Doctor of Philosophy (PhD)
Physics & Astronomy
In this dissertation we analyze how Majorana quasiparticles found on material interfaces of both topological insulators (TIs) and topological superconductors (TSCs) are affected by imperfections within their local environment. While these quasiparticles are predicted to be critical for the construction of quantum computers, they are typically modeled only under pristine conditions. Thus, although quantum computers may require the spatial manipulation of Majorana quasiparticles, these topological material interfaces are commonly studied in static contexts and their response to manipulation remains an open question. We first demonstrate that interface potentials on the topological insulator Bi2Se3 can enable the emergence of Majorana bound states. Specifically, we study how non-helical spin-textures at the boundaries between TIs and SCs affect the proximity-induced superconductivity of the TI-interface state. We furthermore show that the Andreev conductance of lateral heterostructures joining TI-vacuum and TI-SC interfaces yields experimental signatures of the reduced symmetries of the interface. Next, we study the in-gap states that appear at the boundaries of both one-dimensional and two-dimensional TSCs. While massless Majorana quasiparticles are guaranteed to arise by the bulk-boundary correspondence, we find that they could be accompanied by massive Volkov-Pankratov (VP) states which are present only when the interface is sufficiently smooth. We calculate the spin-resolved local density of states of the VP states about the band inversion generated by a magnetic domain wall and find that they are oppositely spin polarized on either side of the topological phase boundary. Finally, we study how topological phase transitions in two-dimensional nanoflakes can be driven not only through magnetic domain walls but additionally through local changes in the system's chemical potential. We calculate the spatial extent of the one-dimensional Majorana modes circulating the boundary of the nanoflake and numerically determine their energy eigenvalues.
Alspaugh, David, "Majorana Quasiparticles in Topological Material Interfaces" (2021). LSU Doctoral Dissertations. 5488.
Sheehy, Daniel E.