Probing SpinâOrbit Coupling and Interlayer Coupling in Atomically

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Probing Spin-Orbit Coupling and Interlayer Coupling in Atomically Thin Molybdenum Disulfide Using Hydrostatic Pressure Xiuming Dou, Kun Ding, Desheng Jiang, Xiaofeng Fan, and Baoquan Sun ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.5b07273 • Publication Date (Web): 08 Jan 2016 Downloaded from http://pubs.acs.org on January 11, 2016

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Probing Spin-Orbit Coupling and Interlayer Coupling in Atomically Thin Molybdenum Disulfide Using Hydrostatic Pressure Xiuming Dou,† Kun Ding,† Desheng Jiang,† Xiaofeng Fan,*,‡ and Baoquan Sun*,† †

State

Key

Laboratory

of

Superlattices and

Microstructures,

Institute

of

Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083, China

‡

College of Materials Science and Engineering, Jilin University, Changchun 130012,

China *Address correspondence to [email protected], [email protected] ABSTRACT: In two-dimensional transition-metal dichalcogenides, both spin-orbit coupling and interlayer coupling play critical roles in the electronic band structure, and are desirable for the potential applications in spin electronics. Here, we demonstrate the pressure characteristics of the exciton absorption peaks (so called excitons A, B and C) in monolayer, bilayer and trilayer molybdenum disulfide (MoS2) by studying the reflectance spectra under hydrostatic pressure and performing the electronic band structure calculations based on density functional theory (DFT) to account for the experimental observations. We find that the valence band maximum splitting at K point in monolayer MoS2, induced by spin-orbit coupling, remains almost unchanged with increasing pressure applied up to 3.98 GPa, indicating that the spin-orbit coupling is insensitive to the pressure. For bilayer and trilayer MoS2,

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however, the splitting shows an increase with increasing pressure due to the pressure-induced strengthening of the interlayer coupling. The experimental results are in good agreement with the theoretical calculations. Moreover, the exciton C is identified to be the interband transition related to the van Hove singularity located at a special point which is approximately 1/4 of total length of Γ-K away from Γ point in Brillouin zone.

KEYWORDS: molybdenum disulfide · valence band maximum splitting · spin-orbit coupling · interlayer coupling · Hydrostatic pressure

Atomically thin molybdenum disulfide (MoS2) has attracted great attention due to the interesting physical properties, for example, valley spin,1-4 large exciton binding energy,5-9 and strong spin-orbit coupling (SOC)10,11 as well as promising applications in the wide range of electronic devices, such as transistor,12,13 photodetector,14 and diode.15 It has been established that monolayer MoS2 presents a direct band gap at K point of Brillouin zone, which is different from its corresponding few-layer and bulk counterparts with indirect band gaps,16,17 demonstrating the key effect of the interlayer coupling on the electronic band structure of atomically thin MoS2. Concerning the absorption spectra in both monolayer and few-layer MoS2, the double-peak structure related to the excitons A and B, is attributed to the splitting of the valence band maximum (VBM) around K point.16-18 For monolayer MoS2, the splitting is explained as a result of SOC due to the absence of the inversion symmetry.11,19,20 For few-layer and bulk MoS2, however, the corresponding splitting should associate with both SOC and interlayer coupling which could be of interest, but has not been well experimentally studied yet .10,21-23 In addition, the origin of another broad absorption peak related to the exciton C is also disputable which is previously ascribed to the


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parts of Brillouin zone between K and Γ points,10 between M and Γ pionts,24,25 or near Γ point 26,27. The diamond anvil cell (DAC) used for high hydrostatic pressure is widely employed to tune the electronic band structure, and it is expected to be able to precisely identify the optical interband transitions related to conduction band valleys and valence band hills in 2D materials, such as in few-layer MoS2.28-34 Based on the optical reflectance spectrum, it is very convenient to determine the exciton absorption peaks in few-layer MoS2, such as those of the excitons A, B and C. Therefore, it will be able to obtain the energy splitting of VBM at K point by measuring the energy difference between the peaks A and B, assuming that both excitons have the same binding energies. Actually, it has been reported that the energy difference between the exciton binding energies of the excitons A and B is only approximately 10 meV, that is smaller than one-tenth of the energy splitting of the VBM at K point.35 Moreover, it is found that the exciton binding energy is insensitive to the applied pressure,36-38 making it possible to obtain the pressure characteristics of the interband transition energies by measuring the absorption peaks of related excitons. In this article, we report a systematical study, both in experiment and theory, on the VBM splitting at K point for monolayer, bilayer and trilayer MoS2 under hydrostatic pressure applied up to 4.90 GPa. The pressure dependence of the VBM splitting deduced from the energy difference between the absorption peaks A and B is characterized by the reflectance spectra at room temperature. For monolayer MoS2, the VBM splitting remains almost unchanged response to the pressure, showing that the SOC is insensitive to the pressure. For bilayer and trilayer MoS2, however, the VBM splitting increases with increasing pressure due to the enhanced interlayer coupling. The observed pressure behaviors are consistent with the results from density


