HfS2 van der Waals

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Broken-Gap Type-III Band Alignment in WTe/HfS van der Waals Heterostructure 2

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Chengan Lei, Yandong Ma, Xilong Xu, Ting Zhang, Baibiao Huang, and Ying Dai J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b07862 • Publication Date (Web): 26 Aug 2019 Downloaded from pubs.acs.org on August 27, 2019

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The Journal of Physical Chemistry

Broken-Gap Type-III Band Alignment in WTe2/HfS2 van der Waals Heterostructure Chengan Lei, Yandong Ma,* Xilong Xu, Ting Zhang, Baibiao Huang, and Ying Dai* School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Shandanan Street 27, Jinan 250100, China

ABSTRACT: Van der Waals heterostructures (vdWHs) are attracting a lot of interest for fundamental studies and fabricating novel devices. Currently, most vdWHs exhibit type-I or type-II band alignment, and few systems have been shown to be in the type-III class. Herein, we show firstprinciples evidence that WTe2/HfS2 vdWH possesses the long-sought type-III band alignment with a broken gap, providing a promising platform for developing tunnel field-effect transistor. Moreover, the electronic features of WTe2/HfS2 vdWH can be effectively modulated via external strain and electric field. Particularly, the interesting transition from type-III to type-II band alignment can be observed in WTe2/HfS2 vdWH upon applying strain or electric field, which holds great potential for designing multifunctional device. Our study not only predicts an extraordinary vdWH with type-III band alignment but also provides an outstanding candidate for realizing multiple-band-alignment transformation. 1. INTRODUCTION Van der Waals heterostructures (vdWHs)—stacks of atomic thin two-dimensional (2D) layered materials (e.g., graphene or transition-metal dichalogenides)—have simulated intensive research interest as they allow flexible integration of highly distinct 2D materials at atomic scale, thus providing a versatile platform for diverse electronics and optoelectronics.1-14 An essential feature of such heterostructures is the band alignment, which can be classified into three types, namely, straddling type-I, staggered type-II and broken-gap type-III.15 And each type of band alignment corresponds to particular device applications. Type-I band alignment is beneficial for spatially confining electrons and holes so that efficient recombination can be achievable, and hence type-I band alignment is favorable for applications in optical devices.16,17 Different from type-I band alignment, the large band offset in type-II band alignment allows significant carrier separation, which is useful for unipolar electronic device applications and photocatalysis.18,19 While for type-III band 1

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alignment, it can facilitate the engineering of the conduction to valence band transition energy, thus holding unique promise in tunnel field effect transistors and wavelength photodetectors.20,21 Considering those valuable applications, intensive research has been devoted to vdWHs. However, most vdWHs reported to date harbor a type-I or type-II band alignment, and few vdWHs have been shown to be with a type-III band alignment, which severely limits the applications of 2D materials in tunnel field effect transistors. 2D transition-metal dichalcogenide (TMDC) semiconductors are promising building blocks for novel vdWHs.22 In TMDCs, individual layers are held together by vdW interactions, without surface dangling bonds.5 The vdWHs built up from 2D TMDCs would in principle offer atomically regulated interfaces and thereby sharp band edges.23,24 To date, about 40 stable compounds of TMDCs have been obtained, which introduces more versatility, including conductors and semiconductors with varying bandgaps.25-27 Unusual behaviors, like the valley polarization,28 superconductivity29 and lattice symmetry-induced valley Hall effect,30 are also observed. With such versatility, existing TMDC-based vdWHs have already led to the observation of numerous interesting physical phenomena.22 Most of these TMDC-based vdWHs possess the type-II band alignment with interband transition.25 Nonetheless, the extensive library of 2D TMDCs with selectable material properties offers a plethora of opportunities for achieving vdWHs with a type-III band alignment. Remarkably enough, in this work, we show that the type-III band alignment can be manifested in WTe2/HfS2 vdWH. As both WTe2 and HfS2 are standard 2D semiconducting TMDCs and have been extensively studied in electronic and photoelectric devices, the WTe2/HfS2 vdWH deserves high experimental feasibility.31-33 Using first-principles calculations, we systematically investigate the electronic properties of WTe2/HfS2 vdWH and unveil the underlying physical mechanism for such band alignment. We also investigate the strain and electric field engineering effects on the electronic behaviors of WTe2/HfS2 vdWH and find that its electronic properties are sensitive to external strain and electric field. Importantly, the transition between type-II and type-III band alignments can be easily induced in WTe2/HfS2 vdWH by applying a small external strain or electric field. Our findings will pave the avenue for designing high-performance tunnel field-effect transistors and multiplepurposed optoelectronic devices based on this novel vdWH. 2. METHODS All calculations are performed based on density functional theory (DFT) as implemented in the Vienna ab initio Simulation Package (VASP).34 The projected augmented wave (PAW) is adopted to describe the ionic potential.35 The generalized gradient approximation (GGA) in the form of Perdew2


