Materials tuned to the neighbourhood of a zero temperature phase transition often show the emergence of novel quantum phenomena. Much of the effort to study these new effects, like the breakdown of the conventional Fermi-liquid theory of metals has been focused in narrow band electronic systems. Ferroelectric crystals provide a very different type of quantum criticality that arises purely from the crystalline lattice. In many cases the ferroelectric phase can be tuned to absolute zero using hydrostatic pressure or chemical or isotopic substitution. Close to such a zero temperature phase transition, the dielectric constant and other quantities change into radically unconventional forms due to the quantum fluctuations of the electrical polarization. The simplest ferroelectrics may form a text-book paradigm of quantum criticality in the solid-state as the difficulties found in metals due to a high density of gapless excitations on the Fermi surface are avoided. We present low temperature high precision data demonstrating these effects in pure single crystals of SrTiO 3 and KTaO 3 . We outline a model for describing the physics of ferroelectrics close to quantum criticality and highlight the expected 1/T 2 dependence of the dielectric constant measured over a wide temperature range at low temperatures. In the neighbourhood of the quantum critical point we report the emergence of a small frequency independent peak in the dielectric constant at approximately 2 K in SrTiO 3 and 3 K in KTaO 3 believed to arise from coupling to acoustic phonons. Looking ahead, we suggest that ferroelectrics could be used as systems in which to controllably build in extra complexity around the quantum critical point. For example, in ferroelectric or antiferroelectric materials supporting mobile charge carriers, quantum paraelectric fluctuations may mediate new effective electron-electron interactions giving rise to a number of possible states such as superconductivity.The study of quantum matter at low temperatures has given rise to a fascinating and often surprising catalogue of phenomena important to our understanding of nature 1 and to technological development 2 . In particular, the study of materials close to a continuous low temperature phase transition or so called quantum critical point forms an important branch of research within condensed matter physics. A chief reason for this is that close to such a transition, materials become highly degenerate and new states of matter are frequently found to emerge. In fact, it turns out that many materials end up being close to or within the quantum critical regime. This is because quantum critical phenomena can affect materials over a wide range of temperatures, pressures and other variables. In electrically conducting materials, the standard model of the metallic state, Landau's Fermi liquid theory is seen to breakdown close to the low temperature boundary between a magnetic and paramagnetic phase and is replaced with other forms of novel quantum liquid. For example, in some weakly magnet...

Up to now, the crystallographic structure of the magnetoelectric perovskite EuTiO 3 has been considered to remain cubic down to low temperature. Here we present high-resolution synchrotron x-ray powder-diffraction data showing the existence of a structural phase transition, from cubic P m-3m to tetragonal I 4/mcm, involving TiO 6 octahedra tilting, in analogy to the case of SrTiO 3 . The temperature evolution of the tilting angle and of the full width at half maximum of the (200) cubic reflection family indicate a critical temperature T c = 235 K. This critical temperature is well below the recent anomaly reported by specific-heat measurement at T A ∼ 282 K. By performing atomic pair distribution function analysis on diffraction data, we provide evidence of a mismatch between the local (short-range) and the average crystallographic structures in this material. Below the estimated T c , the average model symmetry is fully compatible with the local environment distortion, but the former is characterized by a reduced value of the tilting angle compared to the latter. At T = 240 K, data show the presence of local octahedra tilting identical to the low-temperature one, while the average crystallographic structure remains cubic. On this basis, we propose that intrinsic lattice disorder is of fundamental importance in the understanding of EuTiO 3 properties.