Doctor of Philosophy (Ph.D.)
In this dissertation, we study Andreev transport and Josephson effects in topological superconducting heterostructures. We study consider two platforms: quantum Hall-superconductor (QH-SC) heterostructures and Josephson junctions. In the first platform, we study QH graphene-SC systems with a focus on the influence symmetry-breaking effects have on Andreev transport. In graphene, valley and spin degeneracy lead to an approximate SU(4) symmetry that is reflected in the approximate 4-fold degeneracy of graphene's Landau levels (LL). We develop an effective low-energy description of Andreev edge states that takes into account the correction to the drift velocity of the QH-SC edge modes due to SU(4) symmetry-breaking effects. We show that Zeeman and valley splitting effects can be used to demonstrate Andreev edge state interference. We also present numerical simulations of Andreev conversion in the lowest LL of canted antiferromagnetic graphene. In the second platform, we analyze Josephson effects and the microwave response of Josephson junctions. We propose a theory for a Leggett collective mode in Dirac semimetals-based Josephson junctions and simulate the microwave response of the junction. We also study Landau-Zener transitions (LZT) between Andreev bound states in Josephson junctions. We present a protocol using superconducting quantum interference devices to differentiate between LZTs between Andreev states, which mimic signatures of Majoranas, and systems with real Majoranas.
© The Author
Cuozzo, Joseph Jude, "Electronic Transport In Topological Superconducting Heterostructures" (2022). Dissertations, Theses, and Masters Projects. William & Mary. Paper 1673281504.