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functional theory (DFT) calculation. As for the exciton C, it shows a blueshift for monolayer and almost no shift for bilayer and trilayer MoS2 with increasing pressure. Combined with the DFT calculation, the peak C is attributed to the van Hove singularity located at a special point which is approximately 1/4 of total length of Γ-K away from Γ point in Brillouin zone.

RESULTS AND DISCUSSION For monolayer MoS2, the lattice structure has the hexagonal symmetry with space group P-6m2. The six sulfur (S) atoms near each molybdenum (Mo) atom form a trigonal prismatic structure with the mirror symmetry in c direction, as shown in Figure 1a. The atomically thin MoS2 samples are prepared by micromechanical exfoliation method from a natural bulk MoS2 (SPI supplies) on to a thinned SiO2/Si substrate (see Supporting Information). Regions of monolayer, bilayer and trilayer MoS2 are identified by their optical contrasts with an optical microscope and further confirmed using photoluminescence (PL) measurements (Figure 1d). PL and reflectance spectra are collected at room temperature by an optical confocal microscope setup (details are presented in Supporting Information). The hydrostatic pressure is applied by the DAC device whose image is shown in Figure 1b, and the top view microscope image of the pressure chamber is shown in Figure 1c (details of the DAC device are given in the Supporting Information). The theoretical calculations are performed based on DFT using accurate frozen-core full-potential projector augmented-wave (PAW) pseudopotentials, as implemented in the VASP code39. The generalized

gradient

approximation

(GGA)

with

the

parametrization

of

Perdew-Burke-Ernzerhof (PBE)40 and added van der Waals corrections41 are used (details are presented in Supporting Information).


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Figure 1d shows the PL spectra of monolayer, bilayer and trilayer MoS2 at zero pressure. As can be seen, the peak labeled A at 1.826 eV dominates the PL spectrum of monolayer MoS2. In addition, a weak peak shoulder labeled B can be found at 1.990 eV. For bilayer and trilayer MoS2, peaks A show a slight redshift which are located at 1.817 and 1.814 eV, respectively. Besides the peaks A and B, peaks I appear for the bilayer and trilayer MoS2 which are located at 1.490 and 1.420 eV, respectively. The peak I is related to the K-Γ indirect interband transition and the red-shift following the increase of layer number is due to the up-shift of VBM at Γ point.16,29 The reflectance spectra of the monolayer, bilayer and trilayer MoS2 at zero pressure are displayed in Figure 1e. Three absorption peaks correspond to excitons A, B and C. For monolayer MoS2, the energy positions of peaks A and B are 1.879 and 2.020 eV, respectively, exhibiting blueshifts of 53 and 30 meV with respect to the exciton emission peaks in the PL spectra. Here, the value of blueshift may be related to the difference in excitation power (see supporting information) and stokes shift.37,42,43 The splitting of the VBM at K point, i.e. the energy difference of the peaks A and B , is 141 meV in monolayer MoS2 and it increases up to 164 and 173 meV in bilayer and trilayer MoS2, respectively. The peak C in monolayer MoS2 is observed at the peak energy of 2.820 eV which agrees with the experimentally and theoretically reported result.18,27,44 Figure 2a shows the reflectance spectra of monolayer MoS2 in the pressure range from 0.58 to 3.98 GPa, in which the oscillations and broadening of the measured data line is due to the interference effect of the reflectance spectra (see supporting information). At 3.98 GPa, the three absorption peaks A, B and C can still be resolved despite of the strong interference effect, and blueshift to approximately 2.000, 2.140 and 2.900 eV, respectively. The energies of peaks A, B and C as a function of the


