Structural and electronic properties of two-dimensional stanene and graphene heterostructure
- Liyuan Wu^{1},
- Pengfei Lu^{1, 4}Email author,
- Jingyun Bi^{1},
- Chuanghua Yang^{2},
- Yuxin Song^{4},
- Pengfei Guan^{3}Email author and
- Shumin Wang^{4, 5}
Received: 3 August 2016
Accepted: 9 November 2016
Published: 25 November 2016
Abstract
Structural and electronic properties of two-dimensional stanene and graphene heterostructure (Sn/G) are studied by using first-principles calculations. Various supercell models are constructed in order to reduce the strain induced by the lattice mismatch. The results show that stanene interacts overall weakly with graphene via van der Waals (vdW) interactions. Multiple phases of different crystalline orientation of stanene and graphene could coexist at room temperature. Moreover, interlayer interactions in stanene and graphene heterostructure can induce tunable band gaps at stanene’s Dirac point, and weak p-type and n-type doping of stanene and graphene, respectively, generating a small amount of electron transfer from stanene to graphene. Interestingly, for model \( \mathrm{S}\mathrm{n}\left(\sqrt{7}\right)/\mathrm{G}(5) \) , there emerges a band gap about 34 meV overall the band structure, indicating it shows semiconductor feature.
Keywords
First-principles Stanene Graphene Heterostructure Structural propertiesBackground
Two-dimensional (2D) materials, such as graphene [1–6], silicene [7–13], germanene [14–16], hexagonal boron nitride (hBN) [17, 18], and transition metal dichalcogenides (TMDs, such as MoS_{2}) [19, 20], have received considerable attention recently because of their outstanding properties and potential applications. These 2D layers can be integrated into a multilayer stack (vertical 2D heterostructure) and have been widely studied experimentally and theoretically, such as graphene/silicene (G/Si) [21, 22], graphene/hexagonal boron nitride (G/hBN) [23, 24], silicene/HBN [25], silicene/GaS [26, 27], TMDCs/graphene [28, 29], stacked TMDCs [30, 31], phosphorene/MoS2 [32], and phosphorene/graphene [33]. The resulting artificial 2D heterostructures provide access to new properties and applications far beyond their simplex components.
Most recently, a new 2D material, stanene (the form of 2D stannum), firstly proposed by Liu et al. [34], has been mentioned as a host material for topological insulator (TI), which are new states of quantum matter with an insulating bandgap in the bulk while conducting states at the edges and protected by time reversal symmetry [35–40]. For instance, stanene and its derivatives could support a large-gap 2D quantum spin Hall (QSH) state and thus enable the dissipation less electric conduction at room temperature. Moreover, stanene could also provide enhanced thermoelectricity [41], topological superconductivity [42], and the near-room-temperature quantum anomalous Hall (QAH) effect [43]. Zhu et al. [41] have reported the successful fabrication of 2D stanene with metallic features on the Bi_{2}Te_{3} (111) substrate by molecular beam epitaxy (MBE). Xu et al. [44] found that varying substrate conditions AB(111), where A = Pb, Sr, Ba and B = Se, Te, considerably tunes electronic properties of stanene, and the supported stanene gives either trivial or QSH states, with significant Rashba splitting induced by inversion asymmetry.
Technically, it is possible to fabricate a heterostructure of stanene on a suitable substrate, in order to form honeycomb-like bilayer atomic structure. Stanene has a hexagonal lattice, as well as the requirement of lattice status of the substrate. The lattice mismatch between the substrate and the stanene should be small, and it should be energetically favorable to stanene to grow in a quasi-two-dimensional growth mode. As one of the popular 2D materials, we propose a question whether stanene can grow on a graphene substrate or stanene/graphene (Sn/G) can form a 2D heterostructure with promising structural and electronic properties.
In this work, we design a new 2D stanene/graphene heterostructure and study its geometric and electronic properties by using first-principles calculations. The results show that stanene interacts overall weakly with graphene via vdW interactions. Therefore, their intrinsic electronic properties can be preserved in stanene/graphene heterostructure. Moreover, interlayer interactions in stanene/graphene heterostructure can induce tunable band gaps at stanene’s Dirac point, and weak p-type and n-type doping of stanene and graphene, respectively. Our paper is organized as follows. In the “Methods” section, we describe the details of computational methods. The results and discussions are presented in the “Results and Discussion” section. Finally, a brief summary is summarized in the “Conclusions” section.
Methods
Our theoretical calculations are performed in the framework of density functional theory (DFT) [45] as implemented in the Vienna ab initio simulation package (VASP) [46]. Valence wave functions are treated by the projector augmented wave (PAW) [47, 48] method that uses pseudopotential operators but keeps the full all-electron wave functions. The interlayer interaction is checked by various exchange-correlation energy functionals, including the local density approximation (LDA) [49], the Perdew–Burke–Ernzerhof (PBE) [50] generalized gradient approximation (GGA), and the PBE with vdW corrections: the vdW-D2 functionals [51]. The plane-wave energy cutoff is set to be 400 eV. We have checked the convergence of k points, and a 5 × 5 × 1 k-sampling generated by the Monkhorst–Pack scheme [52] with Gamma centered for the Brillouin zone is adopted. The structural optimization is allowed to relaxed until the maximum force on each atom becomes at least less than 0.01 eV/Å and the maximum energy change between two steps is smaller than 10^{−5} eV. A vacuum layer of at least 20 Å is used.
