Executive Summary : | Over the past decade, realizing new topological phases of matter with their exotic boundary states have been one of the intense areas of research in condensed matter physics leading to the discoveries of different topological materials in three dimensions. Being a surface probing technique, scanning tunneling microscopy (STM) has been instrumental in exploring the unusual properties of these boundary states. However, this successful journey hardly encompasses the studies of these topologically protected robust states and exciting tunable properties emerging from the application of varieties of perturbations in the lower dimensional structures such as microcrystals and thin films. One of the reasons behind this is the cleanliness of the grown sample surfaces where any ex-situ treatment massively contaminates both the sample surface and the STM making those electronic states fragile. In this research proposal, we propose to investigate the various topologically nontrivial electronic states and their tunability with a wide range of perturbations combining ultra-high vacuum instrumentation, growth of quantum structures and thin films and STM under a single unified ultrahigh vacuum space. Under this proposal, mainly two materials namely SnTe and AlBi in their lower dimensional forms will be studied implementing various perturbations, e.g., structural phase transition, inducing strain, doping magnetic and nonmagnetic atoms, thickness engineering etc. These modifications have been predicted to show striking topological phenomena from the surface Dirac states such as anomalous quantum Hall effect, strain induced flat bands, new higher order topological insulating phases, building block for topological transistor, etc. In a broader view, this proposed research is search for the tunable properties of the electronic states in the lower dimension that intertwine dimensionality and geometry with band topology giving rise to the novel topological quantum systems providing higher degree of control for application in quantum technology. |