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pressure are displayed in Figure 2d. It is found that below 4 GPa, the exciton emission peaks versus pressure show a good linear characteristic.29 Linear fittings as shown by the blue lines are employed to fit the experimental data, and the obtained pressure coefficients of the excitons A, B and C are 24.4 ± 1.0, 23.5 ± 1.6 and 11.8 ± 4.0 meV/GPa, respectively, showing the peaks A and B have the nearly same blueshift rate response to the pressure. Based on the fitting lines, the energy positions of the peaks A, B and C at zero pressure are 1.905, 2.050 and 2.850 eV, respectively, which are larger than the corresponding energy positions measured at ambient pressure outside the DAC, as shown by the open squares in Figure 3d. It implies that different environment at the sample location can have some influence on the exciton characteristics of the atomically thin 2D materials.45 Figure 2b exhibits the reflectance spectra of bilayer MoS2 in the pressure range from 0.03 to 4.65 GPa. It is found that the peak A moves up to the energy position of 1.981 eV at 4.65 GPa. The peak B shifts to 2.110 eV at 2.48 GPa, and could not be resolved when the pressure is larger than 2.48 GPa due to the spectral interference effect. The peak C, however, shows a slight redshift as the pressure increases from 0.03 to 4.65 GPa. The energy evolutions of the peaks A, B and C as a function of the pressure are summarized in the Figure 2e. The obtained pressure coefficients of the peaks A, B and C are 24.5 ± 0.1, 31.9 ± 0.1 and -2.6 ± 1.3 meV/GPa, respectively. Figure 2c shows the reflectance spectra of trilayer MoS2 for the pressure range from 0.65 to 4.90 GPa. The excitons A and B show blueshift to the energy positions of 1.985 and 2.190 eV at 4.90 GPa, respectively. The peak C in trilayer MoS2 also exhibits a slight redshift as the pressure increasing from 0.65 to 4.90 GPa. Figure 2f displays the energies of the peaks A, B and C as a function of the pressure. The obtained pressure coefficients of the peaks A, B and C are 25.6 ± 1.3, 32.2 ± 1.6 and -2.5 ± 3.0 meV/GPa, respectively.


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To understand the experimental results of the VBM splitting due to the SOC and interlayer coupling effects, we perform the calculation of electronic band structures of monolayer, bilayer and trilayer MoS2 based on DFT theory. Figures 3a-f show the electronic band structures of monolayer, bilayer, and trilayer MoS2 calculated either with (Figures 3d, e, f) or without SOC (Figures 3a, b, c) at zero pressure. For monolayer MoS2, it is found (Figures 3a, d) that the calculated SOC-induced energy splitting of the VBM at K point is 151 meV, by contrast, it is a case of degeneracy without SOC effect. The calculated splitting value is very close to the measured value of 141 meV. For bilayer MoS2, the interlayer coupling induced VBM splitting is 74 meV (Figure 3b). It is found that the corresponding VBM splitting can increase up to 166 meV considering both SOC and interlayer coupling effects (Figure 3e). This calculated value is in well agreement with the measured VBM splitting of 164 meV. Unlike the monolayer, bilayer MoS2 possesses both time-reversal and inversion symmetries. As a result, the inter-layer SOC is absent, and the VBM splitting should originate from the contributions of both intra-layer SOC and interlayer coupling. This may like the situation of so-called “the hidden spin in each layer” in bilayer MoS2.46,47 For trilayer MoS2, Figure 3c shows that the VBM is split into three bands with the splitting of 49 and 55 meV as a result of interlayer coupling. However, the split VBM turns into two main bands with a separation of 175 meV when the SOC (both intra-layer and inter-layer SOC) and interlayer coupling are considered (Figure 3f). The calculated value is in well agreement with the measured splitting of 173 meV. It is known that the states near K point are mainly constituted by the d orbital wave function of Mo atoms. Since the Mo atoms are in the middle of the sandwich structure, it is expected that the peak A , related to the K-K direct transition, is less influenced by interlayer coupling.29 As a result, the peaks A of monolayer, bilayer and trilayer


