We describe an extension of a lattice dynamical model for displacive-type ferroelectrics which might be applied to high-temperature superconductors. The model is based on the instability of the oxygen ion ${\mathrm{O}}^{2-}$, dynamically described by an on-site nonlinear electron-ion coupling, and on the valence instability of the cation [e.g., Cu(I), Cu(III)], represented by a nonlinear electron-electron interaction which provides a pairwise coupling of the electrons. The equivalent quantum-mechanical Hamiltonian describes an extended Peierls-Hubbard system. The most important outcome of the model is that a ferroelectric instability is a necessary condition for paired electron states which indicate the possibility of superconductivity. Depending on the strength of the coupling constants, either a ferroelectric or a superconducting state results.

Superconductivity was discovered in 1911 by Kamerlingh Onnes and Holst in mercury at the temperature of liquid helium (4.2 K). It took almost 50 years until in 1957 a microscopic theory of superconductivity, the so-called BCS theory, was developed. Since the discovery a number of superconducting materials were found with transition temperatures up to 23 K. A breakthrough in the field happened in 1986 when Bednorz and Müller discovered a new class of superconductors, the so-called cuprate high-temperature superconductors with transition temperatures as high as 135 K. This surprising discovery initiated new efforts with respect to fundamental physics, material science, and technological applications. In this brief review the basic physics of the conventional low-temperature superconductors as well as of the high-temperature superconductors are presented with a brief introduction to applications exemplified from high-power to low-power electronic devices. Finally, a short outlook and future challenges are presented, finished with possible imaginations for applications of room-temperature superconductivity.

We have recently predicted and subsequently verified experimentally by specific heat measurements that EuTiO₃ undergoes a structural phase transition at elevated temperature T _S = 282 K. The origin of the phase transition has been attributed to the softening of a transverse acoustic mode stemming from an oxygen octahedral rotation analogous to SrTiO₃. Here we demonstrate that the theoretical interpretation is correct by using high-resolution laboratory X-ray powder diffraction which evidences a cubic to tetragonal phase transition in EuTiO₃. The room temperature structure could be refined in with a = 3.9082(2) Å and at 100 K the refinement in the tetragonal space group resulted in a = 5.5192(2) and c = 7.8164(8) Å.

A comparative analysis of the structural phase transitions of EuTiO${}_3$ and SrTiO${}_3$ (at $T_{\mathrm{S}}$ $=$ 282 and 105 K, respectively) is made on the basis of phonon-dispersion and density functional calculations. The phase transition of EuTiO${}_3$ is predicted to arise from the softening of a transverse acoustic zone boundary mode caused by the rotations of the TiO${}_6$ octahedra, as also found for the phase transition of SrTiO${}_3$. Although the temperature dependence of the soft mode is similar in both compounds, their elastic properties differ drastically because of a large difference in the double-well potentials associated with the soft zone boundary acoustic mode. DOI: http://dx.doi.org/10.1103/PhysRevB.84.184114 ©2011 American Physical Society