⇦Chinese Physics Letters, 2022, Vol. 39, No. 12, Article code 127301 Two-Dimensional Electron Gas in MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ Heterojunction by First Principles Calculation Ruiling Gao (高瑞灵)1†, Chao Liu (刘超)1†, Le Fang (方乐)1†*, Bixia Yao (姚碧霞)1, Wei Wu (吴伟)1, Qiling Xiao (肖祁陵)1, Shunbo Hu (胡顺波)1, Yu Liu (刘禹)1*, Heng Gao (高恒)1,2,3,4, Shixun Cao (曹世勋)1, Guangsheng Song (宋广生)2, Xiangjian Meng (孟祥建)4, Xiaoshuang Chen (陈效双)4, and Wei Ren (任伟)1* Affiliations 1Physics Department, State Key Laboratory of Advanced Special Steel, Materials Genome Institute, Shanghai Key Laboratory of High Temperature Superconductors, International Center of Quantum and Molecular Structures, Shanghai University, Shanghai 200444, China 2Key Laboratory of Green Fabrication and Surface Technology of Advanced Metal Materials (Ministry of Education), Anhui University of Technology, Maanshan 243002, China 3State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China 4State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China Received 18 August 2022; accepted manuscript online 26 October 2022; published online 22 November 2022 †These authors contributed equally to this work.
*Corresponding authors. Email: renwei@shu.edu.cn; fangle@shu.edu.cn; ly4209@shu.edu.cn Citation Text: Gao R L, Liu C, Fang L et al. 2022 Chin. Phys. Lett. 39 127301    Abstract Van der Waals (vdW) layered two-dimensional (2D) materials, which may have high carrier mobility, valley polarization, excellent mechanical properties and air stability, have been widely investigated before. We explore the possibility of producing a spin-polarized two-dimensional electron gas (2DEG) in the heterojunction composed of insulators MoSi$_{2}$N$_{4}$ and VSi$_{2}$N$_{4}$ by using first-principles calculations. Due to the charge transfer effect, the 2DEG at the interface of the MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ heterojunction is found. Further, for different kinds of stacking of heterojunctions, lattice strain and electric fields can effectively tune the electronic structures and lead to metal-to-semiconductor transition. Under compressive strain or electric field parallel to $c$ axis, the 2DEG disappears and band gap opening occurs. On the contrary, interlayer electron transfer enforces the system to become metallic under the condition of tensile strain or electric field anti-parallel to $c$ axis. These changes are mainly attributed to electronic redistribution and orbitals' reconstruction. In addition, we reveal that MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ lateral heterojunctions of armchair and zigzag edges exhibit different electronic properties, such as a large band gap semiconductor and a metallic state. Our findings provide insights into electronic band engineering of MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ heterojunctions and pave the way for future spintronics applications.
cpl-39-12-127301-fig1.png
cpl-39-12-127301-fig2.png
cpl-39-12-127301-fig3.png
cpl-39-12-127301-fig4.png
cpl-39-12-127301-fig5.png
cpl-39-12-127301-fig6.png
cpl-39-12-127301-fig7.png
cpl-39-12-127301-fig8.png
 DOI:10.1088/0256-307X/39/12/127301 © 2022 Chinese Physics Society Article Text High charge carrier mobility and quantum transport properties (e.g. quantum Hall effect) of a two-dimensional electron gas (2DEG) can provide device basis for research and development of emerging electronics, especially a 2DEG with spin polarization is of great significance to advent of spintronics.[1-3] The intriguing 2DEG at interface of insulators LaAlO$_{3}$ and SrTiO$_{3}$ has attracted great interest due to its unique application potential for nanoscale oxide devices.[4] Numerous studies have reported on the 2DEG and its creation or manipulation from a variety of oxide heterojunctions for decades.[5-14] In general, formation of a 2DEG in complex oxide superlattice requires expensive preparation including the pulsed laser deposition or molecular beam epitaxy. Meanwhile, the single-atomic layer graphene exfoliated from bulk graphite opened up the field of 2D materials.[15] Now, 2D materials are widely under investigation through experiments and theories, focusing on their rich electronic properties such as ultra-high surface sensitivity to the environment,[16] high carrier mobility,[17] spin valley coupling,[18] and the metal surface state of topological insulators.[19] Recently, the layered 2D materials of MoSi$_{2}$N$_{4}$ and WSi$_{2}$N$_{4}$ have been successfully synthesized using the chemical vapor deposition (CVD) in experiment,[20] which turned out to be semiconductors with high carrier mobility, strong mechanical properties, and air stability. Therefore, MoSi$_{2}$N$_{4}$ and its family compounds MA$_{2}$Z$_{4}$ (M = transition metal element; A = Si, Ge; Z = N, P, As) were extensively studied.[21] Among them, there were reports on the carrier mobility,[22] optical properties,[23,24] and valley polarization of intrinsic materials,[25,26] as well as the regulation of Schottky barrier at the interface of MA$_{2}$Z$_{4}$/metal heterojunctions,[27,28] the defect effect,[29,30] and the strain or electric field control of bilayer MA$_{2}$Z$_{4}$.