Engineering of flat bands and Dirac bands in two-dimensional covalent organic frameworks (COFs): relationships among molecular orbital symmetry, lattice symmetry, and electronic-structure characteristics

Abstract

An effective framework for the band engineering in 2D covalent organic frameworks is revealed by describing the fundamental relationships among the electronic structures, the lattice symmetries, and the frontier molecular orbitals of building units.

Vanishing Electronic Band Gap in Two-Dimensional Hydrogen-Bonded Organic Frameworks

“…Controlling the symmetry of the lattices between the square (using donor 4) and hexagonal (using donor 3 ) results in very different band structures. The evolution of the band structures in these HOFs is similar to that in 2D COFs, with the overall symmetry originating from both lattice symmetry and molecular orbital symmetry Figure b).…”

Emergence of a Two-Dimensional Topological Dirac Semimetal Phase in a Phthalocyanine-Based Covalent Organic Framework

“…In our recent study on hexagonal COFs, we were able to interpret the electronic characteristics of the COF bands by analyzing the frontier MOs of the building units together with the lattice symmetry in the framework of a TB model. , Here, we chose to extend our approach to the tetragonal F-Pc COFs to further illustrate the topological phase transition induced by the A u - B g band inversion. In the spirit of our earlier work, we adopted an ( A u , B g x , B g y )-orbital hopping model in a square lattice to describe the electronic structure of the F-Pc COF. Detailed descriptions of the TB model are provided in the SI.…”

On-Surface Synthesis toward Two-Dimensional Polymers

“…However, topological defects, boundaries, and edges are usually introduced by irradiation or substrate engineering, − resulting in a random distribution fashion. Compared to inorganic monolayers, 2D organic structures hold the advantage of an atomically precise topology and distribution through synthetic control over monomer precursors. , In particular, abundant organic building blocks coupled with diverse combinations, as built in the Reticular Chemistry Structural Resource, offer a rich variety of lattice, orbital, and spin symmetries. , As a result, 2D polymers become an ideal platform to realize Archimedean nets, such as honeycomb, hexagonal, square, Kagome, and Lieb lattices, featuring topologically nontrivial Dirac/flat bands and other exotic electronic structures. − In particular, topological insulators, distinguished from conventional insulators in a way that they hold robust metallic surface or edge states residing inside a bulk band gap, have also been theoretically predicted in organic frameworks. , The large number of organic building blocks endows them as ideal platforms to achieve exotic topological properties, rendering significant implications in electronic/spintronic and quantum computing applications.…”

“…Theoretical advances offer a very fruitful illustration of the electronic properties, where experimental data are sparse . It is worth pointing out that the conceptual, theoretical description of the impact of topology on electronic structure originates from perfect and long-range ordered 2D π-conjugated polymers, so that the structure–symmetry–property relationships can be established . For this purpose, synthesis of 2D polymers with a high degree of structural order will definitely bring new frontiers in physics.…”