# Also in the Article

Ab initio calculations
This protocol is extracted from research article:
Creation of two-dimensional layered Zintl phase by dimensional manipulation of crystal structure

Procedure

First-principles calculations based on density functional theory (DFT) were performed using generalized gradient approximation with the Perdew-Burke-Ernzerhof functional (33), as implemented in the Quantum Espresso package (34). The cutoff energy for the plane wave basis is set to 50 rydberg. The norm-conserving, optimized, designed nonlocal pseudopotentials were generated using Opium (35). The lattice parameters and atomic positions were fully relaxed until the pressures and forces are less than 10−2 kbar and 10−7 (in arbitrary units). For the k-point sampling from the Brillouin zone, the Monkhorst-Pack grids (8 by 8 by 8 and 8 by 8 by 1) (36) were used for the bulk and slab calculations, respectively. The interlayer binding energy was calculated from the total energy difference between bulk and isolated layers. To maintain the atomic structures of the layers, which are unstable, the unit cell and atomic positions were fixed for the binding energy calculations. The relativistic effect was fully considered by including spin-orbit coupling (SOC) in a noncolinear scheme. The DFT band structures and projected density of states (PDOS) of 3D-ZnSb, 2D-LiZnSb, and 2D-ZnSb were calculated including SOC. PDOS shows that the energy bands near the Fermi level mainly are composed of s- and p-orbitals of both Zn and Sb in all the three systems. Similarly, the contribution from the Li orbitals in 2D-LiZnSb is negligible in the band structure, as presented in fig. S9B. The energy bands of 3D-ZnSb and 2D-LiZnSb show that they are both semiconductors with an indirect gap of 0.05 and 0.29 eV for 3D-ZnSb and 2D-LiZnSb, respectively. These results are in good agreement with the previous first-principles band calculations (22, 37). From the first-principles total energy calculations, the cohesive energy (ΔEcoh) is obtained by using$ΔEcoh=[EZnSb−(EZn+ESb)]/nZnSb$(1)where EZnSb, EZn, and ESb are the total energies of ZnSb, Zn, and Sb, respectively, and nZnSb is the number of ZnSb per unit cell. The cohesive energies of 3D-ZnSb and 2D-ZnSb were calculated as −5.23 and − 4.65 eV per ZnSb, respectively. Although these results show that 3D-ZnSb is more stable, the cohesive energy of 2D-ZnSb is reasonably large enough, indicating that the 2D-ZnSb exists as a stable material, which can be synthesized in experiments. The Li alloying energy (ΔELi alloying) can be obtained from(2)where ELiZnSb and ELi are the total energies of 2D-LiZnSb and Li, respectively, and nLi is the number of Li per unit cell. With respect to the reference energies of 3D-ZnSb and 2D-ZnSb, the Li alloying energies for 3D-ZnSb and 2D-ZnSb were calculated as −2.19 and − 2.77 eV and per Li, inferring that Li-alloyed 2D-LiZnSb is energetically most stable. The interlayer binding energy (Einter) of 2D-ZnSb was calculated in comparison to 3D-ZnSb (fig. S7). A unit cell of 2D-ZnSb comprises two distinct ZnSb layers; one has Sb atoms buckled upward, while the other has Sb atoms buckled downward with respect to the Zn atoms. A close inspection of the atomic structure reveals that there are two possibilities to separate the layers, enabling the calculations of two interlayer binding energies, which are indicated by the red dashed lines in fig. S7. To separate them, the Sb-Sb bonding should be broken in the red dashed line 3 case, while the interlayer Sb-Sb bonding should be broken for the red dashed line 4 case. The interlayer binding energies of 2D-ZnSb are calculated as 328 and 306 meV per atom for lines 3 and 4 cases, respectively. These values are definitely weaker than typical 3D primary bondings, thus concluding that the crystal structure of 2D-ZnSb presents a high anisotropy as a prominent aspect for layered materials. The bonding strengths at the red dashed lines in fig. S7 are calculated as 872 and 697 meV per atom for lines 1 and 2 cases, respectively. Again, they near the chemical bonding regime, exhibiting the sp3 nature of the bondings and the 3D nature of the material. Last, we calculated the exfoliation energy of 2D-ZnSb using the proposed method (38), as shown in fig. S7. We relaxed the structures of the isolated layer of 2D-ZnSb. Regardless of how the interlayer bonds are broken, we obtained the same stable structure after the structural relaxation of bilayer 2D-ZnSb, not monolayer 2D-ZnSb, indicating that the monolayer of 2D-ZnSb is not a stable form. The exfoliation energy calculation results in 183 meV per atom, which again indicates that the bilayer of 2D-ZnSb can be easily exfoliated from the layered 2D-ZnSb, as one can expect from the layered structure of 2D-ZnSb. From the binding energy calculation of 2D-ZnSb, one may imagine the monolayer of 2D-ZnSb. We obtained the relaxed crystal structures and electronic energy band structures of the monolayer of 2D-ZnSb (fig. S9). The crystal structure is presented in the inset of fig. S9D. We cannot obtain the relaxed structure of the planar monolayer structure. Before the relaxation of atomic position and cell parameter, the cohesive energy of monolayer is −3.46 eV per ZnSb (1.18 eV per ZnSb higher than that of 2D-ZnSb). Because of the large total energy difference from 3D-ZnSb and 2D-ZnSb phases, one can hardly imagine a freestanding monolayer. The bilayer ZnSb has a semiconducting band structure with an indirect bandgap of 0.27 eV.

Note: The content above has been extracted from a research article, so it may not display correctly.

Q&A