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Burke-Ernzerhof (PBE) approach is used for describing the exchange correlation interaction.36 A cutoff energy of 500 eV is set for the plane-wave expansion. The thickness of the vacuum region is set to be about 16 Å to eliminate the interactions between adjacent layers. Crystal structures are fully relaxed with the force tolerance of 0.01 eV/Å, and the convergence criterion for energy is set to be 10-6 eV. 7×7×1 and 9×9×1 grids for k-point sampling are used for geometry optimization and static electronic structure calculations, respectively. A long-range van der Waals interaction is incorporated employing the DFT-D2 method.37 The phonon spectra is obtained using the PHONOPY code.38 The ab initio molecular dynamics (AIMD) simulations are performed using the canonical ensemble with a Nosé thermostat.39 3. RESULTS AND DISCUSSION The crystal structures of 2D WTe2 and HfS2 are shown in Figure 1a and 1b. 2D WTe2 features the H phase, in which the Te atoms from two opposite surfaces are eclipsed. While for 2D HfS2, it adopts the T phase, where the S atomic ring from the top-layer is rotated by 60° with respect to that from the bottom-layer. The optimized lattice constants for 2D WTe2 and HfS2 are found to be 3.55 and 3.64 Å, respectively, which agree well with previous studies.40-42 The electron localization function (ELF) for both systems are shown in Figure 1d and 1e, from which we can see the covalent character for the W(Hf)-Te(S) bonding. Figure 1f and 1g present the band structures and partial density of states (PDOS) for 2D WTe2 and HfS2. 2D WTe2 is a direct-gap semiconductor with a band gap of 1.07 eV, whose valence band maximum (VBM) and conduction band minimum (CBM) both locate at the K point. While for 2D HfS2, it also shows semiconducting properties, but with an indirect band gap of 1.28 eV. The VBM of 2D HfS2 lies at the  point and the CBM locates at the M point. Besides, the band structures of two systems are also calculated using HSE06 functional.43 As can be seen in Figure S1, the shapes of the bands are consistent with the PBE results, but the band gaps are increased, which are found to be 1.98 eV for HfS2 and 1.47 eV for WTe2. And similar to most of the other semiconducting 2D TMDCs,22,25 for both structures, the CBM is mainly contributed by metal d orbital, while the VBM is dominated by chalcogen p and metal d orbitals; see Figure 1f and 1g.

