van der Waals trilayers and superlattices: modification of electronic structures of MoS₂ by intercalation

Abstract

We perform a comprehensive first-principles study of the electronic properties of van der Waals (vdW) trilayers via intercalating a two-dimensional (2D) monolayer (ML = BN, MoSe₂, WS₂, or WSe₂) between a MoS₂ bilayer to form various MoS₂/ML/MoS₂ sandwich trilayers. We find that the BN monolayer is the most effective sheet to decouple the interlayer vdW coupling of the MoS₂ bilayer, and the resulting sandwich trilayer can recover the electronic structures of the MoS₂ monolayer, particularly the direct-gap character. Further study of the MoS₂/BN superlattices confirms the effectiveness of the BN monolayer for the decoupling of the MoS₂–MoS₂ interaction. In addition, the intercalation of a transition-metal dichalcogenide (TMDC) MoSe₂ or WSe₂ sheet makes the sandwich trilayer undergo an indirect-gap to direct-gap transition due to the newly formed heterogeneous S/Se interfaces. In contrast, the MoS₂/WS₂/MoS₂ sandwich trilayer still retains the indirect-gap character of the MoS₂ bilayer due to the lack of the heterogeneous S/Se interfaces. Moreover, the 3D superlattice of the MoS₂/TMDC heterostructures also exhibits similar electronic band characters to the MoS₂/TMDC/MoS₂ trilayer heterostructures, albeit a slight decrease of the bandgap compared to the trilayers. Compared to the bulk MoS₂, the 3D MoS₂/TMDC superlattice can give rise to new and distinctive properties. Our study offers not only new insights into electronic properties of the vdW multilayer heterostructures but also guidance in designing new heterostructures to modify electronic structures of 2D TMDC crystals.

---

Introduction

Many experiments have demonstrated that two-dimensional (2D) transition-metal dichalcogenides (TMDCs) such as 2D MoS₂ and WS₂ crystals possess novel electronic,^1–4 optical,^5–8 catalytic,^9,10 and mechanical properties.^11–14 For example, electronic properties of 2D MoS₂ crystals can be sensitive to the number of layers, that is, the MoS₂ monolayer exhibits a direct bandgap with a value of ∼1.8 eV while a bilayer MoS₂ exhibits an indirect bandgap with a value of ∼1.5 eV.¹⁵ As a result, significant enhancement of photoluminescence has been observed when MoS₂ is thinned to a single layer.^8,14 Previous study has also shown that when the MoS₂ bilayer is pulled apart into two separated monolayers, the direct transition (K–K) is insensitive to the separation while the indirect transition (Γ–K) increases dramatically.¹⁶ It seems that the distance between the two monolayers or the interlayer vdW interaction can notably affect the electronic structures of two-dimensional (2D) layered TMDCs. Thus, one may ask two closely related questions: “can the MoS₂ bilayer be effectively decoupled via intercalation of a 2D sheet without being pulled far too apart?” or “To what extent, can the intercalation of a 2D sheet affect electronic properties of the MoS₂ bilayer?” The intercalation of a 2D sheet into the MoS₂ bilayer gives rise to a hybrid trilayer, coined as the vdW heterostructures by Geim and Grigorieva.¹⁷ Recently, successful fabrication of multilayer vdW heterostructures by stacking one layer on top of another in a precisely controlled sequence has been demonstrated experimentally.^18–20 The artificial vdW heterostructures can exhibit new and unusual properties that differ from their own constituent layers. For example, the vertical field-effect transistor and memory cell made of TMDC/graphene heterostructures^19,21–23 as well as layered hybrids of MoS₂ and WS₂ have been realized in the laboratory.²⁴ Previous theoretical studies suggest that the direct-gap character of the MoS₂ monolayer can be retained in certain MoS₂ heterobilayer structures whose electronic properties can be further tuned by an in-plane strain or a vertical electric field.^25–29 In addition, the insulating BN monolayer is a good substrate for protecting high quality graphene electronics.³⁰ A type-I band alignment for the BN monolayer and MoS₂ monolayer is also reported.²⁵ 3D heterostructures such as superlattices are predicted to possess new properties that differ from their corresponding bulk structures, thereby opening a new way of materials design.³¹

The focus of this study is to investigate effects of intercalation of either an insulating BN monolayer or a semiconducting TMDC monolayer (MoSe₂, WS₂, or WSe₂) into a MoS₂ bilayer on the electronic properties of the vdW trilayer heterostructure and the corresponding vdW superlattice. Our computational results suggest that the BN monolayer is an ideal sheet to decouple the MoS₂ bilayer while a MoSe₂ or WSe₂ sheet can turn the indirect-gap of the MoS₂ bilayer into a direct-gap trilayer.

