SU Schrieffer and Heeger

In a seminal paper [4], Su, Schrieffer, and Heeger discussed the energetics of solitons using a simple model of free electrons interacting with the lattice described by the Hamiltonian ... 

After the discovery of the metallic behaviour of PAc (Shirakawa et al., 1977) most of the work on theoretical models concentrated on this polymer. This built on the earlier studies of Longuet-Higgins and Salem (1959) and others who used the Hiickel model to demonstrate that the backbone of PAc in its ground state has a bond alternated structure, Fig. 9.8(b), rather than one with equal length C-C bonds, Fig. 9.8(a). In 1979 a Hiickel tight binding model was introduced that provided the basis for much of the subsequent discussion of themolecular and electronic structure of PAc (Su, Schrieffer and Heeger, 1979 and 1980). It is now usually referred to as the SSH model. In the adiabatic... 

That form will be important for the formulation of the Su, Schrieffer and Heeger (SSH) theory as we will show later. Note that the neutral radical defect has a non-zero spin that is experimentally detected by ESR measurements. Charged solitons are defects that may be generated by the reduction or the oxidation of the chain, i.e. the monoanions or monocations created, respectively, have no spin as illustrated in the following formulae and in Fig. 36.12 for an oxidative doping such as... 

Fig. 36.13. Top Pople and Walmsley misfit, bottom Su, Schrieffer and Heeger soliton defect.

In a TT-electron theory the ion represents the CH group, so there are three ionic degrees of freedom per unit cell. These ionic degrees of freedom may be formally represented as collective, normal modes. Su, Schrieffer, and Heeger, in their treatment of frans-polyacetylene, introduced a simplification to this problem (Su et al. 1970). This simplification was to consider only the normal mode that predominantly couples to the tr-electrons. For polyacetylene this is the carbon bond stretching vibration. Thus, projecting the ionic coordinates onto the chain axis, denoted by the x-axis, we have the Su-Schrieffer-Heeger (SSH) Hamiltonian, defined as,... 

To test this hypothesis one can start by writing down a Hamiltonian for the soliton. Generalizing the theory of Su, Schrieffer, and Heeger... 

For polyacetylene, many authors apply the so-called SSH Hamiltonian introduced by Su, Schrieffer, and Heeger (1980), which is an alternative to the Longuet-Higgins model. The difference is only in the handling of the a core potential function f and in the parametrization of the model. 

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