Geometric and electronic structures of two-dimensionally polymerized triptycene: covalent honeycomb networks comprising triptycene and polyphenyl

Abstract

Based on the density functional theory with the generalized approximation, we investigated the geometric and electronic structure of two-dimensional covalent networks consisting of triptycene and phenyl groups, which are alternately arranged in a hexagonal manner. Calculated total energies of the networks are a few tens meV per atom higher than that of an isolated benzene, indicating that the networks are energetically stable. All networks were semiconductors with a moderate band gap at the Γ point, value of which inversely proportional to the length of polyphenyl connecting the triptycene. According to a kagome topology of π electrons distributed on the sp 2 hydrocarobons, the characteristic kagome energy bands consisting of a flat dispersion band and a Dirac cone emerge in valence and conduction states of which structure is sensitive to the mutual orientation of phenyl groups with respect to the polymer chain.

Flat-band engineering in tight-binding models: Beyond the nearest-neighbor hopping

“…V, artificial materials are promising candidates, due to the tunability of the hopping parameters. For solid-state systems, recent studies of first-principles calculations imply that carbon-based materials [65][66][67][68] , and pyrochlore oxides 69 will be promising candidates. Although the exact flatness will be spoiled by the additional hoppings in the real solid-state systems, our method will serve as a good starting point to search the materials with nearly flat bands penetrating the dispersive bands, which also show the intriguing physics.…”

Flat bands and higher-order topology in polymerized triptycene: Tight-binding analysis on decorated star lattices

“…1 B). The first principles calculations have revealed the characteristic band structure of this class of materials [17], namely, π electrons on sp 2 hydrocarbons form kagome-type network, which supports the multiple flat bands with surprisingly good flatness, as well as the massless Dirac dispersion around K and K points.…”

“…Such tight-binding models provide a simplified description of electronic structures in a sense that six carbon atoms are reduced to one site. Nevertheless, they are useful to capture the characteristic electronic structures arising from the kagome network, as demonstrated in the previous work based on the first-principles calculations [17].…”

“…Since three C 6 rings on each triptycene molecule form 120-degree structure, it is possible to construct a twodimensional network of triptycene molecule by placing them on a honeycomb lattice and connecting the neighboring C 6 rings by other molecules, such as acenes [16] or phenyls [17]. We call the materials thus obtained as polymerized triptycene.…”

“…For a series of polymerized triptycene, one can consider the materials in which the number of phenyls connecting the triptycene molecules is more than one [17]. If there are two phenyls, the corresponding tight-binding model can be obtained by increasing the number of sites inserted in the bonds connecting the triangles ( Fig.…”