Physics of complex metals: Temperature-dependent resistivities in ionic superconductors and stable quasicrystals

Elementary phase-space arguments for electron-phonon scattering in metals give the temperature-dependent resistivity \ensuremath{\rho}(T)\ensuremath{\sim}${\mathit{T}}^{\mathit{n}}$ with n\ensuremath{\ge}3. Similarly for electron-electron scattering n=2. To explain n=1 for superconductive (Bi,Sr${)}_{4}$${\mathrm{CuO}}_{6+\mathrm{\ensuremath{\delta}}}$ over the range 7T700 K one can assume a structural model with punctured semiconductive domain walls. There is strong evidence for this model not only in oxide perovskites, but also in Chevrel compounds such as ${\mathrm{EuMo}}_{6}$${\mathrm{S}}_{8\mathrm{\ensuremath{-}}\mathit{y}}$${\mathrm{O}}_{\mathit{x}}$, which also exhibit linear \ensuremath{\rho}(T) over a narrower temperature range. In the domain-wall model recoil energy and momentum are absorbed by the walls, much as umklapp momentum is absorbed by the crystal as a whole in pure polyvalent metals. A wide range of experimental data support the model. By-products of the model are explanations of carrier freeze-out as measured by diverse anomalies in the Hall resistance, the correlation of ${\mathit{T}}_{\mathit{c}}$ with the slope of the linear background tunneling conductance of Pb-Bi-O superconductors, a simple qualitative explanation for the first- (second-) order electronic (structural) phase transition observed near x=0.21 in well-annealed ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$, and an explicit mechanism for the origin of c-axis linear resistivities in intercalated Bi-Sr cuprates. A similar microstructural model explains the linear temperature dependence of the hopping conductance in stable ternary quasicrystals. The key factor common to both ionic superconductors and stable quasicrystals is their multinary composition which creates hierarchies of saddle points in the local conductance.