Exploring the effects of doping on polar order and lattice dynamics in strontium titanate

Strontium titanate is an incipient ferroelectric in which superconductivity emerges at exceptionally low doping levels. Stabilizing the polar phase through strain or chemical substitution has been shown to significantly enhance the superconducting critical temperature, and the polar instability plays a pivotal role in most proposed superconducting pairing mechanisms. To investigate the effects of doping on the nature of the polar order in strontium titanate, we develop a simplified free energy model which includes the degrees of freedom necessary to capture the relevant physics in a doped, biaxially compressively strained system. We simulate the ferroelectric and antiferrodistortive phase transitions using the Monte Carlo method for different doping levels, and comment on the doping dependence of the transition temperatures and the formation of polar nanodomains. The temperature-dependent phonon spectral function is calculated using Langevin dynamics to investigate the lattice dynamics of the doped system. Finally, we calculate the electron phonon coupling constant and place our results in the broader context of proposed pairing mechanisms in strontium titanate.