[31-33] Here, we explore the possibility of producing a spin-polarized 2DEG at the insulator/insulator MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ interface by using first-principles electronic-structure calculations. The 2DEG composed of insulator materials heterojunction has been found in the BaHfO$_{3}$/SrTiO$_{3}$ perovskite heterojunction.[12] However, the 2DEG in the important 2D van der Waals (vdW) heterojunction is what we focus on. Importantly, it can be tuned by different stackings, lattice strain, and electric field, resulting in metal-to-semiconductor transition. In addition, the lateral MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ heterojunction has also been studied, and we find that the armchair type behaves as a large band gap semiconductor, while the zigzag case has a metallic state. Our findings suggest that the MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ heterojunctions with adjustable bandgap under strain and electric field will be promising for quantum materials and devices. In this Letter, we present the calculation methods, stability of MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ heterojunction and its electronic structure, strain effect of the most stable vertical heterojunction, electric field effect of the most stable vertical heterojunction, and finally a summary.
cpl-39-12-127301-fig1.png
Fig. 1. (a) Top and (b) side views of MSi$_{2}$N$_{4}$ monolayer. (c)–(e) Side views of AA, AB, and AC stacking bilayer structures for MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ vertical heterojunctions. (f) and (g) Top views of armchair and zigzag monolayer structures for MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ in-plane lateral heterojunctions.
Our first-principles calculations were performed using the projected augmented-wave method,[34] which is implemented in the Vienna ab initio simulation package (VASP).[35] The generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof type was employed to treat the exchange-correlation interaction.[36] A vacuum buffer space of 20.00 Å was used to prevent coupling between the two adjacent slabs. The kinetic energy cutoff was set to 500.00 eV. During structural relaxation, all atoms were allowed to relax until the Hellmann–Feynman force on each atom is less than 0.01 eV/Å. The Brillouin-zone integration was carried out using $15 \times 15\times 1$ for the geometry optimization and the total energy at $\varGamma$-centered grids. Unless mentioned otherwise, spin-orbit coupling (SOC) was considered and the vdW interaction was described using the DFT + D2 method[37] in all calculations. In order to better describe the 3$d$ electrons of V, the GGA + $U$ method was employed, in which the effective on-site Coulomb interaction $U$ was set to 3.00 eV.[26] The Bader charge analysis[38] was utilized to determine the electron charge transfer. The phonon dispersion curves were calculated by the Phonopy code[39] with a supercell of $2 \times 2\times 1$ using the finite displacement method, and a $3 \times 3\times 1$ $k$-mesh. First, we discuss the layered structural stacking and stability of different heterojunctions. In Figs. 1(a) and 1(b) the top and side views of monolayer MSi$_{2}$N$_{4}$ (M = Mo, V) with a space group $P6m1$ are presented. Similar to the structure of MnBi$_{2}$Te$_{4}$, its basic unit consists of seven atoms (N–Si–N–M–N–Si–N) of covalent connection, whereas the different layers are coupled by weak vdW interaction. The lattice constants of MoSi$_{2}$N$_{4}$ and VSi$_{2}$N$_{4}$ are 2.91 Å and 2.88 Å, respectively, which are consistent with the previous reports.[20] Figures 2(a) and 2(b) show that the monolayer MoSi$_{2}$N$_{4}$ has an indirect band gap of 1.76 eV,[20] and the monolayer VSi$_{2}$N$_{4}$ has a direct band gap of 0.43 eV with $U = 3.00$ eV.[26] The lattice mismatch ratio of MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ heterojunction is as small as 0.87%, because of their isostructural property. Here, three configurations are considered for different stackings of MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ vertical heterojunctions, namely AA, AB and AC, as shown in Figs. 1(c)–1(e). Our numerical results show that the AC heterojunction is preferred from calculated total energies, since AC is lower than AA and AB by 71.10 and 0.14 meV/unitcell, respectively. Moreover, the phonon dispersion curves of AC were calculated as shown in Fig. S1 in the Supplementary Material. The frequencies of all phonon branches throughout the Brillouin zone are positive, except for very small negative values near $\varGamma$ point that can be ignored within the numerical noise,[40] and even completely eliminated.[41] In the following, the most stable structure AC stacking will be our focus of discussion. Furthermore, we have constructed in-plane lateral heterojunctions of armchair and zigzag edges, examples of such nanosheet supercells are shown in Figs. 1(f) and 1(g). To study the electronic properties of each system, the isolated monolayer MoSi$_{2}$N$_{4}$ and VSi$_{2}$N$_{4}$ are separately semiconductors with 1.76 and 0.43 eV band gaps,[20,26] as shown in Figs. 2(a) and 2(b). When they are stacked on each other, the electronic structures would be modified significantly. Figures 2(c)–2(e) show the band structures of AA, AB and AC heterojunctions including the spin-orbit coupling. It can be found that AA and AB are indirect-band-gap type-II semiconductors' heterojunctions with gaps of 65.50 and 153.80 meV, which may be suitable in the field of optoelectronics due to their high efficiency charge separation and collection properties.