This work reports an analytical method for determining electrical resistivity (ρ) and sheet resistance (R_S) of isotropic conductors. The method is compared with previous numerical solutions and available experimental data showing a universal behavior for isotropic conductors. An approximated solution is also reported allowing one to easily determine ρ and R_S for samples either with regular or arbitrary shapes.

A procedure for determining the electrical resistivity of anisotropic materials is presented. It offers several improvements to the well-known Montgomery method. One improvement, in particular, is the ability to obtain the electrical resistivity for all three axes of an orthorhombic crystal analytically, rather than using the iterative approach suggested by Montgomery for the third axis. All necessary equations are derived and their application in determining the tensor components of the electrical resistivity is explained in detail. Measurements on isotropic specimens were executed in order to test the foundations of the method. Measurements on anisotropic samples are compared with measurements obtained by using the standard four-probe method, revealing good agreement.

Thermal expansion of ${\mathrm{Li}}_{0.9}{\mathrm{Mo}}_6{\mathrm{O}}_{17}$ is $a$-axis dominated which reduces the separation of the conducting chains at low temperature enhancing the interchain coupling. This destabilizes the Luttinger-liquid fixed point leading to an electronic charge- (or spin-) density wave dominated by Coulomb repulsion, as predicted by theories for Luttinger liquids.

${\text{SrTiO}}_3$ undergoes a cubic-to-tetragonal phase transition at 105 K. This antiferrodistortive transition is believed to be in competition with incipient ferroelectricity. Substituting strontium by isovalent calcium induces a ferroelectric order. Introducing mobile electrons to the system by chemical nonisovalent doping, on the other hand, leads to the emergence of a dilute metal with a superconducting ground state. The link between superconductivity and the other two instabilities is a question gathering momentum in the context of a popular paradigm linking unconventional superconductors and quantum critical points. We present a set of specific-heat, neutron-scattering, dielectric-permittivity, and polarization measurements on ${\text{Sr}}_{1-x}{\text{Ca}}_x{\text{TiO}}_3$ $\left(0<x<0.009\right)$ and a study of low-temperature electric conductivity in ${\text{Sr}}_{0.9978}{\text{Ca}}_{0.0022}{\text{TiO}}_{3-\delta }$. Calcium substitution was found to enhance the transition temperature for both antiferrodistortive and ferroelectric transitions. Moreover, we find that ${\text{Sr}}_{0.9978}{\text{Ca}}_{0.0022}{\text{TiO}}_{3-\delta }$ has a superconducting ground state. The critical temperature in this rare case of a superconductor with a ferroelectric parent is slightly lower than in ${\text{SrTiO}}_{3-\delta }$ of comparable carrier concentration. A three-dimensional phase diagram for ${\text{Sr}}_{1-x}{\text{Ca}}_x{\text{TiO}}_{3-\delta }$ tracking the three transition temperatures as a function of $x$ and $\delta$ results from this study, in which ferroelectric and superconducting ground states are not immediate neighbors.