Metallic bands in chevron-type polyacenes

Abstract

We present electronic structure calculations based on a single-parameter plane wave expansion method for basic graphene building blocks, namely n-oligophenylenes and n-oligoacenes, revealing excellent agreement with density-functional theory. When oligophenylene molecules are joined through meta (zigzag) or ortho (chevron) junctions, the resulting molecular dimers and polymers exhibit a semiconducting character. While zigzag dimers of oligoacenes also exhibit gapped electronic structures, their chevron-phase features a sharp metallic band at the Fermi energy. This zero-point-energy state, which transforms into Dirac-like band in chevron polymers, survives at the outer elbows of the dimer irrespective of the molecular length, and has the same origin as reported for the polyacetylene and topologically induced edge states at edge-decorated graphene nanoribbons. These findings assist the engineering of topological electronic states at the molecular level and complement the toolbox of quantum phases in carbon-based nanostructures.

Fig. 1. n-oligophenylenes vs. n-oligoacenes. (A and C) The HOMO–LUMO separation (E_g) calculated within our EBEM (blue) approach for n-oligo-phenylenes (A) and n-oligoacenes (C) molecules as a function of the molecular length (n being the number of fused phenyl rings). DFT calculations using GGA (red) and HSE (green) functionals as well as experimental data (grey) are extracted from ref. 35 and 36, respectively, and presented for comparison. (B and D) EPWE calculated band structures for the corresponding infinite polymers, i.e., n-poly(para-phenylene) or 3-AGNR (B) and n-polyacenes or 2-ZGNR (D).The red lines in (C) and (D) mark the gapless molecular length and the 2-ZGNR Dirac-point degeneracy, respectively. (E) The HOMO and LUMO positions obtained from EBEM (blue) are appended in (B) and (D) at the momenta marked by green lines [π/(n + 1)d]. (E) Molecular orbitals taken at the HOMO and LUMO position for benzene (top), p-quaterphenyl (middle), and pentacene (bottom).

Fig. 2. NP and NA molecular dimers. (A) The potential landscapes used as EBEM inputs for the zigzag and chevron phases of NP and NA (N = 4) kinked isomers. (B) The LDOS for the zigzag (green) and chevron (red) phase of 4P and for the zigzag 4A phase (blue). (C) The spatial distribution of wave functions for the first and second HOMOs and LUMOs of the three cases in (B). (D) The LDOS for the chevron phase of NA molecules for different N values. (E) Top: The spatial distribution of DOS taken at the HOMO, LUMO, and at the zero-point-energy (ZPE, Fermi level) for the case of 4A chevron phase, and Bottom: the wave functions at ZPE for different N values. (F) Left: The potential landscape for two joined kinked 4A isomers forming chevron phase and the corresponding LDOS (middle) and wave function (right) taken at ZPE.

Fig. 3. Chevron oligoacene polymer vs. polyacetylene. (A) Band structure of NA chevron-type polymers for N = 2–5. The N = 2 polymer is equivalent to 3ZGNR. (B) Band structure of polyacetylene (left) and its chevron-type (right) for M = 2–4, where M defines the number of carbon dimers per arm. The inset of (B) presents the potential landscape for the straight polyacetylene (M = 1) polymer and the corresponding M = 3 chevron-type (blue), which defines the edge of 4A chevron-type oligoacene shown in light brown.