[42] It is predicted that AA and AB may have great electron and hole mobilities, because the second-order partial differential of the valence band minimum (VBM) and conduction band maximum (CBM) to momentum $k$ is large.[20,43] When the SOC is taken into account, the degenerate energy levels could have a large Zeeman splitting at the $K$ and $K'$ points, corresponding to the value 128.80 meV. It is also found that the valley polarization energies are 2.20 and 1.50 meV in the AA and AB, which correspond to effective magnetic fields of about 11 T and 7 T, respectively, according to the value of 0.1–0.2 meV/T in the experiments.[44-46] Remarkably, the most stable AC heterojunction exhibits spin-gapless semiconductor behavior that has a finite bandgap for one spin channel and a zero gap for the other, which is useful for the tunable spin transport applications.[47] Meanwhile, it suggests that a 2DEG exists at the interface of AC heterojunctions. Interestingly, electronic states in energy range of 0.00–0.54 eV are contributed by only one type of spin as shown in Fig. 2(f). We verify that same electronic properties of AA, AB and AC can be maintained in superlattice, compared with the structures with vacuum. In addition, MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ lateral heterojunction monolayers consists of 3 unit cells of MoSi$_{2}$N$_{4}$ and VSi$_{2}$N$_{4}$, with armchair and zigzag interfaces, appear to be semiconductor (band gap of 421.70 meV) and metal, as shown in Figs. 2(g) and 2(h), respectively.
cpl-39-12-127301-fig2.png
Fig. 2. The band structures of (a) monolayer MoSi$_{2}$N$_{4}$, (b) monolayer VSi$_{2}$N$_{4}$, (c)–(e) AA, AB and AC stackings, (f) AC vertical heterojunction (spin-resolved without SOC), (g) armchair, and (h) zigzag lateral heterojunctions, respectively. The black and red colors in (f) are for spin-up and spin-down electrons, respectively.
cpl-39-12-127301-fig3.png
Fig. 3. For the AC heterojunction, (a) the energy change with interlayer Mo–V separation projected along $c$ direction, (b) band structures for different layer spacings.
To further understand the electronic structure of AC heterojunction, we first determine the optimal value of the interlayer spacing as shown in Fig. 3(a). An excessive reduction of the layer spacing makes its stability drastically reduced, from the optimal value of 9.77 Å, corresponding to the above-mentioned spin-gapless semiconductor. At the same time, we analyze the electronic structures of the different layer spacings. As shown in Fig. 3(b), when the layer spacing is extremely reduced, the strong interaction at the interface results in a metallic result. As the interaction decreases with the increase of the layer spacing, the AC heterojunction behaves as a semiconductor with a band gap of 38.00 meV. Therefore, the delicate interaction between MoSi$_{2}$N$_{4}$ and VSi$_{2}$N$_{4}$ is the main reason why it becomes a spin-gapless semiconductor. In order to understand the charge transfer at interlayer, the differential charge density $\Delta \rho$ can be calculated as \begin{align} \Delta \rho =\rho(\mathrm{whole})-\rho({\mathrm{MoSi_{2}N_{4}}})-\rho({\mathrm{VSi_{2}N_{4}}}),\notag \end{align} where $\rho$ (whole), $\rho$ (MoSi$_{2}$N$_{4}$), $\rho$ (VSi$_{2}$N$_{4}$) denote the charge density of the whole vdW heterojunction, and of the corresponding pure monolayers of MoSi$_{2}$N$_{4}$ and VSi$_{2}$N$_{4}$, respectively. Figure 4(a) shows the accumulation of more electrons on V atom, depletion of electrons on Mo atom, resulting in a strong charge transfer at the AC heterojunction interface. We further perform the projected density of states (PDOS) analysis on the atom of each layer. Figures 4(b) and 4(c) correspond to the upper MoSi$_{2}$N$_{4}$ and the lower VSi$_{2}$N$_{4}$, respectively. Due to the polarity difference of two layers, the V atom state passes through the Fermi level such that the entire system is metalized. Meanwhile, the VBM after stacking is mainly derived from the contribution of Mo-$d$ and N-$p$ orbital in MoSi$_{2}$N$_{4}$, while the CBM is contributed by the V-$d$ orbital of VSi$_{2}$N$_{4}$ in Fig. 4(e). More precisely, Bader analysis reveals that a small amount of electric charge transfers from MoSi$_{2}$N$_{4}$ to VSi$_{2}$N$_{4}$ in Fig. 4(f), which is consistent with the above results. It is worth noting that there is a much larger layer spacing of Mo and V atom, about 9.77 Å, than that of bilayer transition metal dichalcogenides (about 6.00 Å).[48,49] Compared with AA and AB stackings, AC has the smallest layer spacing, smaller than AA and AB by 0.46 and 0.05 Å, which indicates that there is a strong interaction between the upper and lower layers. These findings further confirm that after the formation of a heterojunction by insulating MoSi$_{2}$N$_{4}$ and VSi$_{2}$N$_{4}$, a spin-polarized 2DEG is generated due to the electronic redistribution at interface.