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Figure 1. Top and side views of the crystal structure of 2D (a) WTe2 and (b) HfS2. The black rhombus and rectangle mark the unit cells. (c) Brillouin zone of 2D WTe2 and HfS2 with marking the highsymmetry points. Electron localization functions (ELFs) of 2D (d) WTe2 and (e) HfS2. The band structures and partial density of states of 2D (f) WTe2 and (g) HfS2. The Fermi level is set to 0 eV. To construct WTe2/HfS2 vdWH, the unit cell of 2D WTe2 is used to match the unit cell of 2D HfS2. The lattice mismatch between them is only 1.1%, which is so small that the experimental fabrication of such vdWH would be highly achievable. Therefore, we consider six high-symmetry stacking patterns, which are shown in Figure S3: in the atop-I (II) pattern, Te atom sites above Sup atom and W atom lies above Hf (Sdown) atom; in the fcc-I (II) pattern, Te atom is above Sdown atom and W atom sites above Sup (Hf) atom; in the hcp-I (II) pattern, Te atom lies above Hf atom and W atom is above Sdown (Sup) atom. To assess the most stable configuration, the interface binding energies are calculated, which are defined as 𝐸𝑏 = 𝐸𝑡𝑜𝑡𝑎𝑙 ― 𝐸𝑊𝑇𝑒2 ― 𝐸𝐻𝑓𝑆2. Here 𝐸𝑡𝑜𝑡𝑎𝑙, 𝐸𝑊𝑇𝑒2 and 𝐸𝐻𝑓𝑆2 is the energy of WTe2/HfS2 vdWH, 2D WTe2 and 2D HfS2, respectively. The corresponding results are summarized in Table S1, from which we can see that the most stable configuration for WTe2/HfS2 vdWH is fcc-I pattern; see Figure 2a. We wish to emphasize that in experiment, the most stable configuration is highly possible to be achieved.44,45 While for the other metastable configurations, the possibility for their experimental realization is relatively low, but they can be obtained through additional modulations.46 So in the following, we only focus on the fcc-I pattern for WTe2/HfS2 vdWH unless otherwise specified. And for more information about the other patterns, please see Figure S3 in Supporting Information. 4


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To confirm the stability of WTe2/HfS2 vdWH, we first study its phonon dispersions. As shown in Figure 2d, there is no imaginary phonon branch in the whole Brillouin zone, indicating its high dynamical stability. And from the phonon spectra we can also observe that there are three low frequency optical vibration modes (marked by the red line in Figure 2d) close to the acoustic vibration modes, which implies the relative week interlayer coupling in the heterostructure.47,48 The weak interlayer interaction can also be visualized through analyzing the ELF of WTe2/HfS2 vdWH, which is shown in Figure 2e. It can be seen that no electron is localized at the region between 2D WTe2 and HfS2, suggesting the weak van der Waals interaction. To confirm its thermal stability, we also perform AIMD for WTe2/HfS2 vdWH at 500 K for 5 ps. As presented in Figure S2, no structure deformation is observed and total energy exhibits a small amplitude of fluctuation, suggesting the thermal stability of WTe2/HfS2 vdWH.

Figure 2. (a) Crystal structure of WTe2/HfS2 vdWH from top and side views. (b) Schematic diagrams of the band alignment between 2D WTe2 and HfS2 before and after forming heterostructure. (c) Band structure and partial density of state (PDOS) of WTe2/HfS2 vdWH. The Fermi level is set to 0 eV. (d) Phonon spectra of WTe2/HfS2 vdWH. (e) Electron localization functions of WTe2/HfS2 vdWH. (f) Plane-averaged charge density difference of WTe2/HfS2 vdWH. Insets of (f) are the corresponding three-dimensional (3D) isosurface of the electron density difference, where the red and green isofurfaces represent electron accumulation and depletion, respectively, and the isosurface value is 0.00018 e Å−3. 5



