Topological phases of polyacenes

Abstract

The introduction of Su-Schrieffer-Heeger model has led to a major breakthrough in the area of one-dimensional topological insulators, even though this model was primarily formulated on an organic polymer called $trans$-polyacetylene in order to explain its anomalous conductivity. In this study, a group of seven tight-binding models has been introduced which are formulated on another organic polymer called polyacene, where a variety of topological phases have been observed in six models. Topological properties of the most common geometric isomers known as $cis$-polyacene, and $trans$-polyacene have been investigated along with five additional modified polyacene structures. Although their geometric structures differ by several symmetries, tight-binding band structures of $cis$-polyacene and $trans$-polyacene are found the same, and again their topological characters are found totally opposite. The $trans$-polyacene is nontrivial as it exhibits topological phase with nonzero winding number, while the $cis$-polyacene is topologically trivial, although both the structures adhere to the same set of symmetries required for the topological character of BDI class. However, $cis$-polyacene possesses additional mirror symmetry in the real space but lacks inversion symmetry. Additional two modified structures of $trans$-polyacene and three modified structures of $cis$-polyacene have been considered in order to induce the nontrivial topology. Pair of flat bands is found both in modified $trans$-polyacene and $cis$-polyacene structures such that they are topologically nontrivial for $trans$-polyacene while trivial for $cis$-polyacene. Topological character of all the models is different.

arXiv comment21 pages, 35 figures, 1 table, title is changed