Emergence of localized in-gap states in conjugated polymers of branched topology

Using cryogenic scanning tunneling microscopy and spectroscopy, we investigated cross-linked phenyelene-based polymers with various branched morphology at a single-molecule resolution. We found that localized states that are in the band gap of un-branched polymers emerge at the branch junctions. These in-gap states can be shifted close to the Fermi level through three means: extending the length of branch arms, coupling adjacent branches in hyperbranched structures, or increasing the number of branch arms. Single-band tight-binding calculations can reproduce all experimental results and provide quantitative relationships between the energy level shifts and the branching geometry. Our discovery evidences the emergence and development of in-gap states in the band structures of conjugated systems with fractional dimensions.