Optical Conductivity Studies of Small Polaron Hopping in Sm$_{\mathrm{1-x}}$Sr$_{\mathrm{x}}$TiO$_{3}$ Epitaxial Films

We present our findings in the optical conductivity in a doping-controlled metal-to-Mott-insulator transition. These samples, grown using hybrid MBE, span the transition from the Mott insulator SmTiO$_{3}$ to metallic, lightly-doped SrTiO$_{3}$. Zhou and Goodenough have studied a wide range of rare earth titanates and found that SmTiO$_{3}$ has thermally activated transport. We plan to measure the optical conductivity of doped samples to determine the conduction mechanism. Using FTIR spectroscopy, we extract the optical conductivity in the 0.06-2.5 eV range. If conduction in Sm$_{\mathrm{1-x}}$Sr$_{\mathrm{x}}$TiO$_{3}$ is due to small polarons, it will have a distinct optical conductivity feature, related to the DC transport, as described by David Emin. Alternatively, conduction could be due to variable-range hopping between defects. Further, from the combination of DC and optical conductivity, we can also test the prediction of Yee and Balents that the metal-to-insulator transition is first-order with percolative phase separation between metallic and localized regions. Such a sample would have a distinct Drude tail plus polaron contributions to its conductivity.