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MoS2 show almost the same pressure responses and the obtained three pressure coefficients are all approximately 25 meV/GPa (see Figure 2). However, the pressure characteristics of the VBM splitting show much different behaviors. For monolayer MoS2, the VBM splitting is entirely due to the spin-splitting bands induced by the strong SOC. As the SOC is a relativistic effect mainly determined by the inner orbits of an atom, it represents, therefore, an atomic property.48 Thus the VBM splitting is insensitive to the pressure which is confirmed by nearly the same pressure coefficients of peaks A and B obtained by experiment (see Figure 2d) and calculation (see Figure S5a). For bilayer MoS2, the VBM splitting is 187 meV at 2.48 GPa, by contrast, it is 164 meV at zero pressure, giving rise to a increscent splitting of 23 meV (see Figure 2e). The pressure-induced increase of the splitting corresponds to the different pressure coefficients of excitons A and B. Owing to the insensitive of intra-layer SOC to the pressure, the increased VBM splitting for bilayer case arises from the increased interlayer coupling. The increased interlayer coupling leads to an increased blueshift of the peak B at a rate of 31.9 meV/GPa. By contrast, it is 24.5 meV/GPa for peak A, being the nearly same blueshift rate as the monolayer case. For trilayer MoS2, the VBM splitting increases from 173 meV at zero pressure to 206 meV at 4.9 GPa (Figure 2f). Again, the VBM splitting increase originates from the increased interlayer coupling, and the peak B blueshift is at a rate of 32.2 meV/GPa, and the peak A remains the nearly same pressure response as monolayer MoS2. Figure 3g exhibits the calculated energies of the VBM splitting of monolayer, bilayer and trilayer MoS2, as well as the interlayer distance, i.e. the lattice constant c/2 (see Figure 1a), as a


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function of pressure. As can be seen, as the pressure increases, the interlayer distance decreases, the energies of VBM splitting of both bilayer and trilayer MoS2 quickly increase due to the strengthening of interlayer coupling; while, the energy of VBM splitting of monolayer MoS2 changes little and is insensitive to the pressure. Based on the calculation, from 0 to 5 GPa, the interlayer distance decreases from 6.20 to 5.87 Å, leading to the increases of the VBM splitting of 32 and 36 meV for bilayer and trilayer MoS2, respectively. The calculated values are consistent with the experimentally obtained values of 37 meV = (31.9 - 24.5) meV/GPa × 5 GPa and 33 meV = (32.2 - 25.6) meV/GPa × 5 GPa for bilayer and trilayer MoS2, respectively, according to the measured pressure coefficients of peaks A and B. Next, we will discuss the origin of the peak C. It has been reported that the peak C arises from the nearly-degenerate exciton states related to the transitions among the nesting bands which gives rise to van Hove singularity in the joint density of states for monolayer MoS2.37,49 However, the corresponding position assignment of the peak C related to the interband transition in Brillouin zone remains disputable. According to the pressure characteristics of the peak C observed by the reflectance spectra (see Figure 2), for monolayer MoS2, the peak C shows a blueshift at the rate of 11.8 ± 4.0 meV/GPa. For bilayer and trilayer MoS2, the energy position of peaks C is insensitive to the pressure. We calculate the pressure dependences of the energy gap at different positions (Γ, Λ, M and a special point along Γ-K) of Brillouin zone for monolayer, bilayer and trilayer MoS2, as shown in Figures 4a-c. The calculated pressure coefficients for Γ, Λ, M and a special point along Γ-K are 43.7, 4.2, 34.9 and 16.9 meV/GPa for monolayer; -19.2, -10.8, 31.3 and 1.7 meV/GPa for bilayer; -21.9, -15.5, 29.5 and 2.8 meV/GPa for tirlayer MoS2. Comparing the exprimental and calculated