Computational methods

All calculations are performed within the framework of spin-polarized plane-wave density functional theory (PW-DFT), implemented in the Vienna ab initio simulation package (VASP 5.3).^32,33 The Perdew–Burke–Ernzerhof (PBE) functional and projector augmented wave (PAW) potentials are used.^34–36 The effect of vdW interaction is accounted for by using the dispersion corrected DFT (optB88-vdW functional).^37,38 The vacuum length between two adjacent images in the supercell is longer than 15 Å. An energy cutoff of 500 eV is adopted for the plane-wave expansion of the electronic wave function. Geometric structures are relaxed until the force on each atom is less than 0.01 eV Å⁻¹ and the convergence criteria for energy is 1 × 10⁻⁵ eV.

Note that the optimized MoS₂ monolayer exhibits a cell parameter of 3.18 Å, while the cell parameter of a h-BN monolayer is 2.52 Å, in good agreement with previous results.^39,40 As such, the 5 × 5 BN supercell almost perfectly matches the 4 × 4 MoS₂ supercell with the lattice mismatch less than 1%. For the MoS₂/BN/MoS₂ trilayer, the supercell is fixed while the atomic coordinates are relaxed. For other sandwich systems containing TMDC MoSe₂, WS₂, or WSe₂, a 1 × 1 cell is used due to the fact that their lattice parameters are close to that of MoS₂. In these cases, both the cell length and atomic coordinates are relaxed to obtain the lattice parameters at the lowest total energy. Bader's atom in molecule (AIM) method based on charge density topological analysis is used for computing charge population.⁴¹ Once the optimized structures are obtained, a hybrid functional in the Heyd–Scuseria–Ernzerhof (HSE06) form is used to give more accurate bandgaps.⁴² The spin–orbit (SO) interaction is included in all the band-structure calculations.⁴³

Results and discussion

Intercalation of a MoS₂ bilayer with a BN monolayer

First, DFT/PBE calculations show that monolayer MoS₂ is a semiconductor with a direct bandgap of 1.60 eV (see Table 1), in agreement with previous calculation.²⁹ The MoS₂ bilayer with the most stable C7 stacking, however, is a semiconductor with an indirect bandgap of 1.31 eV. HSE06 calculation enlarges the bandgaps of monolayer and bilayer MoS₂ to 2.06 and 1.81 eV, respectively. For the BN monolayer, PBE calculation shows it is a semiconductor with a wide bandgap of 4.66 eV (Table 2).

Table 1 The distance d (in Å) between two nearest-neighbor monolayers as shown in Fig. 1. The binding energy E_BE (in eV) per formula unit. The computed bandgaps E_g (in eV) of MoS₂ monolayer (ML-MoS₂), bilayer (BL-MoS₂), trilayer (MoS₂/BN/MoS₂) heterostructures and related superlattice (SL) with different stacking orders. The SO effect is included in HSE06 calculation of the bandgap

	ML-MoS2	BL-MoS2	A1B1A1	A1B2A1	A1B1A2	A1B1A3	SL-A1B1	SL-A1B2
d	—	3.09	3.36	3.36	3.36	3.36	3.35	3.35
E BE	—	0.22	0.36	0.36	0.37	0.36	0.38	0.38
E g (PBE)	1.60	1.31-indirect	1.58	1.58	1.58	1.58	1.69	1.69
E g (HSE06)	2.06	1.81-indirect	2.00	—	—	—	—	—

