9 - Kinks in the laboratory

Summary

In this chapter we discuss two laboratory systems where kinks are known to exist. The first system is trans polyacetylene which has a broken Z₂ symmetry as in the λφ⁴ model. The second system is a Josephson junction transmission line, which is a laboratory realization of the sine-Gordon system. Helium-3 is another laboratory system that contains a wide variety of topological defects and the reader is referred to [174] for a discussion. In the third section of this chapter we describe Scott Russell's solitons in water. These solitons are not topological like the others discussed in this book but we include the discussion anyway since the reader's curiosity may have been aroused by the story in the Preface.

Polyacetylene

Polyacetylene consists of a linear chain of CH bonds. A sequence of x units is written as (CH)_x. In the ground state of polyacetylene, the carbon atom forms three σ bonds, one of them is to the H in the CH unit, one to the unit on the left and one to the right. In addition, there is one more electron orbital that can cause bonding. This is called the π electron, and the π bond can form to the left or to the right. Then there are two possible sequences – first when the double (σ and π) bond is to the carbon on the right and the single to the left, the second when the double bond is to the left and the single to the right. These two possibilities are illustrated in Fig. 9.1 [149] in the trans configuration of polyacetylene.