cpl-39-12-127301-fig4.png
Fig. 4. For the AC heterojunction, (a) differential charge density, (b) and (c) PDOS of MoSi$_{2}$N$_{4}$ and VSi$_{2}$N$_{4}$, respectively, (d) spin density, (e) orbital projected band structure, (f) Bader charge analysis. The purple and green colors in (a) denote the charge accumulation and depletion, respectively. The cyan and gray colors in (d) denote the spin majority and minority states, respectively. Isosurface values of difference charge density and spin density are $0.1 \times 10^{-3}$ and $0.5 \times 10^{-2}\,e$/Å$^{3}$.
cpl-39-12-127301-fig5.png
Fig. 5. The band structures of the AC heterojunction under different biaxial strain: (a)–(e) for compressive strain, (f) unstrained, (g) and (h) under tensile strain.
Due to existence of local $d$-orbital at the V atom in VSi$_{2}$N$_{4}$, the magnetic moment was induced in different heterojunctions. The magnetic moments of AA, AB, and AC heterojunctions are all about 1.0$\mu_{\scriptscriptstyle{\rm B}}$. The spin density shows that the magnetism mainly comes from the V atom and the surrounding polarized N atoms, as shown in Fig. 4(d). Mo atoms show no spin polarization due to the weak vdW interaction and large layer spacing, which is consistent with the PDOS results. However, for the lateral heterojunctions, the magnetic moment is very different because of the strong interaction of covalent bonds, where the armchair in-plane heterojunction has the magnetic moment of 1.0$\mu_{\scriptscriptstyle{\rm B}}$/V, while the zigzag case is 0.98$\mu_{\scriptscriptstyle{\rm B}}$/V. Applying lattice strain is an effective way to modulate the electronic structure and macroscopic properties of materials, thus we next investigate the effect of strain on the electronic properties of AC vertical heterojunction. In our calculation, the application of biaxial and uniaxial strain is achieved by changing the in-plane lattice constant. Figure 5 shows the band structures of the AC heterojunction under different strains. It can be seen that as the compressive strain increases, the 2DEG at the interface disappears and a band gap opens up, changing from the spin-gapless semiconductor to the type-II semiconductor. The highest occupied state moves from the $\varGamma$ to $K$ point under the small compressive strain ($-$2% and $-3$%), which meanwhile results in a semiconductor with direct band gap of about 0.45 eV. It is expected to have strong absorption in the infrared light frequency range. Interestingly, it still retains some original properties, such as the 100% spin polarization, valley polarization and Zeeman splitting. When the applied compressive strain is beyond $-3$%, the lowest unoccupied state changes from $K$ to $M$ point, giving rise to an indirect band gap semiconductor again. With the increase of tensile strain, the highest occupied state energy at $\varGamma$ point gradually increases, and the lowest unoccupied state at $K$ point gradually decreases, resulting in closed band gap and good metal behavior. Similarly, we find that a uniaxial strain can also tune the band structure, which is the difference that the electronic band structure responds less sensitively to the uniaxial strain, as shown in Fig. S2. What is more, we also study the variation of AA and AB heterojunctions with strain. Figure S3(a) shows the relative energy value of AA and AB heterojunctions with strain to the reference of AC. It can be seen that AA is extremely unstable and AC is relatively more stable than AB. We also analyze the band structures of AA and AB under different strains in Fig. S3(b). Like AC, the band gaps of AA and AB both increase under $-2$% strain, to 0.36 and 0.41 eV respectively. Under tensile strain, the band gaps are closed so that the AA and AB become metal with the consistent trend of strained AC.
cpl-39-12-127301-fig6.png
Fig. 6. For the AC vertical heterojunction, (a) the orbital projected band structures of metal atoms under compressive strains. (b) PDOS versus energy under 5% tensile (top) and $-5$% compressive (bottom) strains. (c) Mo/V–N bond length, (d) charge density and interlayer Mo–V separation projected along $c$ direction as functions of strain. (e) Phase diagram of magnetic moment and band gap as functions of strain, with indirect band gap semiconductor (IS), direct band gap semiconductor (DS), spin-gapless semiconductor (SGS), and metal (M).
