Symmetry-directed electronic and optical properties in a two-dimensional square-lattice ZnPc-MOF

Abstract

The electronic structure of materials is fundamentally governed by their crystal symmetry. While most research on two-dimensional materials has focused on hexagonal lattices, such as graphene, hexagonal boron nitride, and transition metal dichalcogenides. This work explores a square-lattice system: the experimentally realized phthalocyanine-based metal-organic framework (ZnPc-MOF). Using group representation theory, we classify the electronic bands of ZnPc-MOF monolayer, AA- and AB-stacked bilayers, and twisted bilayers in terms of the irreducible representations (irreps) of their little groups. We find that bands in the AB-stacked bilayer remain two-fold degenerate along the $Y$ and $Y^{\prime }$ high-symmetry lines, as a consequence of the sole presence of two-dimensional irreps along these directions. We further derive optical transition selection rules to interpret the optical conductivity, revealing pronounced polarization-dependent optical responses. Additionally, we investigate the quasicrystalline electronic states in the 45${}^{\circ }$ twisted bilayer (ZnPc-MOF quasicrystal) using the resonant coupling Hamiltonian. Compared to graphene quasicrystals, ZnPc-MOF quasicrystal exhibits weaker resonant coupling strengths, yet its quasicrystalline states lie closer to the Fermi energy, suggesting a greater contribution to low-energy electronic phenomena.

References in corpus (28)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Topological Insulators
• Topological insulators and superconductors
• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides
• Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
• Maximally localized Wannier functions: Theory and applications
• Moire bands in twisted double-layer graphene
• Substrate-induced bandgap in graphene on hexagonal boron nitride
• Flat bands in twisted bilayer transition metal dichalcogenides
• Dirac Electrons in a Dodecagonal Graphene Quasicrystal
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• Quasicrystalline 30° Twisted Bilayer Graphene as an Incommensurate Superlattice with Strong Interlayer Coupling
• Interlayer interaction in general incommensurate atomic layers
• Quasicrystalline electronic states in 30${}^{\circ }$ rotated twisted bilayer graphene
• Complex density wave orders and quantum phase transitions in a model of square-lattice Rydberg atom arrays
• Flat Bands in Twisted Bilayers of Two-Dimensional Polar Materials
• Dodecagonal bilayer graphene quasicrystal and its approximants
• Multi-ultraflatbands tunability and effect of spin-orbit coupling in twisted bilayer transition metal dichalcogenides
• Flat band in twisted bilayer Bravais lattices
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Altermagnetism from interaction-driven itinerant magnetism
• Altermagnetism on the Shastry-Sutherland lattice
• Quasicrystalline electronic states in twisted bilayers and the effects of interlayer and sublattice symmetries
• Electronic structure of 30° twisted double bilayer graphene
• Interlayer hybridization in graphene quasicrystal and other bilayer graphene systems
• Resonant interaction in chiral, Eshelby-twisted van der Waals atomic layers