---

Table 2 Computed PBE E_g (PBE) and HSE06 E_g (HSE) bandgaps of MoS₂/ML/MoS₂ trilayers (ML = MoSe₂, WS₂ or WSe₂) in ABA and ACA stacking (see Fig. 3). The PBE (E_g (PBE)_SL) and HSE06 (E_g (HSE)_SL) bandgaps of MoS₂/ML superlattice (ML = MoSe₂, WS₂, WSe₂) in AB and AC stacking. The unit is eV

	ABA (B = MoSe2)	ACA (C = MoSe2)	ABA (B = WS2)	ACA (C = WS2)	ABA (B = WSe2)	ACA (C = WSe2)
E g (PBE)	0.70	0.75	1.05 (Γ–k)	1.08 (Γ–k)	0.39	0.42
E g (HSE)	0.97	1.02	1.47 (Γ–k)	1.49 (Γ–k)	0.61	0.64
E g (PBE)_SL	0.62 (Γ–k)	0.59 (Γ–k)	0.95 (Γ–k)	0.93 (Γ–k)	0.30	0.35
E g (HSE)_SL	0.88	0.92	1.35 (Γ–k)	1.33 (Γ–k)	0.50	0.54

---

Next, various MoS₂/BN/MoS₂ trilayer systems are built for which the lateral locations of the MoS₂ monolayer and BN monolayer in different supercells are shown in Fig. 1. Specifically, we consider four different stacking orders: A1B1A1, A1B2A1, A1B1A2, and A1B1A3. PBE optimizations show that the total-energy differences among these configurations are typically less than 0.01 eV per formula cell, and the different stacking orders have little effect on the electronic structures. The binding energy of a trilayer, which measures the interlayer vdW interaction per supercell, is defined as: E_BE = 2E_MoS2 + E_BN − E_MoS2/BN/MoS2, where E_MoS2 is the total energy of a MoS₂ monolayer, E_BN is the total energy of a BN monolayer, and E_MoS2/BN/MoS2 is the total energy of a MoS₂/BN/MoS₂ trilayer. As listed in Table 1, the computed binding energies of the MoS₂/BN/MoS₂ heterostructure with A1B1A1, A1B2A1, A1B1A2, and A1B1A3 stacking orders are 0.36 eV, 0.36 eV, 0.37 eV, and 0.36 eV, respectively, reflecting the weak vdW interaction between the MoS₂ layer and BN layer. Taking the A1B1A1 stacking as an example, its electronic structure is shown in Fig. 2c. Clearly, the trilayer retains the direct-gap character of the MoS₂ monolayer. The computed bandgap is 1.58 eV, and both the conduction band minimum (CBM) and valence band maximum (VBM) are located at the K points, both contributed by the MoS₂ layers. Like the PBE calculation, the HSE06 calculation also suggests a direct-gap character but the bandgap increases to 2.00 eV (ESI Fig. S1†). Overall, the intercalated BN layer has little effect on the band edge of MoS₂ layers. To further confirm this conclusion, we remove the BN layer but leave the two MoS₂ layers fixed at the original locations of the trilayer. As shown in Fig. 2b, again, the computed band structure shows a direct-gap character with the bandgap being 1.59 eV, very close to that of the MoS₂/BN/MoS₂ trilayer.

Fig. 1 Top view of a MoS₂ monolayer in three different supercells (marked by the red parallelogram) and a BN monolayer in two different supercells. A3 (B2) can be viewed as a displacement of A1 (B1) in the green-arrow direction shown in A1 (B1). Superimposing the ABA supercells allows us to build different MoS₂/BN/MoS₂ trilayers. An example of A1B1A1 trilayer is shown in the lower right panel.

Fig. 2 Computed electronic band structures (PBE) of (a) monolayer MoS₂; (b) MoS₂/vacuum layer/MoS₂ by removing the BN layer from the MoS₂/BN/MoS₂ trilayer counterpart (in (c)) but with the fixed vertical location of the two MoS₂ layers; (c) MoS₂/BN/MoS₂ with the A1B1A1 stacking; and (d) a 3D superlattice of MoS₂/BN with the AB stacking. The green lines represent MoS₂ layers while the red lines represent BN monolayer.

