Fig. 1. Applications of lattice engineering in the directions of lattice degrees of freedom and quantum degrees of freedom LMCT: Ligand⁃to⁃metal charge transfer; MLCT: metal⁃to⁃ligand charge transfer

Fig. 2. Research timeline of electronic states in lattice engineering^[29-34]

Fig. 3. (a) Atomic model and device application schematic of millimeter⁃sized graphene/h-BN in⁃plane heterostructures ^[37];(b) Schematic representation of the synthesis process from triphenyl⁃metal molecules to 2D organometallic lattices^[39]; (c) Topological properties of the 2D triphenyl⁃lead lattice [band structure without (the left two) and with (the right two) spin⁃orbit coupling]^[39]

Fig. 4. (a) Schematic illustration of the experimental strategy of self-assembly synthesis method of superlattice material^[43]; (b) Low-magnification STEM image of the cross-section of a PbTiO₃/SrTiO₃ superlattice, XRD diffraction image and synchrotron⁃based, in⁃plane X-ray RSM study of the superlattice^[44]; (c) Cross-sectional high-resolution STEM image of a PbTiO₃/SrTiO₃ superlattice, indicating an array of vortex⁃antivortex pairs within each PbTiO₃ layer^[44]

Fig. 5. (a) Schematic diagram of the photocatalytic degradation of fuel and photoinactivation of bacteria by Ce-doped Bi₂MoO₆ photocatalyst^[50]; (b) Illustration of the formation mechanism and evolution process of crystal defects in Ce-doped Bi₂MoO₆ structure^[50]; (c) Schematic diagram of the vacancy⁃ordered crystal structure of Cs₂SnI₆/Cs₂TeI₆^[51]; (d) Schematic diagram of the reorientation of the unit cell to form isolated octahedral units^[51]

Fig. 6. [in Chinese]