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results, it is found that, for monolayer, bilayer and trilayer MoS2, the pressure responses at the special point along Γ-K are reasonably consistent with that of the peak C. Thus the peak C in monolayer, biayer, and trilayer MoS2 is assigned to the van Hove singularity at a special point which is approximately 1/4 of total length of Γ-K away from Γ point, as shown in Figure 4d. CONCLUSION In summary, hydrostatic pressure reflectance spectra and DFT based theoretical calculation are used to probe the VBM splitting due to the SOC and interlayer coupling, as well as the origin of the exciton C in atomically thin MoS2. For monolayer MoS2, the VBM splitting, which is entirely induced by the SOC, remains almost unchanged response to the pressure, showing that the SOC is insensitive to the pressure. For bilayer and trilayer MoS2, the increased VBM splitting is due to the increased interlayer coupling, indicating that the VBM splitting as well as the interlayer coupling can be efficiently tuned by the pressure. In addition, the exciton peak C observed in the reflectance spectra is attributed to the van Hove singularity at a special point which is approximately 1/4 of total length of Γ-K away from Γ point.

METHODS The atomically thin MoS2 samples were prepared by micro-mechanical exfoliation from a natural bulk MoS2 (SPI Supplies) on a thinned SiO2/Si substrate. Regions of monolayer, bilayer, and trialyer MoS2 were identified by their optical contrast with an optical microscopy (Olympus BX41M) and confirmed using PL measurements. The PL and reflectance spectra measured at room temperature were acquired using an optical microscopy setup with a Xenon lamp and a solid-state laser at 454 nm. The PL


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or white light was collected by a 50× objective (NA: 0.35) and spectrally analyzed using a 0.5 m monochromator equipped with a Peltier-cooled silicon charge-coupled device (CCD). The pressure-dependent measurements were obtained using a DAC device. Liquid Argon was used as the pressure-transmitting medium. The pressure was determined based on the shift of the R1 fluorescence line of ruby in the chamber. Conflict of Interest: The authors declare no competing financial interest. Acknowledgment. We acknowledge support from the National Key Basic Research Program of China (Grant Nos. 2013CB922304 and 2013CB933304), the National Natural Science Foundation of China (Grant Nos. 11474275 and 11204297), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (XDB01010200). Supporting Information Available: Experimental setup, Computational Method, Diamond anvil cell (DAC) device, Excitation power dependence of the PL of monolayer MoS2, Interference effect in the reflectance spectra, Band structures of monolayer, bilayer and trilayer MoS2 at 0 and 5 GPa, The calculated energies of excitons A, B and C versus pressure in monolayer, bilayer and trilayer MoS2. This material is available free of charge via the Internet at http://pubs.acs.org.

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(27) Klots, A. R.; Newaz, A. K. M.; Wang, B.; Prasai, D.; Krzyzanowska, H.; Lin, J.; Caudel, D.; Ghimire, N. J.; Yan, J.; Ivanov, B. L.; Velizhanin, K. A.; Burger, A.; Mandrus, D. G.; Tolk, N. H.; Pantelides, S. T.; Bolotin, K. I. Probing Excitonic States in Suspended Two-Dimensional Semiconductors by Photocurrent Spectroscopy. Sci. Rep. 2014, 4, 6608 (28) Nayak, A. P.; Bhattacharyya, S.; Zhu, J.; Liu, J.; Wu, X.; Pandey, T.; Jin, C.; Singh, A. K.; Akinwande, D.; Lin, J.-F. Pressure-Induced Semiconducting to Metallic Transition in Multilayered Molybdenum Disulphide. Nat. Commun. 2014, 5, 3731. (29) Dou, X.; Ding, K.; Jiang, D.; Sun, B. Tuning and Identification of Interband Transitions in Monolayer and Bilayer Molybdenum Disulfide Using Hydrostatic Pressure. ACS Nano 2014, 8, 7458–7464. (30) Nayak, A. P.; Pandey, T.; Voiry, D.; Liu, J.; Moran, S. T.; Sharma, A.; Tan, C.; Chen, C.-H.; Li, L.-J.; Chhowalla, M. Pressure-Dependent Optical and Vibrational Properties of Monolayer Molybdenum Disulfide. Nano Lett. 2015, 15, 346-353. (31) Chi, Z.-H.; Zhao, X.-M.; Zhang, H.; Goncharov, A. F.; Lobanov, S. S.; Kagayama, T.; Sakata, M.; Chen, X.-J. Pressure-Induced Metallization of Molybdenum Disulfide. Phys. Rev. Lett. 2014, 113, 036802. (32) Pena-Alvarez, M.; del Corro, E.; Morales-Garcia, A.; Kavan, L.; Kalbac, M.; Frank, O. Single Layer Molybdenum Disulfide under Direct Out-of-Plane Compression: Low-Stress Band-Gap Engineering. Nano Lett. 2015, 15, 3139-3146. (33) Li, F.; Yan, Y.; Han, B.; Li, L.; Huang, X.; Yao, M.; Gong, Y.; Jin, X.; Liu, B.; Zhu, C. Pressure Confinement Effect in MoS2 Monolayers. Nanoscale 2015, 7, 9075-9082.


