The temperature-dependent normal state resistivity of single-crystal Nd1.85Ce0.15CuO4−δ is theoretically analysed within the framework of the classical electron–phonon model of resistivity, i.e. the Bloch–Gruneisen model. Due to inherent acoustic (low-frequency) phonons (ωac) as well as high-frequency optical phonons (ωop), the contributions to the resistivity have first been estimated. The optical phonons of the oxygen-breathing mode yield a relatively larger contribution to the resistivity compared to the contribution of acoustic phonons. The contribution to resistivity estimated by considering both phonons, i.e. ωac and ωop, along with the zero limited resistivity, when subtracted from single-crystal data, infers a quadratic temperature dependence over most of the temperature range (25 ≤ T ≤ 300 K). The quadratic temperature dependence of ρdiff = [ρexp − {ρ0 + ρe-ph( = ρac + ρop)}] is understood in terms of electron–electron inelastic scattering. The comparison of single-crystal experimental data with the present analysis appears to be favourable.

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We evolve a theoretical model for quantitative analysis of decrease in thermal conductivity (κ) by embedding ErAs nanoparticles in In0.53Ga0.47As crystalline semiconductors. The lattice thermal conductivity by incorporating the scattering of phonons with defects, grain boundaries, electrons, and phonons in the model Hamiltonian are evaluated. It is noticed that the ErAs nanoparticles provide an additional scattering mechanism for phonons. The embedding of ErAs nanoparticles in In0.53Ga0.47As crystalline semiconductors, the phonon scattering with point defects and grain boundaries become more efficient, which cause in the decrease of thermal conductivity up to half of its value of pure crystal. Conclusively, the temperature dependent of thermal conductivity is determined by competition among the several operating scattering mechanisms for the heat carriers. Numerical analysis of thermal conductivity from the present model shows similar results as those revealed from experiments.

The observed frequency dependent optical response of alkali-metal-doped fulleride superconductors (T c ≈ 19 K) has been theoretically analysed. The calculations of the optical conductivity, σ (ω), have been made within the two-component schemes: one is the coherent Drude carriers (electrons) responsible for superconductivity and the other is incoherent motion of carriers from one atom to other atom of C 60 molecule to a pairing between Drude carriers. The approach accounts for the anomalies reported (frequency dependence of optical conductivity) in the optical measurements for the normal state. The model has only one free parameter, the relaxation rate. The frequency dependent relaxation rates are expressed in terms of memory functions. The coherent Drude carriers form a sharp peak at zero frequency and a long tail at higher frequencies, i.e. in the infrared region. However, the hopping of carriers from one atom to the other (incoherent motion of doped electrons) yields a peak value in the optical conductivity centred at mid-infrared region. It is found that both the Drude and hopping carriers will contribute to the optical process of conduction in the K 3 C 60 and shows similar results on optical conductivity in the mid-infrared as well as infrared frequency regions as those revealed from experiments.