Majorana Edge-to-bound State Transition in Interferometric Superconductor Rings

Overview & Synopsis

Manipulating flux quanta in topological superconductors is central to vortex braiding in quantum computing. Their interferometric superconducting rings can host either topologically protected edge states with fluxes confined inside the central hollow area or vortex bound states in flux cores at the annulus walls. Here we demonstrate a strategy to drive topological edge states into vortex bound states by tuning the relative scale of vortex size and annulus width in nano-ring interferometric device on 2M-WS$_2$ topological superconductor. Near its superconducting transition where the coherence length exceeds the annulus width, Little-Parks oscillations exhibit expected periods for flux bundles in ring-center, consistent with edge states residing at inner and outer rims of the annulus. Upon cooling, where the coherence length shrinks below the annulus width, the unexpectedly increased oscillation period reflects multiple fluxes distributed along annulus region in flux necklace configuration, implying a transition from extended edge states to localized vortex bound states. Ginzburg-Landau simulations and local density-of-states calculations with Bogoliubov-de Gennes equations reveal that large values for both Ginzburg-Landau parameter and flux-pinning energy are vital for such a transition. Our findings provide a novel strategy for understanding flux manipulation towards flux braiding and topological quantum computing.