We consider a two-peak model for the phonon density of states to investigate the nature of electron pairing mechanism for superconducting state in fullerides. We first study the intercage interactions between the adjacent C₆₀ cages and expansion of lattice due to the intercalation of alkali atoms based on the spring model to estimate phonon frequencies from the dynamical matrix for the intermolecular alkali-C₆₀ phonons. Electronic parameter as repulsive parameter and the attractive coupling strength are obtained within the random phase approximation. Transition temperature, 𝑇_c, is obtained in a situation when the free electrons in lowest molecular orbital are coupled with alkali-C₆₀ phonons as 5 K, which is much lower as compared to reported 𝑇_c (≈ 20 K). The superconducting pairing is mainly driven by the high frequency intramolecular phonons and their effects enhance it to 22 K. To illustrate the usefulness of the above approach, the carbon isotope exponent and the pressure effect are also estimated. Temperature dependence of electrical resistivity is then analysed within the same model phonon spectrum. It is inferred from the two-peak model for phonon density of states that high frequency intramolecular phonon modes play a major role in pairing mechanism with possibly some contribution from alkali-C₆₀ phonon to describe most of the superconducting and normal state properties of doped fullerides.

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 C₆₀ 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 K₃C₆₀ and shows similar results on optical conductivity in the mid-infrared as well as infrared frequency regions as those revealed from experiments.

The anomalous temperature-dependent electrical resistivity ρ(𝑇) of La_0.875Sr_0.125MnO₃ manganite nanoparticles (particle size 18 nm) is theoretically analysed. ρ(𝑇) exhibits semiconducting phase in lowtemperature regime (20 𝐾 < 𝑇 < 53 K), shows a minima near 53 K and increases with 𝑇 at high temperatures (53 𝐾 < 𝑇 < 170 K). The resistivity in metallic phase (𝑇 > 53 K) is theoretically analysed by considering the strong spin-fluctuation effect, which is modelled using Drude–Lorentz type function. In addition to the spin fluctuation-induced contribution, the electron–phonon and electron–electron $ ρ_e–e(𝑇) = 𝐵𝑇² contributions are also incorporated for complete understanding of experimental data. The contributions to the resistivity by inherent acoustic phonons ( ρ_ac) as well as high-frequency optical phonons ( ρ_op) were estimated using Bloch–Gruneisen (BG) model of resistivity. It is observed that the resistivity contribution due to electron–electron interaction shows typical quadratic temperature dependence. Spin fluctuation-induced resistivity is dominant over electron–electron and electron–phonon contributions in overall temperature range in the manganite nanoparticles. Resistivity in the semiconducting phase is discussed with small polaron conduction (SPC) model. SPC model consistently retraces the low-temperature resistivity behaviour (𝑇 < 53 K). Finally, the theoretically calculated resistivity compared with experimental data is found to be consistent in wide range of temperature.