  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 SrTiO3 and KTaO3. We outline a model for describing the
physics of ferroelectrics close to quantum criticality and highlight the
expected 1/T2 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 2K in SrTiO3 and 3K in KTaO3 believed
to arise from coupling to acoustic phonons. Looking ahead, we suggest that in
ferroelectric 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.
