Topological character and chiral solitons in double Peierls-distorted chains

Chiral edge states have played an important role in understanding condensed matter systems such as quantum Hall systems and topological insulators. In 1D electronic systems, Peierls-distorted atomic chains such as polyacetylene have two topologically different ground states and thus have topological edge states between them. The edge states---topological solitons---show novel properties of charge-spin separation and fractional charge. Here, we present theoretical results on the topological properties of double Peierls-distorted chains with interchain coupling. The double Peierls chains support a dynamically generated topological structure with four-fold symmetric ground states and have topological solitons with a new degree of freedom, chirality, which is absent in a single chain. We also discuss experimental evidence of the chiral solitons in the 1D charge-density wave (CDW) system of indium atomic nanowires on silicon substrates.