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We present a small polaron hopping model for interpreting the strong temperature (T ) dependence of the electrical conductivity, σ , observed at high (h) temperatures along DNA molecules. The model takes into account the one-dimensional character of the system and the presence of disorder in the DNA double helix. Percolation-theoretical considerations lead to analytical expressions for the high temperature multiphonon-assisted small polaron hopping conductivity, the hopping distance and their temperature dependence. The experimental data for lambda phage DNA (λ-DNA) and poly(dA)-poly(dT) DNA follow nicely the theoretically predicted behaviour (ln σ h ∼ T −2/3 ). Moreover, our model leads to realistic values of the maximum hopping distances, supporting the idea of multiphonon-assisted hopping of small polarons between next nearest neighbours of the DNA molecular 'wire'. The low temperature case is also investigated.

We study the thermoelectric coefficients of a multi-level quantum dot (QD) weakly coupled to two electron reservoirs in the Coulomb blockade regime. Detailed calculations and analytical expressions of the power factor and the figure of merit are presented. We restrict our interest to the limit where the energy separation between successive energy levels is much larger than the thermal energy (i.e., the quantum limit) and we report a giant enhancement of the figure of merit due to the violation of the Wiedemann-Franz law when phonons are frozen. We point out the similarity of the electronic and the phonon contribution to the thermal conductance for zero dimensional electrons and phonons. Both contributions show an activated behavior. Our findings suggest that the control of the electron and phonon confinement effects can lead to nanostructures with improved thermoelectric properties.

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Based on the generalized molecular crystal model (GMCM) and theoretical percolation arguments we investigate small polaron hopping transport in 1D disordered systems at high temperatures. Correlation (cr) effects are taken into account. An analytical expression for the temperature dependence of the electrical conductivity, lnσ(h,cr)∼T(-1/2), is obtained. This result reproduces satisfactorily the experimental data reported for λ-DNA and for poly(dA)-poly(dT) DNA, considering DNA as a one-dimensional disordered molecular wire in which small polarons are the charge carriers. lnσ(h,cr) versus T(-1/2) plots permit the evaluation of the maximum hopping distance. The results indicate that correlation effects are probably responsible for large hopping distances in DNA samples.