Figure 6(a) shows the orbital projection band structure under $-3$% and $-5$% strains. It shows that the CBM contributed by the V-$d_{z^{2}}$ orbital at $K$ point gradually moves up, while the contribution of V-$d_{x^{2}-y^{2}}$ orbital at $M$ point shows no shift. That leads to the conversion of a direct band gap to an indirect band gap semiconductor. In addition, we plot the PDOS for AC heterojunction under $-5$% and 5% strain in Fig. 6(b). The Mo-$d$ orbital and N-$p$ orbital show strongly hybridized interaction at the VBM, while the V-$d$ orbital and N-$p$ orbital have diminishing hybridization at the CBM upon strain. In fact, it is found that the hybridization of the Mo-$d_{x^{2}-y^{2}}$ orbital and N-$p$ orbital of VBM is strong near the Fermi level under $-5$% strain, and the Mo-$d_{z^{2}}$ state has smaller contribution. However, under 5% tensile strain more $d_{z^{2}}$ orbital and less $d_{x^{2}-y^{2}}$ orbital states of metal and N-$p$ orbitals are hybridized at the Fermi level. Figure 6(c) shows the dependences of Mo/V–N bond lengths on the applied strain. As the compressive strain increases, the decreasing Mo/V–N bond length tends to strengthen in-plane bonding, thus resulting in more $d_{x^{2}-y^{2}}$ orbital states of metal atoms occupied. On the contrary, as the tensile strain increases, the increasing Mo/V–N bond length favors out-of-plane bonding, leading to more $d_{z^{2}}$ orbital states of metal atoms occupied. This is consistent with the analysis of the PDOS. In Fig. 6(d), we find that the compressive strain increases the distance between Mo and V atoms in an approximately linear fashion. It is also natural that the tensile strain gives the smaller Mo–V distance and the stronger interlayer interaction. In addition, as the tensile strain increases, the electronic transfer at the interface goes up significantly, while the compressive strain inhibits its occurrence and even changes the direction of electronic transfer. The weakening of the interlayer interaction occurs under compressive strain, showing a semiconductor property similar to that of an isolated system. Therefore, one can confirm that the electrons redistribution, orbitals reconstruction, and the variation of layer spacing are the reasons for the strain tuned band gap. Figure 6(e) shows the magnetic moment and band gap changes as functions of strain. Overall, the change of magnetic moment with strain is not obvious, staying at about 1.0$\mu_{\scriptscriptstyle{\rm B}}$. It can be seen that as the compressive strain increases, the band gap increases from IS to DS, and then slightly decreases from DS to IS. On the tensile strain side, the band gap keeps closed and shows a metal state. In addition to the strain engineering, the effect of the vertical electric field[50] on the electronic properties of AC heterojunction is investigated. We define that the positive and negative fields are parallel and anti-parallel to the $c$-axis direction, respectively. Figure 7 shows the band structure of AC heterojunction as a function of electric field. When a parallel electric field (parallel to $c$ axis) is applied, the energy of the highest occupied state at $\varGamma$ point gradually decreases, and the lowest unoccupied state at $K$ point gradually increases, thus the 2DEG disappears and changes from the spin-gapless semiconductor to type-II semiconductor. Of course, the application of electric field does not affect some key properties, such as valley polarization, high electron-hole mobility, and 100% spin polarization. On the other hand, under the anti-parallel electric field (anti-parallel to $c$ axis), the energy of the highest occupied state at $\varGamma$ point increases and the lowest unoccupied state at $K$ point decreases, which results in a metallic state. Figure S4 in the Supplementary Material shows the band structures of AA and AB under different electric fields, which are insensitive to the effect of electric field.
cpl-39-12-127301-fig7.png
Fig. 7. The band structures of AC heterojunction under different electric fields: (a) and (b) with the same electric field strength but opposite directions, (b)–(f) with the same electric field direction but increasing strength.