We also compute the effective mass at the K point corresponding to the MoS₂ monolayer and A1B1A1 trilayer, respectively. The directional dependence of the effective mass at the K point is small. For the MoS₂ monolayer, m^*_e = 0.44m₀ for the electron at CBM and m^*_h = 0.55m₀ for the hole at VBM are in agreement with the previous studies.^4,44 For A1B1A1, m^*_e = 0.44m₀ and m^*_h = 0.59m₀, similar to those of the monolayer, which indicates that the carrier mobility of the monolayer is also retained by the trilayer.

To confirm that the BN monolayer is an ideal sheet to decouple the interlayer coupling of the MoS₂ bilayer, we also compute electronic structures of the 3D superlattice of hybrid BN/MoS₂ layers. A superlattice with two different stacking orders (A1B1 and A1B2) of MoS₂ and BN layers is considered and our calculations show that the two stacking orders give nearly the same results. For both stacking orders, the optimized cell parameters are a = b = 12.62 Å and c = 9.86 Å. As shown in Fig. 2d, the superlattice exhibits a direct gap of 1.69 eV, and both the VBM and CBM are located at the K point and both are contributed by MoS₂ layers as in the case of the MoS₂/BN/MoS₂ trilayer system. The slightly enhanced bandgap compared to the trilayer system is largely due to a slight reduction of the cell parameters a and b. In summary, results of both the vdW trilayer and superlattice show that the alternatively stacked BN and MoS₂ monolayers can retain the direct-gap character of the MoS₂ monolayer. In other words, the BN monolayer is an effective divider to decouple the interlayer coupling for MoS₂.

Intercalation of a MoS₂ bilayer by MoSe₂, WS₂ or WSe₂ monolayer

Previous experimental and theoretical studies demonstrate that the MoS₂ bilayer is a semiconductor with an indirect bandgap.^27,29,45 Recent theoretical studies of TMDC heterobilayers also show that the interlayer interaction due to heterointerfaces (e.g., S/Se) can notably affect the electronic properties. Thus, it is interesting to study the extent to which the intercalation of a heterogeneous TMDC monolayer between two MoS₂ bilayers affects the electronic properties.

Previous theoretical studies show that the C7 and T stacking patterns give the lowest energy for many heterobilayers,^27,29 and the electronic structure is more or less the same with different stacking orders. Here, we adopt two different stacking orders for the trilayers (see Fig. 3), namely, the ABA and ACA. For the ABA trilayer, the interface AB is in C7 stacking, while for the ACA trilayer, the interface AC is in T stacking. Again, we find that the two stacking orders give rise to nearly the same electronic properties.

Fig. 3 Top and side views of MoS₂/MX₂/MoS₂ (M = Mo, W; X = S, Se) trilayers with (a and b) ABA stacking with a C7 interface and (c and d) ACA stacking with a T interface, respectively.

The polarization within the S/Se interfaces is responsible for the direct-gap character of heterobilayers in previous studies.^26,27 The MoS₂/MoSe₂/MoS₂ trilayer entails two S/Se interfaces. In view of the MoS₂ bilayer possessing an indirect bandgap, the intercalation of the MoSe₂ monolayer induces an indirect to direct transition. As shown in Fig. 4a, the MoS₂/MoSe₂/MoS₂ trilayer exhibits a direct bandgap of 0.69 eV. The VBM is located at the K point and is mainly contributed by the MoSe₂ layer, while the CBM is also located at the K point and is mainly contributed by MoS₂ layers. It is desirable that CBM and VBM are contributed from two different TMDC monolayers, particularly for the electron–hole separation. ESI (Fig. S2†) shows a more accurate HSE06 computation of band structures of the trilayers. The computed bandgap is 0.97 eV, wider than that from PBE computation. However, the electronic structures and the VBM and CBM are similar to those based on PBE computation.

Fig. 4 Computed band structures (PBE) of (a) MoS₂/MoSe₂/MoS₂, (b) MoS₂/WS₂/MoS₂, and (c) MoS₂/WSe₂/MoS₂ trilayer with ABA stacking, respectively. Computed band structures (PBE) of (d) MoS₂/MoSe₂ superlattice, (e) MoS₂/WS₂ superlattice, and (f) MoS₂/WSe₂ superlattice with the AB stacking, respectively. The green lines mark contribution from MoS₂ layers while the red lines mark contribution from the MoSe₂, WS₂ or WSe₂ layer.

