Plastic deformation of SrTiO₃ single crystals generates a superstructure of line dislocations seen in X-ray and neutron diffraction. Enhancement of superconductivity and anisotropic conductivity occurs along these dislocation structures. Nano-spectroscopy is a tool that can measure the optical properties of SrTiO₃ with sufficient spatial resolution to image these structures.

Phase-resolved hyperspectral imaging using a scanning near-field optical microscope measured nanoscale variations in the optical phonon response in plastically deformed SrTiO₃. This technique generates a large amount of multi-dimensional data, which require new modes of analysis to understand. Principal component analysis extracted the principal variations and reduced the dimensionality of the data. The complex principal variations were then mapped onto linear variations in the real physical parameters of the system through a novel method of constrained linear regression. The result is a nanoscale map of variations in the damping, frequency and other parameters of the optical phonon due to the presence of dislocation structures at the surface. These parameters can be related to local disorder and strain. 

Fluctuations in the optical phonon response exhibit a periodic texture of lines correlated with the nano-scale surface corrugations perpendicular to the strained axis. These nanoscale maps of the system parameters will be used to understand the enhancement of superconductivity observed at low temperatures.