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The band structure and PDOS of WTe2/HfS2 vdWH are depicted in Figure 2c. By comparing with the band structures of individual 2D WTe2 and HfS2 shown in Figure 1, we can see the band structure of WTe2/HfS2 vdWH is a rough sum of those of each constituent. However, the CBM of WTe2/HfS2 vdWH lies below the Fermi level, and the VBM locates above the Fermi level. Namely, its highest valence band edge from WTe2 is above the lowest conduction band edge from HfS2. This strongly suggests that the heterostructure harbors a broken-gap type-III band alignment. We also employ HSE06 functional to confirm its band alignment, and the corresponding band structure is shown in Figure S1. Clearly, type-III band alignment is preserved. Considering of expensive computational costs of HSE06 functional, we only use PBE functional in the following. It should be noted that such type-III vdWHs might possess obvious negative differential resistance (NDR) phenomenon, due to the existence of band-to-band tunneling.49 To reveal the underlying mechanism of such band alignment, the schematic diagram is plotted in Figure 2b. The work function, an intrinsic reference for band alignment, is calculated using the following equation: Φ = Evac − Ef. Here, Evac is the energy level of a stationary electron in the vacuum nearby the surface, and Ef is the Fermi level. Before contacting with each other, the work function of 2D WTe2 and HfS2 are 4.56 eV and 6.30 eV, respectively. Upon forming heterostructure, electrons would spontaneously flow from WTe2 to HfS2 due to the large difference in their work functions. Accordingly, the Fermi levels of 2D HfS2 and WTe2 shift upwards and downwards, respectively, and then they reach at the same level. The resultant work function of the vdWH is 5.07 eV, which is as expected slightly lower than that of 2D HfS2 and higher than that of 2D WTe2. Meanwhile, as HfS2 in WTe2/HfS2 vdWH accumulates charges and WTe2 depletes charges, a build-in electric field pointing from WTe2 to HfS2 occurs. Accompanying with the charge accumulation and depletion upon forming the vdWH, the valence band edge of WTe2 up-shifts over the Fermi level and the conduction band edge of HfS2 down-shifts below the Fermi level. Thus, the broken-gap type-III band alignment is observed in WTe2/HfS2 vdWH. We wish to emphasize that, in such a vdWH, the electrons are prone to tunnel directly from VBM of WTe2 layer to CBM of HfS2 layer, i.e., the band-to-band tunneling (BTBT) transport, which is robust against the thermal distribution and is highly desirable for tunnel field-effect transistors. To support this formation mechanism, we investigate the charge redistribution in WTe2/HfS2 vdWH. The plane-averaged charge density difference for the vdWH is calculated using the formula Δρ(z) = Δρ(WTe2/HfS2) − Δρ(WTe2) − Δρ(HfS2). Here, Δρ(WTe2/HfS2), Δρ(WTe2) and Δρ(HfS2) represent the plane-averaged charge density of WTe2/HfS2 vdWH, isolated WTe2 layer and isolated HfS2 layer, respectively. The calculated plane-averaged charge density difference as well as the threedimensional isosurface of the charge density difference are shown in Figure 2f, from which it can be 6


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clearly seen that WTe2 layer exhibits a charge depletion, while the HfS2 layer shows a charge accumulation, indicating the electron transfer between WTe2 and HfS2. To further quantify such charge redistribution, we carry out Bader charge analysis, which reveals that the transferred electron from WTe2 layer to HfS2 layer in WTe2/HfS2 vdWH is 0.035 e. This firmly establishes that a built-in electric field is formed in WTe2/HfS2 vdWH, and validates the formation mechanism mentioned above. As 2D materials, the electronic properties of WTe2/HfS2 vdWH are expected to be tunable by applying external strain, which has been widely used in 2D systems.40,50-53 Then, we first investigate the biaxial strain-engineering effect on the electronic properties of WTe2/HfS2 vdWH. The biaxial strain is defined as ε = (a-a0)/a×100%, where a and a0 are the lattice parameters of the strained and unstrained systems, respectively. The moderate strain ranges from −5% to 5% is considered here. Figure 3a shows the band structures of WTe2/HfS2 vdWH under various biaxial strain. When applying tensile strain, the VBM of WTe2 layer at the K point (marked by the orange lines) shifts down obviously with respect to the Fermi level with increasing strain, meanwhile, the VBM at the  point shifts up slightly. Under > 3% strain, the highest valence band of WTe2 layer at the  point shifts above that at the K point, that is, the VBM of WTe2 layer moves from the K point to the  point, giving rise to a direct-to-indirect gap transition. While for HfS2 layer, the CBM at the M point shifts up with respect to the Fermi level when increasing tensile strain. And under > 3% strain, the CBM of HfS2 lies above, instead of below, the Fermi level. Therefore, the band structure of WTe2/HfS2 vdWH transforms from the type-III band alignment to type-II band alignment under tensile biaxial strain. This suggests that WTe2/HfS2 vdWH can also be used for various optoelectronics and solar energy conversion devices as type-II band alignment can effectively facilitate the spontaneous separation of electron-hole pairs.54 Such intriguing transition between type-III and type-II band alignments is extremely valuable for designing multi-valued logic devices.21 As shown in Figure 3a, different form the cases with tensile strain, WTe2/HfS2 vdWH under biaxial compressive strain always exhibits the type-III band alignment, with the VBM from WTe2 at the  point locating above the CBM from HfS2 around the M point In addition the topmost valence band from WTe2 at the M point gradually rises with increasing compressive strain and even overlaps with the CBM from HfS2 under -5% strain. It is worth mentioning that biaxial strains may modify the interlayer charge transfer and further change the band structure. Therefore, we calculate the evaluation of Bader charge transfer between WTe2 and HfS2 layers with biaxial strain. As shown in Figure S5, within the strain range of -5%~5%, Bader charge transferred from WTe2 layer to HfS2 layer decreases with increasing strain. 7



