Interactions of atoms with their environment govern many physical phenomena including heterogeneous chemical reactions producing either desirable or non-desirable products that occur often at surfaces and interfaces. Despite the tremendous progress in surface science achieved during the last decades, a deeper, more complete understanding of the fundamental mechanisms of atomic-scale surface interactions remains a major scientific challenge. One tool that is well suited to address some of the related challenges is scanning probe microscopy, which reveals the physical, chemical, biological, and optical properties of surfaces in real space with high-resolution.

In this thesis, I will show that a recently developed scanning probe microscopy method referred to as tuned-oscillator atomic force microscopy (TO-AFM) can be used for advanced material characterization. The main breakthrough introduced by TO-AFM is the ease of its application for high-resolution characterization compared to existing modulation techniques. TO-AFM enables robust, high-resolution material characterization with picometer and pico-Newton resolution with only one control loop, while alternative modulation techniques require at least two and most commonly three interacting control loops. To establish its usefulness, its imaging and spectroscopy performance will be illustrated with layered materials, ionic crystals, and metal oxides as model systems. This part of the thesis will also include an analysis of the contrast mechanism of high-resolution scanning probe microscopy images with simultaneous TO-AFM and scanning tunneling microscopy measurements.

In the last part of the thesis, applications of the developed methodologies and instrumentation to exotic materials will be given. For example, I will demonstrate an ability to probe and modify the charge carrier densities of perovskites with a scanned probe, which may advance the epitaxial growth of high-temperature superconducting thin films by fine-tuning the local charge carriers during the growth. Most prominently, however, I will present the results of my investigations into the growth and characterization of epitaxial topological crystalline insulators employing scanning probe microscopy and spectroscopy experiments and discuss them in the light of complementary ab initio density functional theory calculations. The effect of local symmetry on topological surface states of topological crystalline insulators will be highlighted in particular, ultimately providing a gateway for the tuning of the surface states by tailoring the surface topography. This effect of broken local symmetry on topological surface states opens new horizons for spin-orbit based electronic devices, which span transistors, quantum dots, and microwave circuits.