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(34) Fan, X.; Chang, C. -H.; Zheng, W. T.; Kuo, J. –L.; Singh, D. J. The Electronic Properties of Single-Layer and Multilayer MoS2 under High Pressure. J. Phys. Chem. C 2015, 119, 10189-10196. (35) Berghäuser, G.; Malic, E. Analytical Approach to Excitonic Properties of MoS2. Phys. Rev. B 2014, 89, 125309. (36) Shi, H. L.; Pan, H.; Zhang, Y. W.; Yakobson, B. I. Quasiparticle Band Structures and Optical Properties of Strained Monolayer MoS2 and WS2. Phys. Rev. B 2013, 87, 15530. (37) He, K.; Poole, C.; Mak, K. F.; Shan, J. Experimental Demonstration of Continuous Electronic Structure Tuning via Strain in Atomically Thin MoS2. Nano Lett. 2013, 13, 2931–2936. (38) Feng, J.; Qian, X.; Huang, C.-W.; Li, J. Strain-Engineered Artificial Atom as a Broad-Spectrum Solar Energy Funnel. Nat. Photonics 2012, 6, 866–872. (39) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169. (40) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865. (41) Grimme, S. Semiempirical GGA-Type Density Functional Constructed with a Long-Range Dispersion Correction. J. Comput. Chem. 2006, 27, 1787−1799. (42) Steinhoff, A.; Rösner, M.; Jahnke, F.; Wehling, T. O.; Gies, C. Influence of Excited Carriers on the Optical and Electronic Properties of MoS2. Nano Lett. 2014, 14 ( 7) 3743– 3748 (43) Zhao, W.; Ghorannevis, Z.; Chu, L.; Toh, M.; Kloc, C.; Tan, P.-H.; Eda, G. Evolution of Electronic Structure in Atomically Thin Sheets of WS2 and WSe2. ACS Nano 2013, 7, 791– 797.


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(44) Kozawa, D.; Kumar, R.; Carvalho, A.; Kumar Amara, K.; Zhao, W.; Wang, S.; Toh, M.; Ribeiro, R. M.; Castro Neto, A. H.; Matsuda, K.; Eda, G. Photocarrier Relaxation Pathway in

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(b)

(a) Mo

c/2

S

Gasket

(c)

Diamond Anvil Gasket

(d)

Peak A

Ruby

Sample Liquid Argon

Diamond Anvil

(e)

Peak B Reflectance

PL intensity (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Monolayer Peak I Bilayer

Peak A Peak B Monolayer Bilayer Trilayer

Trilayer 1.4

1.6 1.8 2.0 Photon energy (eV)

2.2

1.8

2.0

2.2

2.4

Peak C 2.6 2.8

Photon energy (eV)

Figure 1. (a) Schematic diagram of the lattice structure of MoS2. (b) Side-view image of the DAC device which consists of a pair of diamond anvils and gasket. The pressure chamber is marked by the rectangle zone. (c) Top-view microscope image of the pressure chamber which is filled by the pressure transmitting medium of liquid argon. (d) PL spectra of monolayer, bilayer and trilayer MoS2, each plot is normalized by its intensity maximum. Peaks A, B and I are marked. The optical microscope images of the monolayer, bilayer and trilayer MoS2 are shown. (e) Reflectance spectra of monolayer, bilayer and trilayer MoS2. Peaks A, B, and C are marked.


