  We use apertureless scattering near-field optical microscopy (SNOM) to
investigate the nanoscale optical response of vanadium dioxide (VO2) thin films
through a temperature-induced insulator-to-metal transition (IMT). We compare
images of the transition at both mid-infrared (MIR) and terahertz (THz)
frequencies, using a custom-built broadband THz-SNOM compatible with both
cryogenic and elevated temperatures. We observe that the character of spatial
inhomogeneities in the VO2 film strongly depends on the probing frequency. In
addition, we find that individual insulating (or metallic) domains have a
temperature-dependent optical response, in contrast to the assumptions of a
classical first-order phase transition. We discuss these results in light of
dynamical mean-field theory calculations of the dimer Hubbard model recently
applied to VO2.
