Supporting Information Single Layer Molybdenum Disulfide under ...
Supporting Information Single Layer Molybdenum Disulfide under Direct Out-of-Plane Compression: Low-Stress Band-Gap Engineering Miriam Peña Álvarez, Elena del Corro, Ángel Morales-García, Ladislav Kavan, Martin Kalbac, Otakar Frank
Experimental details A first characterization of the MoS2 samples is carried out using the Atomic Force Microscope (AFM), in order to unambiguously determine the number of layers in the sample. As an example, Figure S1 shows the AFM image of a single layer of MoS2 on Si/SiO2 substrate, as is evidenced in the depicted height profile on the right. A subsequent Raman study was performed to confirm the information obtained from the AFM.
Figure S1. Atomic Force Microscopy image and height profile of a single layer of MoS2. The height profile is averaged over the black square indicated in the image.
The samples are prepared by mechanical exfoliation on a silica substrate and then transferred to different substrates1 in order to place them inside the high pressure cell. In Figure S2 we present photographs of one of the samples before and after the transfer. As can be observed, the flake remains unaltered after the transfer procedure. (b)
(a)
1L-MoS2
1L-MoS2
Figure S2. Photographs of the 1L-MoS2 flake on (a) the Si/SiO2 substrate and (b) the Inconel disc, before and after the transfer, respectively. Depending on the characterization technique, a particular anvil cell configuration is used. For the Raman spectroscopy a moissanite (SiC) anvil cell, like that depicted in Figure S3a, is used in order to avoid the overlapping between Raman features of sapphire and MoS2. Both materials present a Raman contribution around 418 cm-1, but fortunately, moissanite does not exhibit any Raman peak in this range. To place the sample in between the small culets of moissanite anvils, the specimen is transferred to an Inconel disc. However, a metallic substrate is not suitable for photoluminescence experiments and a different set-up was used for this characterization. In this case the sample is transferred to a sapphire disc and compressed with a moissanite anvil (as shown in Figure S3b).
(a)
(b)
Figure S3. Anvil cell configurations used for (a) Raman and (b) photoluminescence experiments. Raman spectroscopy results MoS2 is a semiconductor with a band gap in the visible range, close to 2 eV.2 For this reason an enhanced Raman spectrum is observed when exciting with the 632.8 nm laser line, for which the resonance conditions are fulfilled.3 But, as commented in the main text, the axial stress promotes changes in the electronic dispersion curves of MoS2; apart from others, a decrease in the band gap energy. Therefore, a change in the resonant conditions should be expected and detected through an analysis of the Raman intensities. The 632.8 nm spectra exhibits extra Raman peaks very close in frequency to the normal modes, E’ and A1’. Owing to the large overlap of the peaks and thus a higher fitting error, we analyze the combined intensity of those peaks close in frequency, see Figure S4. Despite the scattering shown by the data we can clearly observe a decrease in the intensity of the whole spectrum for stresses above 3 GPa, i.e. after the semiconductor to semimetal transition.
Figure S4. Raman intensity as a function of increasing stress for the 632.8 nm spectra; squares, circles and triangles stand for the combined intensities of [E’(M)+E’], [A1’+’QA+TO’] and [2LA(M)+’E1g+XA’], respectively. Other weaker resonant Raman contributions, not described before, are observed in the 632.8 nm spectra, see Figure 1 of the main document. In Figure S5a-c we present their Raman analysis. We can see an analogous behavior to the one described for the other more intense bands. In particular, the frequency analysis reveals again the three region behavior described in the main text. In the 488.0 nm Raman spectra, only the normal modes, E’ and A1’, can be observed at zero stress, but for stresses around 2 GPa two additional peaks emerge, possibly as a consequence of the electronic transition. The analysis of these bands, shown in Figure S5d-f, is complicated since they appear as weak shoulders of the main peaks. Only in the case of the frequency a clear increasing trend can be observed, which is analogous to the behavior shown by the rest of the Raman peaks after the semiconductor to semimetal transition occur.
Figure S5. Frequency, FWHM and Area as a function of increasing stress for the (a-c) r1, r2 and r3 bands of the 632.8 nm spectra and (d-f) extra bands in the 488.0 nm spectra.
