Scanning tunneling microscopy (STM) provides an opportunity to study the physical and electromagnetic properties of surfaces at the atomic scale. When performed at low temperatures, in high magnetic fields, and with a variety of different probes, it offers a wide range of methods by which novel materials of great practical and theoretical interest can be evaluated, characterized, and even fabricated with atomic precision.

This thesis describes three independent STM studies performed at cryogenic temperatures. In the first, I present an in-situ modification to our 4K STM which permits us to current-bias our samples during STM operation. The modification can be used to study non-equilibrium effects such as spin accumulation induced by a current through a spin Hall material and the spin-momentum locking which is present at the surface of topological insulators.

Next, I examined oxygen-doped aluminum films with anomalously high kinetic inductance. A suggested explanation was the migration of oxygen to the grain boundaries, forming a percolation network separated by Josephson links. To determine the coupling between grains, I studied the films using milliKelvin STM performed with a superconducting tip.

Finally, transport measurements performed by our collaborators indicated the possible presence of a topological Hall effect in thin films of Cr2Te3, induced by the presence of topologically non-trivial magnetic textures called magnetic skyrmions. In order to provide more decisive evidence, I studied the films using spin-polarized STM at 4K.

In addition to the experimental studies, this work explores the theoretical underpinnings of the novel materials which constitute the frontier of our current understanding of condensed matter physics. An emphatically pedagogical viewpoint is adopted throughout as part of a continuing effort to bridge the gap between experiment and theory.