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Scanning near-field optical microscopy is one of the most effective techniques for spectroscopy of nanoscale systems. However, inferring optical constants from the measured near-field signal can be challenging because of a complicated and highly nonlinear interaction between the scanned probe and the sample. Conventional fitting methods applied to this problem often suffer from the lack of convergence or require human intervention. Here, we develop an alternative approach where the optical parameter extraction is automated by a deep learning network. The network provides an initial estimate that is subsequently refined by a traditional fitting algorithm. We show that this method demonstrates superior accuracy, stability against noise, and computational speed when applied to simulated near-field spectra.

We report the Drude oscillator strength D and the magnitude of the bulk band gap E_{g} of the epitaxially grown, topological insulator (Bi,Sb)_{2}Te_{3}. The magnitude of E_{g}, in conjunction with the model independent f-sum rule, allows us to establish an upper bound for the magnitude of D expected in a typical Dirac-like system composed of linear bands. The experimentally observed D is found to be at or below this theoretical upper bound, demonstrating the effectiveness of alloying in eliminating bulk charge carriers. Moreover, direct comparison of the measured D to magnetoresistance measurements of the same sample supports assignment of the observed low-energy conduction to topological surface states.

We resolved the enigma of anisotropic electronic transport in strained vanadium dioxide (VO2) films by inquiring into the role that strain plays in the nanoscale phase separation in the vicinity of the insulator-to-metal transition. The root source of the anisotropy was visualized as the formation of a peculiar unidirectional stripe state which accompanies the phase transition. Furthermore, nanoscale infrared spectroscopy unveils distinct facets of electron-lattice interplay at three different stages of the phase transition. These stages include the initial formation of sparse nonpercolating metallic domains without noticeable involvement of the lattice followed by an electron-lattice coupled anisotropic stripe state close to percolation which ultimately evolves into a nearly isotropic rutile metallic phase. Our results provide a unique mesoscopic perspective for the tunable macroscopic phenomena in strained metal oxide films.