STM investigation of nanoscale inhomogeneity in single-layer FeSe/SrTiO$_{3}$*

FeSe possesses the simplest stoichiometry within the family of iron-based high-$T_{c}$ superconductors. The ability to grow high quality films layer-by-layer using molecular beam epitaxy (MBE) yields opportunities to engineer high-$T_c$ superconducting heterostructures with novel behaviors. In particular, single-layer FeSe deposited on SrTiO$_{3}$ exhibits an order of magnitude increase in $T_c$ from its bulk value, possibly due to strain, charge doping or enhanced electron-phonon coupling from the substrate. We use a combined scanning tunneling microscope (STM) and MBE system to examine single-layer FeSe/SrTiO$_{3}$ at the atomic scale. Using real-space spectroscopic imaging, we investigate the superconducting states in this material, and their perturbation by various nanoscale disorders within the FeSe film and its substrate.