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Exotic topological phases in polyacene chains

Rakesh Kumar Malakar, Asim Kumar Ghosh

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 five tight-binding models has been introduced which are formulated on another organic polymer called polyacene, where exotic topological behavior has been observed. Topological properties of the most common geometric isomers known as $cis$-polyacene, and $trans$-polyacene have been investigated along with three additional modified polyacene structures. Although their geometric structures differ by mirror symmetry, tight-binding band structures of $cis$-polyacene and $trans$-polyacene are found the same, where 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. However, $cis$-polyacene possesses additional mirror symmetry in the real space. Three modified structures of polyacene have been considered in order to induce the nontrivial topology, where exotic topological behavior is noted in two of them.

Exotic topological phases in polyacene chains

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 -polyacetylene in order to explain its anomalous conductivity. In this study, a group of five tight-binding models has been introduced which are formulated on another organic polymer called polyacene, where exotic topological behavior has been observed. Topological properties of the most common geometric isomers known as -polyacene, and -polyacene have been investigated along with three additional modified polyacene structures. Although their geometric structures differ by mirror symmetry, tight-binding band structures of -polyacene and -polyacene are found the same, where again their topological characters are found totally opposite. The -polyacene is nontrivial as it exhibits topological phase with nonzero winding number, while the -polyacene is topologically trivial, although both the structures adhere to the same set of symmetries required for the topological character. However, -polyacene possesses additional mirror symmetry in the real space. Three modified structures of polyacene have been considered in order to induce the nontrivial topology, where exotic topological behavior is noted in two of them.

Paper Structure

This paper contains 10 sections, 44 equations, 24 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. THE trans-POLYACENE MODEL
  3. THE trans-POLYACENE MODEL with bridging bonds
  4. THE cis-POLYACENE MODEL
  5. THE cis-POLYACENE MODEL with bridging bonds
  6. THE NONTRIVIAL cis-POLYACENE MODEL
  7. Discussion
  8. ACKNOWLEDGMENTS
  9. Data availability statement
  10. Conflict of interest

Figures (24)

  • Figure 1: Structure of trans-polyacene. Carbon atoms marked by A, B, C and D constitute a unit cell. One such unit cell is shown within shaded region.
  • Figure 2: Variation of energies (a) and winding number (b) with $v/w$ of trans-polyacene. Top colorbar indicates the variation of $I_{pr}$.
  • Figure 3: Dispersion relations of t-pol model for (a) $v=0.2$, $w=1$; (b) $v=0.5$, $w=0.5$. Energy gap in (a) is shown by green shade.
  • Figure 4: Variation of energies for trans-polyacene when $v/w=0.2$, is shown in ascending order (a). The presence of four edge states at zero energy is found. Top colorbar indicates the variation of $I_{pr}$. Probability density of four edge states are shown in the histogram by different colors (b).
  • Figure 5: Real space configuration of atoms and bonds within trans-polyacene for two extreme cases, (a) when $v\ne 0$ but $w=0$, and (b) when $w\ne 0$ but $v=0$. Free atoms are shown within dotted circles.
  • ...and 19 more figures