Mesoscopic fluctuating domains in strontium titanate

Spatial correlations between atoms can generate a depletion in the energy dispersion of acoustic phonons. Two well-known examples are rotons in superfluid helium and the Kohn anomaly in metals. Here I will present the observation of a large softening of the transverse acoustic mode in quantum paraelectric SrTiO₃ by means of inelastic neutron scattering. In contrast to other known cases, this softening occurs at a tiny wave vector implying spatial correlation extending over a distance as long as 40 lattice parameters. We attribute this to the formation of mesoscopic fluctuating domains due to the coupling between local strain and ferroelectric fluctuations. Thus, a hallmark of the ground state of insulating SrTiO₃ is the emergence of hybridized optical-acoustic phonons. I will discuss how these mesoscopic fluctuating domains may play a role in quantum tunneling, which impedes the emergence of a finite macroscopic polarization and change our understanding of the ground state of quantum paralectrics and their remarkable transport properties.