Observation and manipulation of a phase separated state in a charge density wave material

The 1T polytype of TaS$_\textrm{2}$ has been studied extensively as a strongly correlated system. As 1T-TaS$_\textrm{2}$ is thinned towards the 2D limit, its phase diagram shows significant deviations from that of the bulk material. Optoelectronic maps of ultrathin 1T-TaS$_\textrm{2}$ have indicated the presence of non-equilibrium charge density wave phases within the hysteresis region of the nearly commensurate (NC) to commensurate (C) transition. We perform scanning tunneling microscopy on exfoliated ultrathin flakes of 1T-TaS$_\textrm{2}$ within the NC-C hysteresis window, finding evidence that the observed non-equilibrium phases consist of intertwined, irregularly shaped NC-like and C-like domains. After applying lateral electrical signals to the sample we image changes in the geometric arrangement of the different regions. We use a phase separation model to explore the relationship between electronic inhomogeneity present in ultrathin 1T-TaS$_\textrm{2}$ and its bulk resistivity. These results demonstrate the role of phase competition morphologies in determining the properties of 2D materials.