Photoluminescence results The experimental setup used in this work for the PL measurements (Figure S3b,) precludes the observation of the indirect band-gap and the B exciton of the direct one, since the luminescence backgrounds from moissanite and sapphire overlap with them, see Figure S6. Therefore, under high stress we can only distinguish from the background the A peak corresponding to the direct band-gap, when it is intense as the pre dominant transition.
Figure S6. Superposition of the photoluminescence spectra of MoS2 (mono and few layer) and sapphire and moissanite anvils. Previous results found in the literature4-7 show that the MoS2 substrate may have an effect on its PL spectrum. Recently, it has been reported that the shape of the A peak in the PL spectrum of MoS2 can be related with doping in the sample, and therefore with the substrate. In Figure S7 we compare the A luminescence peak of sapphire and Si/SiO2 supported MoS2 samples. Fortunately, our data reveal almost negligible differences between them, since the A peak is in both cases fitted to two contribution with a similar intensity ratio, as shown in Figure S7.
Figure S7. Photoluminescence spectrum of monolayer MoS2 on sapphire (upper, violet) and Si/SiO2 (lower, red) substrates.
Calculated electronic properties – 1L MoS2 under normal compression In Figure S8 a complete sequence of the electronic dispersion curves with increasing axial stress is presented. In the first region, form 0 to 0.8 GPa we can observe that the direct band-gap at increases while the indirect one () decreases, until the latter becomes smaller in energy. If we continue increasing the stress up to 2.8 GPa we can see that both the conduction band at and the valence band at reach the Fermi level, indicating the transition to a semimetal. From this stress value, compression makes the direct band-gap decrease but, up to 5.1 GPa, no overlapping between the valence and conduction band is observed.
Figure S8. Calculated electronic dispersion curves of 1L-MoS2 with increasing stress. The corresponding stress values are indicated. The whole sequence is divided in three panels according to the electronic state displayed: indirect, direct band-gap semiconductor and semimetal (from left to right). Moreover, the evolution of the Mo-S bonding character with increasing axial stress can be studied in terms of the electron localization function (ELF).8 The topological analysis of ELF surfaces provides a partition of the three-dimensional space into electronic basins corresponding to bonds, lone pairs, and atomic core shells. The ELF iso-surfaces (ELF = 0.85) are presented in blue in Figure S9 for stresses of 0 and 5 GPa. At 0 GPa we can distinguish the Mo cations with low charge density and the S anions concentrating a large blue iso-surface. The almost spherical shape of the ELF at 0 GPa around the S atoms indicates an strong ionic character with slight covalent participation. Interestingly, with increasing stress the covalent character of the bonding steadily increases, as seen by the change in shape of the ELF around the S atoms pointing now towards the
Mo atoms. Moreover, our results reveal the absence of ELF between the S atoms and allow us to discard the appearance of S-S bonding as a consequence of the stress treatment.
(a) 0 GPa
(b) 5 GPa
Figure S9. Electron localization function (ELF) of 1L-MoS2 (a) 0 and (b) 5 GPa. ELF takes the value of 0.85 and is represented by blue iso-surfaces. In addition, the optimized lattice parameters (atom positions) were extracted to visualize the individual changes of the crystal structure as a function of stress. A complete set of parameters is given below as a part of the comparative study, however, a detail depicting the evolution of S-S distance (along c axis) with pressure is shown in Figure S10. As can be seen, the evolution is neither linear, nor uniform. There are very small several gradual changes – around 0.5 and 4.5 – and a more sudden, even though still small, change at ~ 3 GPa, i.e. at the point of semiconductorsemimetal transition. The difference in the evolution before and after this point is ~0.03 Å/GPa.
