Fig. 1. (a) Optimized geometry of Zn₃Si₂ monolayer, with a unit cell labeled by the black dotted line. (b) A zoom-in figure of (a).

Fig. 2. (a) Phonon dispersion of Zn₃Si₂ monolayer, where no soft mode is found. (b) The total energy for the Zn₃Si₂ lattice as a function of simulation time at 300 K. The inset illustrates the snapshots of the optimized crystal structures of the Zn₃Si₂ lattice at 1 ps, 2 ps, and 3 ps.

Fig. 3. (a) The charge density difference with an isovalue of 0.02 e/Å⁻³. The blue and orange mean electron accumulation region and electron depletion region, respectively. (b) ELF of Zn₃Si₂ monolayer with an isovalue of 0.03 e/Å⁻³. (c), (d) Top and side views of VB maximum and CB minimum charge density contours at the Dirac point of Zn₃Si₂ monolayer, respectively.

Fig. 4. The electronic properties of Zn₃Si₂ without SOC. (a) The orbital-resolved band structures for Zn₃Si₂ monolayer (yellow: total p_z orbitals; light grey: total p_y orbitals; blue: total p_x orbitals; olive: total d orbitals). The Fermi level is set to zero. (b) Projected density of states of Zn₃Si₂ monolayer. (c) 3D projection of Dirac cone in the vicinity of the K point.

Fig. 5. (a) The calculated band structures of Zn₃Si₂ monolayer with SOC. The Fermi level is set to zero. (b) The zoom-in around the Fermi level corresponding to the red dotted box in (a), where the inset indicates the first Brillouin zone.

Fig. 6. (a) The ΔE = E_{(spin-polarized)} – E_{(spin-nonpolarized)} with respect to carrier doping calculated in the Zn₃Si₂ monolayer. The negative and positive values on the horizontal ordinate are for the hole and electron dopings, respectively. (b), (c) Spin-polarized band structures in the absence of SOC with the doping concentration of 0.2 hole per atom and 0.2 electron per atom, respectively.