Because of the lack of the S/Se interfaces, as shown in Fig. 4b, the MoS₂/WS₂/MoS₂ trilayer still exhibits an indirect gap of 1.05 eV. The VBM is located at the Γ point and is mainly contributed by the WS₂ monolayer, while the CBM is located at the K point and is mainly contributed by the two MoS₂ layers. Computed band structures based on the HSE06 functional is shown in ESI Fig. S2.† Again, the trilayer still exhibits the indirect-gap character but the bandgap increases to 1.47 eV.

The MoS₂/WSe₂/MoS₂ trilayer still exhibits a direct gap of 0.39 eV due to the presence of the two Se/S interfaces (see Fig. 4c). The VBM at the K point is mainly contributed by the WSe₂ layer, while the CBM at the K point is mainly contributed by MoS₂ layers. Again, as shown in ESI Fig. S2,† HSE06 calculation confirms the main character of electronic properties. To further analyze the effect of the polarization within the Se/S interfaces, charge transfer between neighboring layers is computed (see ESI Table S1†). For MoS₂/MoSe₂/MoS₂ and MoS₂/WSe₂/MoS₂ trilayers, a 0.02 e per unit cell is transferred from the MoSe₂ (or WSe₂) layer to the MoS₂ layer. In contrast, for the MoS₂/WS₂/MoS₂ trilayer with S/S interfaces, the charge transfer between two neighboring layers is nearly zero. This result further demonstrates that the interfacial polarization has an important effect on the electronic properties of the trilayer heterostructures.

Lastly, we consider a 3D superlattice made of hybrid MoS₂ monolayers and other monolayers. As shown in Fig. 4, for each superlattice, two stacking orders including AB with a C7 interface and AC with a T interface are investigated. The binding energies and cell parameters for the AB and AC stacking are close to one another in all the configurations (see ESI Table S1†). For the MoS₂/MoSe₂ superlattice, PBE calculations suggest that its bandgap is still indirect, with a value of 0.62 and 0.59 eV respectively, for the AB and AC stacking. The bandgap is about 0.1 eV less than that of the corresponding trilayer. The CBM is still located at the K point and contributed mainly by the MoS₂ layers (Fig. 4d), while the VBM energy at the Γ and K point differs only by 10 meV, and is mainly contributed by the MoSe₂ layers. On the other hand, the HSE06 calculations suggest that the MoS₂/MoSe₂ superlattice is a direct-gap semiconductor with a value of 0.88 and 0.92 eV, respectively, for the AB and AC stacking. Here, the VBM energy in the K point is 77 meV lower than the Γ point (ESI Fig. S2†). For the MoS₂/WS₂ superlattice, both PBE and HSE06 calculations suggest that it is an indirect-gap semiconductor (Fig. 4e) with a bandgap value 0.95 and 1.35 eV, respectively, for the AB stacking. Finally, both PBE and HSE06 calculations suggest that the MoS₂/WSe₂ superlattice is a direct-gap semiconductor with a value of 0.3 and 0.5 eV for the AB stacking, and 0.35 and 0.54 eV for the AC stacking. Both bandgaps are smaller than those of the corresponding trilayers. Again, the bandgap reduction is mainly due to a slightly enlarged cell parameter (see ESI Table S1†).

Conclusions

In conclusion, our first-principles calculations show that the BN monolayer is a highly effective single sheet to decouple the interlayer vdW interaction of the MoS₂ bilayer. The resulting vdW trilayer heterostructure can recover the electronic structures of a single MoS₂ monolayer, particularly its direct-gap character. Further study of the 3D MoS₂/BN superlattices confirms the effectiveness of the BN monolayer for decoupling the interlayer interaction. Expectedly, this conclusion has implications to MoS₂ based heterostructures as well as to other TMDC-based vdW heterostructures. We have also investigated intercalation of a TMDC MoSe₂ or WSe₂ sheet between two MoS₂ sheets and found that the resulting vdW trilayer undergoes an indirect-gap to direct-gap transition due to the newly formed heterogeneous S/Se interfaces. In contrast, the MoS₂/WS₂/MoS₂ vdW trilayer still retains the indirect-gap character of the MoS₂ bilayer due to the lack of the heterogeneous S/Se interfaces. Again, the 3D superlattice of the MoS₂/TMDC heterostructures also exhibits similar electronic band characters to the MoS₂/TMDC/MoS₂ trilayer, albeit a slight decrease of the bandgap than that of their trilayer counterparts. In view of recent successful fabrication of vdW heterostructures by stacking a graphene sheet on top of MoS₂ sheets or vice versa,¹⁹ the vdW trilayers and superlattices investigated in this study together with their novel properties may be tested in the laboratory in the near future.