Figure S10. Calculated evolution of the S-S distance in 1L MoS2 under uniaxial stress. Theoretical comparative study In order to shed more light into the very different evolution of the electronic structure of 1L MoS2 under normal compression, we have undertaken a theoretical study comparing the effects of the two types of compression (normal vs. hydrostatic) on both the bulk and monolayer MoS 2. The band structures as well as the evolution of individual structural parameters of the atomic configurations were obtained as a function of stress. For the calculations concerning the 1L-MoS2 under hydrostatic pressure the starting structure is simulated as explained in the Methods section of the main document. The compressed configurations are obtained by reducing the S-S distance and the a lattice parameter by an identical factor (keeping the c parameter constant). Such reduction of the coordinates leads to almost analogous stress values along both x (= y) and z directions, i. e. hydrostatic compression. Under these conditions both S-S and Mo-S distances are decreased but the S-Mo-S angle is not modified. To perform calculation in MoS2 bulk structure, it is necessary to include the dispersion correction due to the van der Waals interactions between layers. According to that, we use vdW-DF functional
(optB88-vdW)9 which is a non-local correlation functional that accounts for dispersion interactions observed between MoS2 layers in the bulk structure. The energies were converged with respect to k-points density10 (8x8x2) and the plane-wave cutoff (420 eV), to ensure convergence of the total energy within 10-3 eV for all cases. For the hydrostatic pressure regime, we carry out full-optimized relaxation of the compressed structures, and the subsequent reduction of the a and c lattice parameters is observed for each one of the analyzed pressures. In the case of axial compression along the z direction, the c lattice parameter is reduced while keeping the a parameter frozen; and, consequently, under these conditions only the internal coordinates are relaxed. We first compare the basic trends in the evolution of the band structures for all the four cases, i.e. 1L-uniaxial, 1L-hydrostatic, bulk-uniaxial, and bulk-hydrostatic (Fig. S11, only the highest occupied valence band and lowest unoccupied conduction bands are shown for clarity). At the first sight, the evolution of bulk MoS2 is in general very similar under the two compression regimes (Fig. S11, top). The indirect band-gap is in the bulk samples located between the valence band at the Γ point and the conduction band at the Q point (halfway between K and Γ), in a good agreement with previous works.13 As the stress increases, the conduction band at the Q point is moving downwards in energy with only minor changes of the valence band at the Γ point, thereby gradually closing the band-gap. The metallization is reached at 24.3 GPa for hydrostatic conditions, and at 31.8 GPa for normal uniaxial compression. The former value is in an overall agreement with previous works.14 However, the behavior of monolayer MoS2 is completely different from the bulk, and on top of that the effects of hydrostatic pressure differ considerably from the effects of normal uniaxial compression (Fig. S11, bottom). Firstly, again in line with other works,13 the band-gap under zero strain is direct, at the K point. Under hydrostatic conditions, the conduction band moves upwards
in energy, but at different rates at different symmetry points – faster at K than at Q, while the valence band has the highest energy still at K (only at higher pressures at M). Hence, the band-gap becomes indirect between K and Q, and its energy is increasing with pressure. We note that this is the only case of the four shown, where the band-gap increases with stress. In contrast, 1L-MoS2 under normal compression experiences a very fast reduction of the band gap energy, due to rapid decrease of the conduction band energy at K and simultaneous increase of the valence band energy at Γ, accompanied by an almost immediate transition to an indirect K-Γ gap and subsequently by the transition to a semimetal (see detailed curves in Fig. S8 and Fig. 5).
Figure S11. Band structure evolution of 1L and bulk MoS2 under hydrostatic and uniaxial pressure conditions.
To elucidate, which particular changes in the lattice deformation are responsible for the observed variations in the electronic structure, we analyze the atomic coordinates and their correlation with band gap energy changes separately for bulk (Figure S12) and 1L-MoS2 (Figure S13).
Figure S12. Evolution of individual parameters of the crystal structure of bulk MoS2 with stress, and their influence on the band-gap energy. In bulk, the interlayer S-S distance (the component parallel to z is plotted in Fig. S12) undergoes the most prominent changes upon the application of stress, both hydrostatically and uniaxially, at similar rates (~0.25% compression at 30 GPa). The band-gap energy follows the change in interlayer distance very closely. The other parameters, i.e. intralayer S-S and Mo-S distances, and S-Mo-S angle experience only relatively small changes, and even with opposite signs for the two compression regimes in the case of intralayer S-S distance and S-Mo-S angle. It is thus safe to assume that the interlayer S-S distance, hence increased interaction between the layers, is the most
important factor in the observed band structure changes of bulk MoS2, both for hydrostatic and uniaxial conditions.
Figure S13. Evolution of individual parameters of the crystal structure of 1L-MoS2 with stress, and their influence on the band-gap energy. The difference in the initial indirect gap energy is caused by plotting the values of K-Q for hydrostatic and K-Γ for uniaxial, since they become the dominant ones with the application of the respective stress regime. The utmost importance of the size of the interlayer S-S distance for the bulk samples is well documented in the completely different behavior of the monolayer under the two compression regimes. There, no direct correlation between the individual parameters and band-gap evolution can be observed, hence it is their combination which matters. In the same time, the evolution of the intralayer S-S distance with stress points to the most crucial difference between the two regimes
– while the monolayer becomes gradually less compressible under hydrostatic conditions, the compression is almost linear under uniaxial stress. At compression (parallel to z) of ~15%, the stress needed under each regime differs by a factor of more than 4.
