Enriching Majorana Zero Modes

My various projects in graduate school have centered around a common theme: harnessing relatively well-understood phases of matter and combining them to create exotic physics. They also involve Majoranas, or more accurately, defects that bind Majorana zero modes and are the centerpiece for topological quantum computation. We exploit and enrich this Majorana zero mode by employing topological superconductors, time crystals, and quantum dots and combining them together. Our first project involved joining Majorana nanowires and quantum dots to simulate the SYK model, a zero-dimensional strongly interacting phase with connections to black holes and holography. We follow by explaining how to combine spontaneous symmetry-breaking with topological superconductivity to recover parafermion physics in one dimension. We explain an exact mapping that relates fermions to parafermions, illustrating a deep connection between different one-dimensional phases of matter. We finally show that enhancing the topological superconductor with a time crystal, a phase of matter that spontaneously breaks time-translation symmetry, creates an anomalous zero mode that displays 4Tperiodicity in the Floquet drive. By combining these different phases in judicious ways we achieve exotic physics unattainable by the constituent parts. Our work thus illustrates profitable directions for harnessing Majorana zero modes to study the physics of exotic matter.