Novel condensed-matter systems that host exotic electronic states provide many opportunities for new device technologies based on spintronics and topotronics. A wide variety of materials systems are under investigation internationally, each with its own advantages and disadvantages. Two promising families of materi- als are investigated via scanning probe microscopy (SPM) in this thesis. These materials are group-V elemental two dimensional (2D) materials which possess non-trivial topologies, and rare-earth nitrides (RENs) that are intrinsic ferro- magnetic semiconductors. First, the geometry of the moiré patterns (MPs) in multi-layered 2D group-V materials are investigated by scanning tunneling mi- croscopy (STM). The MPs arising from the superposition of various 2D allotropes of bismuth and antimony are characterised and accurately modelled with a sim- ple superposition model. A general, analytical model for the predictions of MPs is also derived. Secondly, a method for overcoming the fast degradation of RENs in ambient atmosphere is developed using a removable samarium capping layer. The removal of the cap is performed through sputtering and thermal treatment, and characterised with atomic force microscopy, scanning electron microscopy, energy dispersive x-ray spectroscopy and other techniques. The removable cap enables further ex-situ surface characterisation of RENs. Lastly, a preliminary study of room temperature nitridation of gadolinium in ultra-high vacuum is also presented.