References (1)
Li, H.; Wu, J.; Huang, X.; Yin, Z.; Liu, J.; Zhang, H. ACS Nano 2014, 8, 6563.
(2)
Mak, K.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. Phys. Rev. Lett. 2010, 105, 136805.
(3)
Pimenta, M. A.; del Corro, E.; Carvalho, B. R.; Fantini, C.; Malard, L. M. Acc. Chem. Res.
2014, 48, 41. (4)
Buscema, M.; Steele, G.; van der Zant, H. J.; Castellanos-Gomez, A. Nano Res. 2014, 7,
561. (5)
Dhakal, K. P.; Duong, D. L.; Lee, J.; Nam, H.; Kim, M.; Kan, M.; Lee, Y. H.; Kim, J.
Nanoscale 2014, 6, 13028. (6)
Sercombe, D.; Schwarz, S.; Pozo-Zamudio, O. D.; Liu, F.; Robinson, B. J.; Chekhovich,
E. A.; Tartakovskii, I. I.; Kolosov, O.; Tartakovskii, A. I. Sci. Rep. 2013, 3, 3489. (7)
Scheuschner, N.; Ochedowski, O.; Kaulitz, A.-M.; Gillen, R.; Schleberger, M.; Maultzsch,
J. Phys. Rev. B 2014, 89, 125406. (8)
Savin, A. J. Mol. Struc.: THEOCHEM 2005, 727, 127.
(9)
Klimeš, J.; Bowler, D. R.; Michaelides, A. J. Phys.: Condens. Matter 2010, 22, 022201.
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Monkhorst, H.; Pack, J. Phys. Rev. B 1976, 13, 5188.
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Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.;
Chiarotti, G. L.; Cococcioni, M.; Dabo, I.; Dal Corso, A.; de Gironcoli, S.; Fabris, S.; Fratesi, G.; Gebauer, R.; Gerstmann, U.; Gougoussis, C.; Kokalj, A.; Lazzeri, M.; Martin-Samos, L.; Marzari,
N.; Mauri, F.; Mazzarello, R.; Paolini, S.; Pasquarello, A.; Paulatto, L.; Sbraccia, C.; Scandolo, S.; Sclauzero, G.; Seitsonen, A. P.; Smogunov, A.; Umari, P.; Wentzcovitch, R. M. J. Phys.: Condens. Matter 2009, 21, 395502. (12)
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Nayak, A. P.; Bhattacharyya, S.; Zhu, J.; Liu, J.; Wu, X.; Pandey, T.; Jin, C.; Singh, A. K.;
Akinwande, D.; Lin, J.-F. Nat. Commun. 2014, 5, 3731.
Experimental details A first characterization of the MoS2 samples is carried out using the Atomic Force Microscope (AFM), in order to unambiguously determine the number of layers in the sample. As an example, Figure S1 shows the AFM image of a single layer of MoS2 on Si/SiO2 substrate, as is evidenced in the depicted height profile on the right. A subsequent Raman study was performed to confirm the information obtained from the AFM.
Figure S1. Atomic Force Microscopy image and height profile of a single layer of MoS2. The height profile is averaged over the black square indicated in the image.
The samples are prepared by mechanical exfoliation on a silica substrate and then transferred to different substrates1 in order to place them inside the high pressure cell. In Figure S2 we present photographs of one of the samples before and after the transfer. As can be observed, the flake remains unaltered after the transfer procedure. (b)
(a)
1L-MoS2
1L-MoS2
Figure S2. Photographs of the 1L-MoS2 flake on (a) the Si/SiO2 substrate and (b) the Inconel disc, before and after the transfer, respectively. Depending on the characterization technique, a particular anvil cell configuration is used. For the Raman spectroscopy a moissanite (SiC) anvil cell, like that depicted in Figure S3a, is used in order to avoid the overlapping between Raman features of sapphire and MoS2. Both materials present a Raman contribution around 418 cm-1, but fortunately, moissanite does not exhibit any Raman peak in this range. To place the sample in between the small culets of moissanite anvils, the specimen is transferred to an Inconel disc. However, a metallic substrate is not suitable for photoluminescence experiments and a different set-up was used for this characterization. In this case the sample is transferred to a sapphire disc and compressed with a moissanite anvil (as shown in Figure S3b).
