. Since the energy spacing between these pockets and the VBM (∼ 0.8 eV) is smaller than the indirect gap of MoSe 2 (∼ 1.1 eV) we rule out the possibility of these pockets being a part of the conduction band of MoSe 2 . The resulting Fermi surface after potassium deposition shows two concentric circular shaped pockets around the center of the BZ, as well as the aforementioned pockets at the K points (Fig. 4d). The circular pockets around Γ are identified as the first and second QWSs, whereas the pockets at K as resulting from the surface states of 8 potassium. We furthermore conduct first-principles calculations of potassium layers formed on the surface of bulk MoSe 2 and find that our experimental observation is in qualitative agreement with two atomic monolayers of potassium deposited on the surface of MoSe 2 , as shown in Fig. 4c. The possibility of directly accessing the conduction band of bulk and monolayer TMDCs through intercalation and adsorption of alkali metals has been theoretically predicted [35]. Our results suggest that adsorption of alkali metals on the surface of bulk MoSe 2 results in the formation of QWSs and a nearly free 2DEG rather than electron doping and providing access to the conduction band.

Discussion
The splitting of the valence band along the Γ − K high symmetry direction of the monolayer MoS 2 and other TMDCs which is due to strong spin-orbit coupling (because of the high mass of the elements) and lack of inversion symmetry, has been suggested in previous theoretical studies as well as our first-principles calculations here [7,17]. For the bulk, this splitting is caused by the combination of interlayer interaction and spin-orbit coupling.
In this case, there is no spin splitting between these two bands and they are indeed spindegenerate (Kramers' degeneracy) due to the presence of inversion symmetry along with time reversal symmetry. But, the strong spin-orbit coupling in TMDCs results in enhanced splitting of these spin-degenerate bands at the K point of the BZ (see Fig. 1d) [33]. Our results resolve these two distinct bands at the corners of the BZ through ARPES measurements and theoretical first-principles calculations. Furthermore, we have provided the first momentum-resolved experimental evidence of the spin-split valence band of monolayer MoS 2 grown on HOPG substrate. However, further spin-resolved ARPES measurements are needed to confirm the spin configuration of these two split bands.
Recently, experimental evidence and theoretical prediction of valley confinement has been suggested in monolayer MoS 2 . Specifically, it has been suggested that the split valence band at neighboring K points of the BZ (K and K ) posses opposite out of plane spin configurations [18][19][20]. The spin-orbit splitting observed in our study of monolayers of MoS 2 paves the way to more detailed studies of spin and valley physics in TMDCs. It also serves as a guide for spintronics and valleytronics applications of TMDCs.
Our results also track the evolution of the band structure of MoSe 2 throughout the surface deposition process with an alkali metal (potassium). We note that short after the deposition 9 process has started potassium atoms sit on the surface of MoSe 2 in a manner that results to the partial formation of the first QWS (see second panel in Fig. 4a). Consequently, the first QWS appears in full, as shown in the third panel of Fig. 4a, and finally the first two QWSs are completely formed. In the process of surface deposition, 2D conduction channels (quantum well states) emerge on the surface of the semiconducting MoSe 2 (with an indirect insulating energy gap of ∼ 1.8 eV) and, as a consequence, the electronic behavior of the system changes dramatically. This tunable feature can be utilized to quantitatively control the electronic properties of this quasi-2D material. Our investigation of the dynamical process in which a nearly free 2DEG is formed on TMDCs could have important implications for future optoelectronics studies and applications of TMDCs using surface manipulations by elements such as alkali metals on bulk, few-layers, and monolayers of these materials.
In conclusion, we have conducted detailed high-resolution ARPES and first-principles calculations studies of the electronic structure of both bulk and monolayer TMDCs. We Sample growth. To prepare MoS 2 films, molybdenum chloride (MoCl5) and sulfur powder were used as precursors and the growth of monolayer films was carried out in a CVD chamber. The ultrasonicated cleaned HOPG substrates were loaded into the CVD chamber 6 cm away from the central hot zone. Argon (Ar) gas was used as carrier gas in a pressure of 3 torr. Single crystals of MoSe 2 were grown by the chemical vapor transport method, using I 2 as the transporting agent. They were formed in silver-colored, graphitelike, single crystalline platelets up to 10 × 10 mm 2 in surface area and 2 mm in thickness (inset in Fig. 1a).
First-principles calculation methods. First-principles calculations of the electronic structures were performed using HGH-type pseudo-potentials [36] and a plane-wave basis set. The main program employed was developed by the ABINIT group [37,38]. Spin-orbit coupling was included, where appropriate, using the relativistic LDA approximation. The experimental resolution was taken into account in the spectral simulations of Figs. 2, 3, and 4, but the matrix elements effect was not considered.  Here, the ARPES measurements were performed at photon energy of hν = 70 eV and temperature of T = 60 K. e, Illustration of the in-situ surface potassium deposition.