Figure 8(a) shows the trend of band gap change with the electric field strength. When the field is along positive direction, the band gap increases as the electric field strength increases. Regardless of parallel and anti-parallel electric fields, the magnetic moment keeps about 1.0$\mu_{\scriptscriptstyle{\rm B}}$ for the studied electric field range. In order to further understand the electric field regulation on the electronic structure, the charge density difference was explored, according to the following formula: \begin{align} \Delta \rho =\rho(E~\mathrm{field})-\rho (\mathrm{no~field}).\notag \end{align}
cpl-39-12-127301-fig8.png
Fig. 8. For the AC vertical heterojunction, (a) the band gap and (d) charge density change as functions of electric field strength. Panel (b) shows the charge density difference at $E = 0.1$ V/Å, the purple and green colors denote the charge accumulation and depletion, respectively. Panel (c) shows PDOS under different electric field strengths. Isosurface values of charge density difference is $0.5 \times 10^{-3}\,e$/Å$^{3}$.
As shown in Fig. 8(b), the charge density on each atom is redistributed after the electric field is applied. Figure 8(c) presents the PDOS under different electric field strengths, in which the highest occupied state is mainly contributed by Mo atom and the lowest unoccupied state is from V atom as in Fig. 4(e). When a parallel electric field is applied, MoSi$_{2}$N$_{4}$ gains more electrons, so that the unoccupied state of the V atoms gradually moves away from the Fermi level, while the fully occupied state gradually moves to the Fermi level and becomes incompletely occupied state. However, when an anti-parallel electric field is applied, VSi$_{2}$N$_{4}$ gains more electrons. The change of V atom is the opposite compared to the case of parallel electric field, so the fully occupied state of the V atoms gradually moves away from the Fermi level, while unoccupied state gradually gets closer to the Fermi level, resulting in a metal. In addition, we analyze the influence of electric field on the electronic transfer at interlayer, as shown in Fig. 8(d). The application of parallel electric field makes the AC heterojunction behave as a semiconductor, and an anti-parallel electric field makes that as a metal, demonstrating that V and Mo atoms are greatly affected by the electric field. In conclusion, we have explored the electronic structures of MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ vdW heterojunctions using first-principles density function theory computations. It is found that a spin-polarized 2DEG at the interface of such two insulators can be effectively tuned by strain and electric field. More precisely, the compressive strain and parallel electric field inhibit electron transfer, transforming a spin-gapless semiconductor to a large direct/indirect band gap type-II semiconductor. However, the tensile strain and anti-parallel electric field promote and change the direction of the transfer of electrons at interlayer, eventually leading to a metallic state. This is mainly explained by using the electronic redistribution and orbital reconstruction mechanism. In addition, MoSi$_{2}$N$_{4}$/VSi$_{2}$N$_{4}$ lateral heterojunctions connected with armchair and zigzag edges are found to be large band gap semiconductor and metal, respectively. Our theoretical predictions provide guidance for exploring strain and electric field tunable electronic property of MA$_{2}$N$_{4}$-based heterojunctions, and design of next-generation spintronic devices. This work was supported by the National Natural Science Foundation of China (Grant Nos. 12074241, 52130204, and 11929401), the Science and Technology Commission of Shanghai Municipality (Grant Nos. 22XD1400900, 20501130600, 21JC1402600, and 22YF1413300), High Performance Computing Center, Shanghai University, Key Research Project of Zhejiang Lab (Grant No. 2021PE0AC02). H.G. acknowledges the supports from the open projects of Key Laboratory of Green Fabrication and Surface Technology of Advanced Metal Materials (Anhui University of Technology), Ministry of Education (Grant No. GFST2022KF08), State