A search for superconductivity in conjugated polymers
The aim of this thesis is to search for a superconducting phase transition in a conjugated polymer with implanted magnetic atoms. To carry out this investigation we have performed a modified worldline quantum Monte Carlo (QMC) algorithm concentrating on the polymer cis-polyacetylene at finite temperatures. The Hamiltonian used is that of the extended Su-Schrieffer-Heeger discrete tight-binding electron-lattice model which incorporates on-site and nearest-neighbour electron-electron Hubbard terms, Brazovskii-Kirova symmetry breaking, and Kondo impurities. We have found that through changing the conduction charge doping level real space-charge pairs, bipolarons, can be stabilised in the presence of magnetic impurities within certain parameter regimes. This has been established through direct observation of the calculated lattice order parameter/staggered lattice distortion and net charge distributions. Thus we have demonstrated that real space charge pairs and magnetic atoms can coexist. In order to search for a second-order phase transition, indicative of possible superconducting behaviour, we have calculated the impurity magnetic staggered and uniform susceptibilities. This was done at discrete temperatures in the 60K – 300K range in the presence of stable hole bipolarons. The results show, at higher temperatures, an enhancement of the staggered over the uniform susceptibility for next-nearest-neighbour impurity separation. This is indicative of anti-ferromagnetic fluctuations arising from indirect exchange. In contrast, at lower temperatures the staggered and uniform susceptibilities converge consistent with the Kondo effect and destruction of the indirect exchange mechanism. When the impurity separation is increased to six lattice sites both susceptibilities are qualitatively the same at all temperatures as the impurities fluctuate independently. Thus the indirect exchange mechanism is short-ranged and the impurities should be relatively close to each other to facilitate anti-ferromagnetic fluctuations in the presence of bound hole pairs. The susceptibility measurements showed no signature of a phase transition within the aforementioned temperature range. The investigation is however inconclusive as lower temperatures proved computationally prohibitive.
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