(a)
(b)
Figure S3. Anvil cell configurations used for (a) Raman and (b) photoluminescence experiments. Raman spectroscopy results MoS2 is a semiconductor with a band gap in the visible range, close to 2 eV.2 For this reason an enhanced Raman spectrum is observed when exciting with the 632.8 nm laser line, for which the resonance conditions are fulfilled.3 But, as commented in the main text, the axial stress promotes changes in the electronic dispersion curves of MoS2; apart from others, a decrease in the band gap energy. Therefore, a change in the resonant conditions should be expected and detected through an analysis of the Raman intensities. The 632.8 nm spectra exhibits extra Raman peaks very close in frequency to the normal modes, E’ and A1’. Owing to the large overlap of the peaks and thus a higher fitting error, we analyze the combined intensity of those peaks close in frequency, see Figure S4. Despite the scattering shown by the data we can clearly observe a decrease in the intensity of the whole spectrum for stresses above 3 GPa, i.e. after the semiconductor to semimetal transition.
Figure S4. Raman intensity as a function of increasing stress for the 632.8 nm spectra; squares, circles and triangles stand for the combined intensities of [E’(M)+E’], [A1’+’QA+TO’] and [2LA(M)+’E1g+XA’], respectively. Other weaker resonant Raman contributions, not described before, are observed in the 632.8 nm spectra, see Figure 1 of the main document. In Figure S5a-c we present their Raman analysis. We can see an analogous behavior to the one described for the other more intense bands. In particular, the frequency analysis reveals again the three region behavior described in the main text. In the 488.0 nm Raman spectra, only the normal modes, E’ and A1’, can be observed at zero stress, but for stresses around 2 GPa two additional peaks emerge, possibly as a consequence of the electronic transition. The analysis of these bands, shown in Figure S5d-f, is complicated since they appear as weak shoulders of the main peaks. Only in the case of the frequency a clear increasing trend can be observed, which is analogous to the behavior shown by the rest of the Raman peaks after the semiconductor to semimetal transition occur.
Figure S5. Frequency, FWHM and Area as a function of increasing stress for the (a-c) r1, r2 and r3 bands of the 632.8 nm spectra and (d-f) extra bands in the 488.0 nm spectra.
Photoluminescence results The experimental setup used in this work for the PL measurements (Figure S3b,) precludes the observation of the indirect band-gap and the B exciton of the direct one, since the luminescence backgrounds from moissanite and sapphire overlap with them, see Figure S6. Therefore, under high stress we can only distinguish from the background the A peak corresponding to the direct band-gap, when it is intense as the pre dominant transition.
Figure S6. Superposition of the photoluminescence spectra of MoS2 (mono and few layer) and sapphire and moissanite anvils. Previous results found in the literature4-7 show that the MoS2 substrate may have an effect on its PL spectrum. Recently, it has been reported that the shape of the A peak in the PL spectrum of MoS2 can be related with doping in the sample, and therefore with the substrate. In Figure S7 we compare the A luminescence peak of sapphire and Si/SiO2 supported MoS2 samples. Fortunately, our data reveal almost negligible differences between them, since the A peak is in both cases fitted to two contribution with a similar intensity ratio, as shown in Figure S7.
Figure S7. Photoluminescence spectrum of monolayer MoS2 on sapphire (upper, violet) and Si/SiO2 (lower, red) substrates.
Calculated electronic properties – 1L MoS2 under normal compression In Figure S8 a complete sequence of the electronic dispersion curves with increasing axial stress is presented. In the first region, form 0 to 0.8 GPa we can observe that the direct band-gap at increases while the indirect one () decreases, until the latter becomes smaller in energy. If we continue increasing the stress up to 2.8 GPa we can see that both the conduction band at and the valence band at reach the Fermi level, indicating the transition to a semimetal. From this stress value, compression makes the direct band-gap decrease but, up to 5.1 GPa, no overlapping between the valence and conduction band is observed.