Key Laboratory of Surface Physics (Fudan University) (Grant No. KF2022_10), and State Key Laboratory of Infrared Physics, Shanghai Institute of Technical Physics, Chinese Academy of Sciences (Grant No. SITP-NLIST-YB-2022-08). R.G. acknowledgments the support of China Scholarship Council. References Quantum Hall Effect in Polar Oxide HeterostructuresSpin and interaction effects in Shubnikov–de Haas oscillations and the quantum Hall effect in GaN/AlGaN heterostructuresNon-linear screening and the background density of 2DEG states in magnetic fieldA high-mobility electron gas at the LaAlO3/SrTiO3 heterointerfaceSpin-polarized two-dimensional electron gas at GdTi O 3 / SrTi O 3 interfaces: Insight from first-principles calculationsElectronic phase separation at the LaAlO3/SrTiO3 interfaceEnhancing Electron Mobility at the LaAlO3 /SrTiO3 Interface by Surface ControlPrediction of a mobile two-dimensional electron gas at the LaSc O 3 / BaSn O 3 (001) interfaceFirst-principles studies of a two-dimensional electron gas at the interface of polar/polar LaAlO3 /KNbO3 superlatticesSuperconductivity at the LaAlO3 /SrTiO3 interfaceFerroelectric control of a spin-polarized two-dimensional electron gasFirst-Principles Prediction of Two-Dimensional Electron Gas Driven by Polarization Discontinuity in Nonpolar/Nonpolar AHfO3 /SrTiO3 (A = Ca, Sr, and Ba) HeterostructuresA high-mobility two-dimensional electron gas at the spinel/perovskite interface of γ-Al2O3/SrTiO3Two-Dimensional Electron Gas with High Mobility Forming at BaO/SrTiO3 InterfaceElectric Field Effect in Atomically Thin Carbon FilmsChemical sensing with 2D materialsRecent Advances in the Carrier Mobility of Two-Dimensional Materials: A Theoretical PerspectiveValley-Engineering Mobilities in Two-Dimensional MaterialsTopological insulators and superconductorsChemical vapor deposition of layered two-dimensional MoSi2 N4 materialsStructure-driven intercalated architecture of septuple-atomic-layer $MA_2Z_4$ family with diverse properties from semiconductor to topological insulator to Ising superconductorPredicted septuple-atomic-layer Janus MSiGeN 4 (M = Mo and W) monolayers with Rashba spin splitting and high electron carrier mobilitiesA van der Waals heterostructure of MoS2 /MoSi2 N4 : a first-principles studyBoosting the photocatalytic hydrogen evolution performance of monolayer C2 N coupled with MoSi2 N4 : density-functional theory calculationsTheoretical evidence of the spin–valley coupling and valley polarization in two-dimensional MoSi2 X4 (X = N, P, and As)Spin-valley coupling in a two-dimensional V Si 2 N 4 monolayerInterfacial Electronic Properties and Tunable Contact Types in Graphene/Janus MoGeSiN4 HeterostructuresTwo-dimensional van der Waals graphene/transition metal nitride heterostructures as promising high-performance nanodevicesTunable electronic and magnetic properties of MoSi2N4 monolayer via vacancy defects, atomic adsorption and atomic dopingEffect of O-doping or N-vacancy on the structural, electronic and magnetic properties of MoSi2N4 monolayerEffect of electric field and vertical strain on the electro-optical properties of the MoSi2 N4 bilayer: A first-principles calculationTuning transport coefficients of monolayer $\mathrm{MoSi_2N_4}$ with biaxial strainSemiconductor-to-metal transition in bilayer MoSi2 N4 and WSi2 N4 with strain and electric fieldProjector augmented-wave methodEfficient iterative schemes for ab initio total-energy calculations using a plane-wave basis setAtoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlationVan der Waals Density Functional for General GeometriesA fast and robust algorithm for Bader decomposition of charge densityPHON: A program to calculate phonons using the small displacement methodLattice-Strain Control of Flexible Janus Indium Chalcogenide Monolayers for Photocatalytic Water SplittingElectrons and phonons in single layers of hexagonal indium chalcogenides from ab initio calculationsSemiconductor Composites: Strategies for Enhancing Charge Carrier Separation to Improve Photocatalytic ActivityAccurate electronic properties and non-linear optical response of two-dimensional MA2Z4Breaking of Valley Degeneracy by Magnetic Field in Monolayer MoSe 2 Magnetic control of valley pseudospin in monolayer WSe2Manipulation of valley pseudospin in WSe 2 / CrI 3 heterostructures by the magnetic proximity effectSpin-gapless semiconductors: Fundamental and applied aspectsInterlayer Coupling and Gate-Tunable Excitons in Transition Metal Dichalcogenide HeterostructuresStacking effects on the electronic and optical properties of bilayer transition metal dichalcogenides MoS 2 , MoSe 2 , WS 2 , and WSe 2 Adsorbate-substrate and adsorbate-adsorbate interactions of Na and K adlayers on Al(111)
