Topological phases in condensed matter systems have received tremendous interest in the past two decades. Theoretical work has shown how topological invariants can be calculated from the band structures in a wide range of insulating systems that contain an energy gap. Broadly speaking, these topological invariants are quantities that are invariant under continuous deformation so long as specific symmetries hold and the energy gap stays open. What separates topological states of matter from traditional phases is the concept of bulk-boundary correspondence. The topology of the vacuum is trivial, so if the bulk of a material is topologically non-trivial, the energy gap must close at the boundary between the two. This creates conducting states at the boundaries, or edges, of the material; the conducting states within the gap have specific properties. Strong, 3Dtopological insulators, such as Bi2Se3 , are materials that are insulating in the bulk with conducting surface states due to bulk-boundary correspondence. The surface states are topologically protected from local perturbations and feature a linear dispersion relation, known as the Dirac cone. Bi2Se3is one of the most widely studied topological insulators due to the relative simplicity of its band structure with a single Dirac cone. In this work, I study the effects of N2 gas on the surface states of Bi2Se3 , which appears to p-type dope the density of states spectra measured with a scanning tunneling microscope. Topological superconductors have also garnered great interest for their potential applications in topological quantum computing. The second half of this dissertation is focused on describing, fabricating, and measuring a potential platform for a possible topological superconducting state known as a Majorana zero mode. These devices feature Nb sputtered onBi2Se3 that is patterned into Josephson junctions with e-beam lithography techniques.
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