Figure S8. Calculated electronic dispersion curves of 1L-MoS2 with increasing stress. The corresponding stress values are indicated. The whole sequence is divided in three panels according to the electronic state displayed: indirect, direct band-gap semiconductor and semimetal (from left to right). Moreover, the evolution of the Mo-S bonding character with increasing axial stress can be studied in terms of the electron localization function (ELF).8 The topological analysis of ELF surfaces provides a partition of the three-dimensional space into electronic basins corresponding to bonds, lone pairs, and atomic core shells. The ELF iso-surfaces (ELF = 0.85) are presented in blue in Figure S9 for stresses of 0 and 5 GPa. At 0 GPa we can distinguish the Mo cations with low charge density and the S anions concentrating a large blue iso-surface. The almost spherical shape of the ELF at 0 GPa around the S atoms indicates an strong ionic character with slight covalent participation. Interestingly, with increasing stress the covalent character of the bonding steadily increases, as seen by the change in shape of the ELF around the S atoms pointing now towards the
Mo atoms. Moreover, our results reveal the absence of ELF between the S atoms and allow us to discard the appearance of S-S bonding as a consequence of the stress treatment.
(a) 0 GPa
(b) 5 GPa
Figure S9. Electron localization function (ELF) of 1L-MoS2 (a) 0 and (b) 5 GPa. ELF takes the value of 0.85 and is represented by blue iso-surfaces. In addition, the optimized lattice parameters (atom positions) were extracted to visualize the individual changes of the crystal structure as a function of stress. A complete set of parameters is given below as a part of the comparative study, however, a detail depicting the evolution of S-S distance (along c axis) with pressure is shown in Figure S10. As can be seen, the evolution is neither linear, nor uniform. There are very small several gradual changes – around 0.5 and 4.5 – and a more sudden, even though still small, change at ~ 3 GPa, i.e. at the point of semiconductorsemimetal transition. The difference in the evolution before and after this point is ~0.03 Å/GPa.
Figure S10. Calculated evolution of the S-S distance in 1L MoS2 under uniaxial stress. Theoretical comparative study In order to shed more light into the very different evolution of the electronic structure of 1L MoS2 under normal compression, we have undertaken a theoretical study comparing the effects of the two types of compression (normal vs. hydrostatic) on both the bulk and monolayer MoS 2. The band structures as well as the evolution of individual structural parameters of the atomic configurations were obtained as a function of stress. For the calculations concerning the 1L-MoS2 under hydrostatic pressure the starting structure is simulated as explained in the Methods section of the main document. The compressed configurations are obtained by reducing the S-S distance and the a lattice parameter by an identical factor (keeping the c parameter constant). Such reduction of the coordinates leads to almost analogous stress values along both x (= y) and z directions, i. e. hydrostatic compression. Under these conditions both S-S and Mo-S distances are decreased but the S-Mo-S angle is not modified. To perform calculation in MoS2 bulk structure, it is necessary to include the dispersion correction due to the van der Waals interactions between layers. According to that, we use vdW-DF functional
(optB88-vdW)9 which is a non-local correlation functional that accounts for dispersion interactions observed between MoS2 layers in the bulk structure. The energies were converged with respect to k-points density10 (8x8x2) and the plane-wave cutoff (420 eV), to ensure convergence of the total energy within 10-3 eV for all cases. For the hydrostatic pressure regime, we carry out full-optimized relaxation of the compressed structures, and the subsequent reduction of the a and c lattice parameters is observed for each one of the analyzed pressures. In the case of axial compression along the z direction, the c lattice parameter is reduced while keeping the a parameter frozen; and, consequently, under these conditions only the internal coordinates are relaxed. We first compare the basic trends in the evolution of the band structures for all the four cases, i.e. 1L-uniaxial, 1L-hydrostatic, bulk-uniaxial, and bulk-hydrostatic (Fig. S11, only the highest occupied valence band and lowest unoccupied conduction bands are shown for clarity). At the first sight, the evolution of bulk MoS2 is in general very similar under the two compression regimes (Fig. S11, top). The indirect band-gap is in the bulk samples located between the valence band at the Γ point and the conduction band at the Q point (halfway between K and Γ), in a good agreement with previous works.13 As the stress increases, the conduction band at the Q point is moving downwards in energy with only minor changes of the valence band at the Γ point, thereby gradually closing the band-gap. The metallization is reached at 24.3 GPa for hydrostatic conditions, and at 31.8 GPa for normal uniaxial compression. The former value is in an overall agreement with previous works.14 However, the behavior of monolayer MoS2 is completely different from the bulk, and on top of that the effects of hydrostatic pressure differ considerably from the effects of normal uniaxial compression (Fig. S11, bottom). Firstly, again in line with other works,13 the band-gap under zero strain is direct, at the K point. Under hydrostatic conditions, the conduction band moves upwards
in energy, but at different rates at different symmetry points – faster at K than at Q, while the valence band has the highest energy still at K (only at higher pressures at M). Hence, the band-gap becomes indirect between K and Q, and its energy is increasing with pressure. We note that this is the only case of the four shown, where the band-gap increases with stress. In contrast, 1L-MoS2 under normal compression experiences a very fast reduction of the band gap energy, due to rapid decrease of the conduction band energy at K and simultaneous increase of the valence band energy at Γ, accompanied by an almost immediate transition to an indirect K-Γ gap and subsequently by the transition to a semimetal (see detailed curves in Fig. S8 and Fig. 5).