Acknowledgements

XCZ is grateful for valuable discussions with Professors Ali Adibi, Eric Vogel, Joshua Robinson, and Ali Eftekhar. The USTC group is supported by the National Basic Research Programs of China (nos 2011CB921400 and 2012CB 922001), NSFC (grant nos 21121003, 11004180, and 51172223), and One Hundred Person Project of CAS, Strategic Priority Research Program of CAS (XDB01020300). The UNL group is supported by ARL (grant no. W911NF1020099), NSF (grant no. DMR-0820521), UNL Nebraska Center for Energy Sciences Research, University of Nebraska Holland Computing Center, and a grant from USTC for (1000plan) Qianren-B summer research.

References

1. B. Radisavljevic, A. Radenovic, J. Brivio, V. Giacometti and A. Kis, Nat. Nanotechnol., 2011, 6, 147–150.
2. H. Wang, L. L. Yu, Y. H. Lee, Y. M. Shi, A. Hsu, M. L. Chin, L. J. Li, M. Dubey, J. Kong and T. Palacios, Nano Lett., 2012, 12, 4674–4680.
3. B. Radisavljevic, M. B. Whitwick and A. Kis, ACS Nano, 2011, 5, 9934–9938.
4. Y. Yoon, K. Ganapathi and S. Salahuddin, Nano Lett., 2011, 11, 3768–3773.
5. K. F. Mak, C. Lee, J. Hone, J. Shan and T. F. Heinz, Phys. Rev. Lett., 2010, 105, 136805.
6. K. F. Mak, K. He, C. Lee, G. H. Lee, J. Hone, T. F. Heinz and J. Shan, Nat. Mater., 2012, 12, 207–211.
7. D. Xiao, G.-B. Liu, W. Feng, X. Xu and W. Yao, Phys. Rev. Lett., 2012, 108, 196802.
8. A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.-Y. Chim, G. Galli and F. Wang, Nano Lett., 2010, 10, 1271–1275.
9. D. Voiry, M. Salehi, R. Silva, T. Fujita, M. Chen, T. Asefa, V. B. Shenoy, G. Eda and M. Chhowalla, Nano Lett., 2013, 13, 6222–6227.
10. H. L. Zhuang and R. G. Hennig, Chem. Mater., 2013, 25, 3232–3238.
11. S. Bertolazzi, J. Brivio and A. Kis, ACS Nano, 2011, 5, 9703–9709.
12. J. Pu, Y. Yomogida, K.-K. Liu, L.-J. Li, Y. Iwasa and T. Takenobu, Nano Lett., 2012, 12, 4013–4017.
13. Y. Li, Z. Zhou, S. Zhang and Z. Chen, J. Am. Chem. Soc., 2008, 130, 16739–16744.
14. K. F. Mak, C. Lee, J. Hone, J. Shan and T. F. Heinz, Phys. Rev. Lett., 2010, 105, 136805.
15. H. J. Conley, B. Wang, J. I. Ziegler, R. F. Haglund, S. T. Pantelides and K. I. Bolotin, Nano Lett., 2013, 13, 3626–3630.
16. E. S. Kadantsev and P. Hawrylak, Solid State Commun., 2012, 152, 909–913.
17. A. Geim and I. Grigorieva, Nature, 2013, 499, 419–425.
18. L. Ponomarenko, A. Geim, A. Zhukov, R. Jalil, S. Morozov, K. N. I. Grigorieva, E. Hill, V. Cheianov, V. Fal'ko and K. Watanabe, Nat. Phys., 2011, 7, 958–961.
19. L. Britnell, R. Gorbachev, R. Jalil, B. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M. Katsnelson, L. Eaves and S. Morozov, Science, 2012, 335, 947–950.
20. S. Haigh, A. Gholinia, R. Jalil, S. Romani, L. Britnell, D. Elias, K. Novoselov, L. Ponomarenko, A. Geim and R. Gorbachev, Nat. Mater., 2012, 11, 764–767.