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Bilayer

Monolayer

(a)

(b)

A B

0.58

0.03

C

Trilayer

(c)

A B

0.65

C

0.91

A B

C

0.60 1.13

1.03

Reflectance

1.10

1.44

1.65

1.98

2.59

2.23

2.07

2.48

2.73 3.52

3.39 3.34

4.06 3.62 4.55 4.23

3.98

4.90

4.65

1.8

2.1

2.4

2.7

3.0

Photon energy (eV)

1.8 2.1 2.4 2.7 Photon energy (eV)

3.0

1.8 2.1 2.4 2.7 Photon energy (eV)

3.0

(f)

(e)

(d)

2.6 2.8

Photon energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Peak C

Peak C

2.6

Peak C 2.4

2.6 2.4 2.4 2.2

Peak B

Peak B

2.2

2.0

2.0

2.0

1.8

1.8 0

1 2 3 Pressure (GPa)

Peak A

Peak A

Peak A 1.8

Peak B

2.2

4

0

1 2 3 4 Pressure (GPa)

0

1 2 3 4 Pressure (GPa)

Figure 2. Reflectance spectra of monolayer (a), bilayer (b) and trilayer (c) MoS2 as pressure increasing from 0.58 to 3.98, 0.03 to 4.65 and 0.65 to 4.90 GPa, respectively. The solid red lines are guides to the eye, obtained by smoothing the original data (black lines). Peaks A, B and C are marked, and three black, red, and green dash lines are drawn for guiding the eye to the energy shifts of peaks A, B and C. The data of photon energies of peaks A, B and C as a function of pressure are shown by black, red and green solid circles, respectively, for monolayer (d), bilayer (e) and trilayer (f)


5

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MoS2 under a liquid argon condition inside the DAC. The data are linearly fitted, as shown by blue lines. Photon energies of peaks A, B and C measured under an ambient pressure outside the DAC are shown by black, red and green open squares, respectively.


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2

1

1

0.21

Monolayer Bilayer Trilayer

2

(a)

1

(b) 0

0

-1

-1

2

2

1

1

0.20

(c)

0 -1

2

6.2

6.1

0.19 0.18

6.0 0.17

(f)

(e)

(d)

1

0

0

-1

-1

(g)

0.16

5.9

0 -1

Γ

Λ

Κ

Μ

Γ Γ

Λ

Κ

Μ

Γ

0.15 0 Γ

Λ

Κ

Μ

Γ

1

2

3

4

Pressure (GPa)

Figure 3. Band structures of monolayer (a), bilayer (b) and trilayer (c) MoS2 at 0 GPa calculated without considering spin-orbit coupling. Band structures of monolayer (d), bilayer (e) and trilayer (f) MoS2 at 0 GPa calculated with considering spin-orbit coupling. (g) The energies of VBM splitting of monolayer, bilayer and trilayer MoS2, as well as layer's distance, as a function of the pressure.


5

Layer's distance (Å)

2

Energy (eV)

Energy (eV)

Trilayer

Bilayer

Monolayer

Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

ACS Nano

(b)

(a)

2.8 Γ Λ Μ Γ−>Λ

2.8 2.7

Energy (eV)

Energy (eV)

2.9

2.6

Γ Λ Μ Γ−>Λ

2.6 2.4 2.2 2.0

2.5 0

1

(c)


0

5

1

(d)


5

2.8

Γ Λ Μ Γ−>Λ

2.6 2.4

Energy (eV)

2.8

Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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2.4

Monolayer Peak C Bilayer Trilayer

2.0

2.2

1.6

2.0 0

1


5

Κ

Λ

Γ

Figure 4. The energy gap between valance band and condcution band at Γ, Λ, M and a special point along Γ-K direction for monolayer (a), bilayer (b) and trilayer (c) MoS2 as a function of pressure. (d) Optical band structures of monolayer, bilayer and trilayer MoS2 along K-Γ direction. The position of peak C is indicated by the van Hove singularity at a special point which is approximately 1/4 of total length of Γ-K away from Γ point, as indicated by vertical dashed lines.


Page 23 of 24

Diamond Anvil Cell

0.65 0.91

A B Trilayer MoS2 C

1.03

Reflectance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Nano

1.44 2.07 2.73 3.52 4.06 4.55 4.90 GPa

1.8 2.1 2.4 2.7 3.0 Photon energy (eV)

TOC graphic


ACS Nano

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TOC graphic 297x420mm (300 x 300 DPI)


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Probing SpinâOrbit Coupling and Interlayer Coupling in Atomically

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