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Figure 3. (a) Band structures of WTe2/HfS2 vdWH under various biaxial strain with orange and blue lines marking the contributions from WTe2 and HfS2 layers, respectively. The Fermi level is set to 0 eV. (b) Variation of charge transfer and binding energy as a function of the interlayer distance for WTe2/HfS2 vdWH. (c) 3D isosurface of the charge density difference for WTe2/HfS2 vdWH under various vertical strain. Red and green isosurfaces correspond to electron accumulation and depletion, respectively. We also investigate the effect of vertical strain, introduced by changing the interlayer distance, on the electronic behaviors of vdWH. In experiment, the interlayer distance is modulated by imposing pressure with a scanning tunneling microscopy tip, inserting hexagonal BN dielectric layer, or vacuum thermal annealing.51,55 Here, we tune the interlayer distance of WTe2/HfS2 vdWH by ±0.5 Å with respect to the equilibrium one. From Figure S4, we can see that the band structure of WTe2/HfS2 vdWH preserves the type-III band alignment with various interlayer distance. This indicates that the unique band alignment of WTe2/HfS2 vdWH can robustly withstand the vertical stress. To get further insight into the effect of vertical strain on WTe2/HfS2 vdWH, the evolution of binding energy and charge transfer as functions of the interlayer distance is also studied. The corresponding results are plotted Figure 3b. One can observe that the binding energy remains negative regardless of changing the interlayer distance, revealing that WTe2/HfS2 vdWH is energetically stable under vertical strain. Besides, the transferred charges increase monotonically with reducing interlayer distance, which can also be visualized from the 3D isosurface of the charge density differences shown in Figure 3c. This is attributed to increased strength of the interlayer interaction. 8


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Besides strain, external electric field is also widely used to tune the electronic properties of 2D materials.56,57 We then study the effect of external electric field on the electronic properties of WTe2/HfS2 vdWH. Herein, the external electric field is applied perpendicular to the stacking layers. The direction of positive electric field is taken as pointing from HfS2 layer to WTe2 layer, while that of the negative electric field is taken as pointing from WTe2 layer to HfS2 layer; see Figure 4a. The band edge positions and band structures of WTe2/HfS2 vdWH under various electric fields are plotted in Figure S6 and Figure 4d. Under negative electric field, the band alignment for WTe2/HfS2 vdWH preserves type-III. With increasing the negative electric field, the band edge positions of WTe2 layer are pulled up, while those of HfS2 layer are pushed down. In other word, the tunneling energy window, defined as the energy difference between VBM of WTe2 and CBM of HfS2, is broadened. As a result, the amount of electrons tunneling from the VBM of WTe2 to the CBM of HfS2 are expected to be increased significantly. This could enhance the tunneling probability in the BTBT process and then further increase the tunneling current, which is promising for applications in tunnel field-effect transistors. When applying positive electric field, the band edges of WTe2 layer are pushed down, while those of HfS2 layer are pulled up, thus inducing the interesting transition from type-III band alignment to type-II band alignment in WTe2/HfS2 vdWH. These different responses of the electronic properties to various electric field are crucial to design novel electronic devices. Based on the above results, we proposed a multiple-purposed device prototype based on WTe2/HfS2 vdWH, which is shown in Figure 4c. The device consists of a source, a drain, a channel, and two gates for introducing the external electric field. By applying negative gate voltage, this device with type-III band alignment can be used for tunnel field-effect transistors. And when applying positive gate voltage, this device with type-II band alignment can be used for unipolar electronic applications. Such kind of multifunctional device deserves further experimental effects. The band evolution under electric field can be easily understood by analyzing the relation between the directions of electric field and intrinsic built-in electric field. As shown in Figure 4a, since the directions of built-in electric field and negative electric field are consistent, built-in electric field is reinforced upon increasing the negative electric field. Then, more charges transfer from WTe2 layer to HfS2 layer, leading to the increase of band offset between WTe2 and HfS2 layers. As a consequence, the band edges of WTe2 shift upward and the band edges of HfS2 shift downward, which then broadens the tunneling energy window of WTe2/HfS2 vdWH. On the contrast, the directions of positive electric field and intrinsic built-in electric field are opposite. When applying positive electric field on WTe2/HfS2 vdWH, the build-in electric field is weakened and then the amount of charges transferred from WTe2 to HfS2 layers is reduced. This would decreases the band offset between WTe2 9