[1] Tsukazaki A, Ohtomo A, Kita T, Ohno Y, Ohno H, and Kawasaki M J S 2007 Science 315 1388
[2] Knap W, Fal'ko V, Frayssinet E et al. 2004 J. Phys.: Condens. Matter. 16 3421
[3] Efros A 1988 Solid State Commun. 67 1019
[4] Ohtomo A and Hwang H 2004 Nature 427 423
[5] Betancourt J, Paudel T R, Tsymbal E Y, and Velev J P 2017 Phys. Rev. B 96 045113
[6] Ariando A, Wang X, Baskaran G et al. 2011 Nat. Commun. 2 188
[7] Xie Y W, Bell C, Hikita Y, Harashima S, Hwang H Y 2013 Adv. Mater. 25 4735
[8] Paudel T R and Tsymbal E Y 2017 Phys. Rev. B 96 245423
[9] Fang L, Chen C, Yang Y et al. 2019 Phys. Chem. Chem. Phys. 21 8046
[10] Gariglio S, Reyren N, Caviglia A, and Triscone J M 2009 J. Phys.: Condens. Matter. 21 164213
[11] Weng Y K, Niu W, Huang X, An M, and Dong S 2021 Phys. Rev. B 103 214101
[12] Cheng J L, Nazir S, and Yang K S 2016 ACS Appl. Mater. Inter. 8 31959
[13] Chen Y, Bovet N, Trier F et al. 2013 Nat. Commun. 4 1371
[14] Cao C, Chen S, Deng J et al. 2022 Chin. Phys. Lett. 39 047301
[15] Novoselov K S, Geim A K, Morozov S V et al. 2004 Science 306 666
[16] Anichini C, Czepa W, Pakulski D, Aliprandi A, Ciesielski A, and Samorì P 2018 Chem. Soc. Rev. 47 4860
[17] Mir S H, Yadav V K, and Singh J K 2020 ACS Omega 5 14203
[18] Sohier T, Gibertini M, Campi D, Pizzi G, and Marzari N 2019 Nano Lett. 19 3723
[19] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
[20] Hong Y L, Liu Z, Wang L et al. 2020 Science 369 670
[21] Wang L, Shi Y, Liu M et al. 2020 arXiv:2008.02981 [cond-mat.mtrl-sci]
[22] Guo S D, Mu W Q, Zhu Y T, Han R Y, and Ren W C 2021 J. Mater. Chem. C 9 2464
[23] Bafekry A, Faraji M, Abdollahzadeh A et al. 2021 New J. Chem. 45 8291
[24] Zeng J, Xu L, Yang Y et al. 2021 Phys. Chem. Chem. Phys. 23 8318
[25] Ai H, Liu D, Geng J, Wang S, Lo K H, and Pan H 2021 Phys. Chem. Chem. Phys. 23 3144
[26] Cui Q, Zhu Y, Liang J, Cui P, and Yang H 2021 Phys. Rev. B 103 085421
[27] Binh N T, Nguyen C Q, Vu T V, and Nguyen C V 2021 J. Phys. Chem. Lett. 12 3934
[28] Pham K D, Nguyen C Q, Nguyen C, Cuong P V, and Hieu N V 2021 New J. Chem. 45 5509
[29] Bafekry A, Faraji M, Fadlallah M M et al. 2021 Appl. Surf. Sci. 559 149862
[30] Bian Y T, Liu G H, Qian S H, Ding X X, and Liu H X 2020 arXiv:2012.04162 [cond-mat.mtrl-sci]
[31] Bafekry A, Stampfl C, Naseri M et al. 2021 J. Appl. Phys. 129 155103
[32] Guo X S and Guo S D 2020 arXiv:2008.08747 [cond-mat.mtrl-sci]
[33] Wu Q, Cao L, Ang Y S, and Ang L K 2021 Appl. Phys. Lett. 118 113102
[34] Blöchl P E 1994 Phys. Rev. B 50 17953
[35] Kresse G and Furthmüller J 1996 Phys. Rev. B 54 11169
[36] Perdew J P, Chevary J A, Vosko S H et al. 1992 Phys. Rev. B 46 6671
[37] Dion M, Rydberg H, Schröder E, Langreth D C, and Lundqvist B I 2004 Phys. Rev. Lett. 92 246401
[38] Henkelman G, Arnaldsson A, and Jónsson H 2006 Comput. Mater. Sci. 36 354
[39] Alfè D 2009 Comput. Phys. Commun. 180 2622
[40] Wang Z and Zhou G 2019 J. Phys. Chem. C. 124 167
[41] Zólyomi V, Drummond N, and Fal'Ko V 2014 Phys. Rev. B 89 205416
[42] Marschall R 2014 Adv. Funct. Mater. 24 2421
[43] Yang J, Zhao L, Shi-Qi L et al. 2021 Nanoscale 13 5479
[44] MacNeill D, Heikes C, Mak K F et al. 2015 Phys. Rev. Lett. 114 037401
[45] Aivazian G, Gong Z, Jones A M et al. 2015 Nat. Phys. 11 148
[46] Hu T, Zhao G, Gao H et al. 2020 Phys. Rev. B 101 125401
[47] Rani D, Bainsla L, Alam A, and Suresh K 2020 J. Appl. Phys. 128 220902
[48] Gao S, Yang L, and Spataru C D 2017 Nano Lett. 17 7809
[49] He J, Hummer K, and Franchini C 2014 Phys. Rev. B 89 075409
[50] Neugebauer J and Scheffler M 1992 Phys. Rev. B 46 16067