Figure S11. Band structure evolution of 1L and bulk MoS2 under hydrostatic and uniaxial pressure conditions.
To elucidate, which particular changes in the lattice deformation are responsible for the observed variations in the electronic structure, we analyze the atomic coordinates and their correlation with band gap energy changes separately for bulk (Figure S12) and 1L-MoS2 (Figure S13).
Figure S12. Evolution of individual parameters of the crystal structure of bulk MoS2 with stress, and their influence on the band-gap energy. In bulk, the interlayer S-S distance (the component parallel to z is plotted in Fig. S12) undergoes the most prominent changes upon the application of stress, both hydrostatically and uniaxially, at similar rates (~0.25% compression at 30 GPa). The band-gap energy follows the change in interlayer distance very closely. The other parameters, i.e. intralayer S-S and Mo-S distances, and S-Mo-S angle experience only relatively small changes, and even with opposite signs for the two compression regimes in the case of intralayer S-S distance and S-Mo-S angle. It is thus safe to assume that the interlayer S-S distance, hence increased interaction between the layers, is the most
important factor in the observed band structure changes of bulk MoS2, both for hydrostatic and uniaxial conditions.
Figure S13. Evolution of individual parameters of the crystal structure of 1L-MoS2 with stress, and their influence on the band-gap energy. The difference in the initial indirect gap energy is caused by plotting the values of K-Q for hydrostatic and K-Γ for uniaxial, since they become the dominant ones with the application of the respective stress regime. The utmost importance of the size of the interlayer S-S distance for the bulk samples is well documented in the completely different behavior of the monolayer under the two compression regimes. There, no direct correlation between the individual parameters and band-gap evolution can be observed, hence it is their combination which matters. In the same time, the evolution of the intralayer S-S distance with stress points to the most crucial difference between the two regimes
– while the monolayer becomes gradually less compressible under hydrostatic conditions, the compression is almost linear under uniaxial stress. At compression (parallel to z) of ~15%, the stress needed under each regime differs by a factor of more than 4.
References (1)
Li, H.; Wu, J.; Huang, X.; Yin, Z.; Liu, J.; Zhang, H. ACS Nano 2014, 8, 6563.
(2)
Mak, K.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. Phys. Rev. Lett. 2010, 105, 136805.
(3)
Pimenta, M. A.; del Corro, E.; Carvalho, B. R.; Fantini, C.; Malard, L. M. Acc. Chem. Res.
2014, 48, 41. (4)
Buscema, M.; Steele, G.; van der Zant, H. J.; Castellanos-Gomez, A. Nano Res. 2014, 7,
561. (5)
Dhakal, K. P.; Duong, D. L.; Lee, J.; Nam, H.; Kim, M.; Kan, M.; Lee, Y. H.; Kim, J.
Nanoscale 2014, 6, 13028. (6)
Sercombe, D.; Schwarz, S.; Pozo-Zamudio, O. D.; Liu, F.; Robinson, B. J.; Chekhovich,
E. A.; Tartakovskii, I. I.; Kolosov, O.; Tartakovskii, A. I. Sci. Rep. 2013, 3, 3489. (7)
Scheuschner, N.; Ochedowski, O.; Kaulitz, A.-M.; Gillen, R.; Schleberger, M.; Maultzsch,
J. Phys. Rev. B 2014, 89, 125406. (8)
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