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and HfS2 layers. Therefore, upon increasing positive electric field on WTe2/HfS2 vdWH, the band edges of WTe2 and HfS2 shift downward and upward, respectively, and even the transition between type-III and type-II band alignments is observed.

Figure 4. (a) Schematic diagram of WTe2/HfS2 vdWH under external electric field. (b) Band offset and Bader charge transfer in WTe2/HfS2 vdWH under electric fields. (c) Schematic diagram of multiple-purposed device based on WTe2/HfS2 vdWH. (d) Band structures of WTe2/HfS2 vdWH under electric fields with orange and blue lines marking the contributions from WTe2 and HfS2 layers, respectively. Insets of (d) represent tunneling energy windows. The Fermi level is set to 0 eV.

4. CONCLUSIONS In summary, through first-principles calculations, we demonstrate that WTe2/HfS2 vdWH exhibits the remarkable type-III broken-gap band alignment. The underlying physical mechanism for forming such band alignment is revealed. We also find that the electronic properties of WTe2/HfS2 vdWH can be effectively modulated by applying external strain or electric field. And most importantly, with applying strain or electric field, the transition between type-III and type-II band alignments can be observed in WTe2/HfS2 vdWH. Our findings thus provide a compelling platform for exploring tunnel field effect transistors as well as multiple-purposed electronic devices. 10


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ASSOCIATED CONTENT Supporting Information Supporting Information Available: Mechanical and electronic characteristics of WTe2, HfS2 monolayers and WTe2/HfS2 vdWH; band structures of HfS2, WTe2 monolayers and WTe2/HfS2 vdWH based on HSE06 functional; AIMD simulation for WTe2/HfS2 vdWH; six different stacking patterns and corresponding band structures of WTe2/HfS2 vdWH; band structures of WTe2/HfS2 vdWH under different vertical strains; the variation of Bader charge transfer as a function of the biaxial strain for WTe2/HfS2 vdWH; band edge positions of the WTe2 and HfS2 layers in WTe2/HfS2 vdWH under various electric fields.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (Y.M.). *E-mail: [email protected] (Y.D.). ORCID Yandong Ma: 0000-0003-1572-7766 Ying Dai: 0000-0002-8587-6874 Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Nos. 11804190 and 21333006), Shandong Provincial Natural Science Foundation of China (Nos. ZR2019QA011 and ZR2019MEM013), Qilu Young Scholar Program of Shandong University, Taishan Scholar Program of Shandong Province, and 111 Project (No. B13029). REFERENCES (1) Novoselov, K.; Mishchenko, A.; Carvalho, A.; Neto, A. C. 2D Materials and van der Waals Heterostructures. Science 2016, 353, aac9439. (2) Geim, A. K.; Grigorieva, I. V. Van der Waals Heterostructures. Nature 2013, 499, 419-425. (3) Gupta, A.; Sakthivel, T.; Seal, S. Recent Development in 2D Materials Beyond Graphene. Prog. Mater. Sci. 2015, 73, 44-126.

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