Results and Discussion
Geometry and Energetics of Stanene/Graphene
For the monolayer graphene and free-standing low-buckled stanene, the lattice constants we obtained from LDA are 2.45 and 4.56 Å, respectively, which agree well with the reported values of 2.46 and 4.67 Å for graphene and stanene, respectively [53, 54]. Note that the lattice mismatch is as large as 7% even when a supercell consisting of 2 × 2 lateral periodicity of graphene and 1 × 1 stanene is employed. And the matched structure usually forms when the mismatch is small. An appropriate supercell in the bilayer system can be obtained by inducing relative rotations between the stanene and graphene substrates. For a 2D hexagonal lattice, it can be realized to get various lattice angles by longer lattice vectors from the primitive unit cell. For example, the angles corresponding to the lattice vectors for \( \sqrt{3}\times \sqrt{3} \), \( \sqrt{7}\times \sqrt{7} \), \( \sqrt{13}\times \sqrt{13} \), \( \sqrt{21}\times \sqrt{21} \), \( \sqrt{31}\times \sqrt{31} \), \( \sqrt{73}\times \sqrt{73} \), and \( \sqrt{97}\times \sqrt{97} \) unit cells are 30°, 19.1°, 13.9°, 10.9°, 9.0°, 5.8°, and 15.3°, respectively.
Heterostructure configurations for the stanene/graphene bilayers (abbreviated as Sn/G)
Sn/G | a (Å) | α (°) | θ (°) | Δ (Å) | L _{Sn} | L _{G} | L _{Sn/G} | Mismatch (%) | Strain (%) | E _{b} (meV) |
---|---|---|---|---|---|---|---|---|---|---|
\( 3/\sqrt{31} \) | 4.53 | 9 | 111.2 | 0.84 | 13.68 | 13.61 | 13.62 | 0.07 | −0.4 | −76 |
\( 2\sqrt{7}/\sqrt{97} \) | 4.55 | 3.8 | 111.3 | 0.82 | 24.12 | 24.07 | 24.07 | 0.29 | −0.2 | −77 |
\( \sqrt{21}/\sqrt{73} \) | 4.56 | 5.1 | 111.3 | 0.82 | 20.89 | 20.88 | 20.87 | 0.48 | −0.1 | −78 |
\( \sqrt{7}/5 \) | 4.61 | 19.1 | 112.2 | 0.80 | 12.06 | 12.22 | 12.20 | 1.8 | 1.1 | −72 |
\( \sqrt{13}/4\sqrt{3} \) | 4.68 | 16.1 | 112.2 | 0.80 | 16.43 | 16.93 | 16.89 | 3.6 | 2.8 | −57 |
where a and a _{0} are the relaxed (bilayer) and unrelaxed primitive lattice constants.
Electronic Structure
where ΔE _{D} is the shift of graphene’s Dirac point (E _{D}) relative to the Fermi level (E _{F}), that is ΔE _{D} = E _{D} − E _{F}. Our calculated charge carrier concentrations are N _{h} (Sn) = 1.4 × 10^{12} cm^{−2} and N _{e} (G) = 1.6 × 10^{11} cm^{−2} for stanene and graphene in bilayer, respectively. These values are larger than the intrinsic charge carrier concentration of graphene at room temperature ( n = πk_{B} ^{2}T^{2}/6ℏν_{F} ^{2} = 6 × 10^{10}cm^{− 2}) [58]. Furthermore, the charge carrier concentrations of both stanene and graphene in Sn/G heterostructure can be tuned via the interfacial spacing [59]. The self-doping phenomenon in Sn/G heterostructure provides an effective and tunable way for new optoelectronic devices.
Conclusions
In conclusion, by first-principle calculations, we found it is possible to synthesize stanene on the graphene substrate without destroying its characteristics of the Dirac-fermion-like linear dispersion around Dirac points, due to the weak van der Waals interlayer interaction. In addition, multiple phases of different crystalline orientation of stanene and graphene could coexist at room temperature based on our energetics analysis. Moreover, interlayer interactions in stanene and graphene heterostructure can induce tunable band gaps at stanene’s Dirac point, and weak p-type and n-type doping of stanene and graphene, respectively, generating a small amount of electron transfer from stanene to graphene. For stanene on graphene, the gap created by the substrate effect is of the same order as that induced by the SOC effect. Interestingly, for model \( \mathrm{S}\mathrm{n}\left(\sqrt{7}\right)/\mathrm{G}(5) \), there exists a band inversion around the Dirac zones at K point and emerges a band gap about 34 meV overall the band structure, indicating that it shows a semiconductor feature. Our fundamental study of the structural and electronic properties of these stanene/graphene heterostructures may provide important insight and useful guideline for the grown and applications of stanene or other 2D vdW heterostructures.
Declarations
Acknowledgements
This work was supported by the National Basic Research Program of China (973 Program) under Grant No. 2014CB643900, the Open Program of State Key Laboratory of Functional Materials for Informatics, the National Natural Science Foundation of China (No. 61675032), the Shanghai Pujiang Program (Grant No. 14PJ1410600), the National Natural Science Foundation for Theoretical Physics Special Fund “Cooperation Program” (No. 11547039), and Shaanxi Institute of Scientific Research Plan projects (No. SLGKYQD2-05).
Authors’ Contributions
LYW carried out the calculations. LYW and PFL wrote the manuscript. JYB, CHY, YXS, and SMW helped in the discussions and analysis of the results. PFL and PFG proposed the initial work, supervised the analysis, and revised the manuscript. All authors read and approved the final manuscript.
Competing Interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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