Spectral density functions for polyacetylene within the Peierls - Hubbard model

D Góra, K Rosciszewski
1996 Journal of Physics: Condensed Matter  
A Peierls-Hubbard Hamiltonian suitable for the description of polyacetylene electronic structure is studied. We employ the Lanczos method to calculate the ground-state properties and single-particle spectral density functions appropriate for the description of the photoemission and the inverse photoemission spectra. The data obtained confirm that the dimerized polyacetylene is more stable than an undimerized one and elucidate how the Coulomb and the electron-phonon interactions open up a
more » ... transfer gap near the Fermi level. In particular we found that the value of the gap increases when the electron-phonon interaction is switched on. D Góra and K Rościszewski Lanczos method applied to small clusters. Such an approach yields deviations from infinitesystem data but the deviations are well understood. That is, the trends in finite-size effects can be inferred from calculations done on several clusters of different sizes. Let us now consider, in detail, the problem of which model is appropriate for the proper description of PA. PA is a linear polymer which consists of CH units forming a quasione-dimensional lattice. Three of the four carbon valence electrons participate in σ -bonds, while one electron participates in the π-bond (sp 2 hybridization). Electronic energies of σ -bonds are at relatively deep levels. The interesting low-energy physical behaviour of PA can be accounted for by taking into account the effective Hamiltonian describing the π-electrons alone. The competition between the lowering of the electronic energy caused the formation of a conjugated single-double-bond structure and the increase of the elastic energy of the polymer (caused by distortion) leads to an equilibrium bond-length modulation (dimerization). The simplest Hamiltonian capable of modelling this situation is the Su-Schrieffer-Heeger (SSH) Hamiltonian [18]. This is a model based on an effective free electron plus 'static' phonons plus the possibility of dimerization. Correlation effects are non-existent. When the SSH model is extended (by adding Coulomb interactions between electrons) we obtain the Peierls Hubbard Hamiltonian [8, 19] :
doi:10.1088/0953-8984/8/46/006 fatcat:3kdyinw4irdpnev6h7vxfihcvi