Band structure of metallic trans-polyacetylene with alkali-metal doping.

Abstract

For the average doping 〈y〉>0.4%, trans-polyacetylene is a mixture of heavily doped, ordered regions and weakly doped (\ensuremath{\sim}0.4%) disordered regions. The sharp increase in magnetic susceptibility that marks the insulator-metal transition is consistent with there still being a small gap in the heavily doped regions or with these regions being metallic. The temperature dependence of the resistivity, although dominated by the weakly doped regions, indicates that in some of the most highly doped samples the heavily doped regions are metallic. To determine whether we can account for metallic behavior, we have calculated the band structure of a heavily doped polyacetylene chain with the electrons in soliton states, as indicated experimentally, taking into account the Coulomb potential of the doping ions and solitons on surrounding chains. The lattice structure used was that determined by x rays for stage-1 potassium-doped polyacetylene. Because the arrangement of the solitons relative to the dopants is unknown, we used two different arrangements: a symmetric one and a staggered one.In calculating the potential of a point charge, the limitation in screening due to the confinement of the electrons on chains was taken into account. Because screening depends on the calculated density of states at the Fermi energy, \ensuremath{\eta}(${\mathit{E}}_{\mathit{F}}$), which, in turn, depends on the potential used to calculate \ensuremath{\eta}(${\mathit{E}}_{\mathit{F}}$), self-consistency was required in the calculations. However, for the high doping level of stage-1 K-doped polyacetylene (16.7%), \ensuremath{\eta}(${\mathit{E}}_{\mathit{F}}$) obtained from the energy levels was found to be relatively insensitive to the value of \ensuremath{\eta}(${\mathit{E}}_{\mathit{F}}$) used in the calculation of the screening, indicating that approximations made in treating the screening have relatively little effect. Calculations were carried out for the symmetric and staggered arrangements for chains of 104 and 296 sites, corresponding to 16 and 48 solitons, respectively. The chains were found to be metallic in all four cases, but there is a small gap two levels below the Fermi energy in the symmetric case. The self-consistent \ensuremath{\eta}(${\mathit{E}}_{\mathit{F}}$) at 300 K for 104-site chains was found to be 0.09 state/eV C-atom, about what is deduced from room-temperature Pauli-susceptibility measurements on highly doped samples, and 0.14 state/eV C-atom for a 296-site chain.