21. S. Bertolazzi, D. Krasnozhon and A. Kis, ACS Nano, 2013, 7, 3246–3252.
22. T. Georgiou, R. Jalil, B. D. Belle, L. Britnell, R. V. Gorbachev, S. V. Morozov, Y.-J. Kim, A. Gholinia, S. J. Haigh and O. Makarovsky, Nat. Nanotechnol., 2013, 8, 100–103.
23. W. J. Yu, Z. Li, H. Zhou, Y. Chen, Y. Wang, Y. Huang and X. Duan, Nat. Mater., 2012, 12, 246–252.
24. A. Anto Jeffery, C. Nethravathi and M. Rajamathi, J. Phys. Chem. C, 2013, 118, 1386–1396.
25. H.-P. Komsa and A. V. Krasheninnikov, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 88, 085318.
26. H. Terrones, F. López-Urías and M. Terrones, Sci. Rep., 2013, 3, 1549.
27. (a) N. Lu, H. Guo, L. Li, J. Dai, L. Wang, W.-N. Mei, X. Wu and X. C. Zeng, Nanoscale, 2014, 6, 2879–2886; (b) H. Guo, N. Lu, L. Wang, X. Wu and X. C. Zeng, J. Phys. Chem. C, 2014, 118 DOI:10.1021/jp501734s.
28. (a) Y. Ma, Y. Dai, M. Guo, C. Niu and B. Huang, Nanoscale, 2011, 3, 3883–3887; (b) J. Kang, J. Li, S-S. Li, J.-B. Xia and L.-W. Wang, Nano Lett., 2013, 13, 5485–5490; (c) J. Kang, S. Tongay, J. Zhou, J. Li, and J. Wu, Appl. Phys. Lett., 2013, 102, 012111.
29. K. Kośmider and J. Fernández-Rossier, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 87, 075451.
30. C. Dean, A. Young, I. Meric, C. Lee, L. Wang, S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim and K. Shepard, Nat. Nanotechnol., 2010, 5, 722–726.
31. K. Novoselov and A. C. Neto, Phys. Scr., 2012, 2012, 014006.
32. G. Kresse and J. Furthmüller, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 54, 11169.
33. G. Kresse and J. Furthmüller, Comput. Mater. Sci., 1996, 6, 15–50.
34. G. Kresse and J. Hafner, Phys. Rev. B: Condens. Matter Mater. Phys., 1993, 47, 558.
35. G. Kresse and D. Joubert, Phys. Rev. B: Condens. Matter Mater. Phys., 1999, 59, 1758.
36. J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865.
37. J. Klimeš, D. R. Bowler and A. Michaelides, J. Phys.: Condens. Matter, 2010, 22, 022201.
38. J. Klimeš, D. R. Bowler and A. Michaelides, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 83, 195131.
39. C. Ataca, H. Sahin and S. Ciraci, J. Phys. Chem. C, 2012, 116, 8983–8999.
40. H. L. Zhuang and R. G. Hennig, J. Phys. Chem. C, 2013, 117, 20440–20445.
41. E. Sanville, S. D. Kenny, R. Smith and G. Henkelman, J. Comput. Chem., 2007, 28, 899–908.
42. J. Heyd, G. E. Scuseria and M. Ernzerhof, J. Chem. Phys., 2006, 124, 219906.
43. Y.-S. Kim, K. Hummer and G. Kresse, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 80, 035203.
44. A. Sengupta, R. K. Ghosh and S. Mahapatra, IEEE Trans. Electron Devices, 2013, 60, 2782–2787.
45. Y. Y. Hui, X. Liu, W. Jie, N. Y. Chan, J. Hao, Y.-T. Hsu, L.-J. Li, W. Guo and S. P. Lau, ACS Nano, 2013, 7, 7126–7131.

---

Footnotes

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4nr00783b

‡ Both authors contributed equally to this work

---