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Interactions and disorder in topological superconducting wires

Dganit Meidan

The prospects of building quantum devices based on topologically ordered states of matter has caused a great deal of excitement. In these systems, emergent excitations known as Majorana zero modes that occur at sample edges obey non- Abelian exchange statistics, and their manipulation is inherently protected from common sources of decoherence. While their existence is known to be reasonably stable to imperfect conditions such as impurities and weak electron- electron interactions, aspirations to observe and manipulate Majorana zero-modes in proximity coupled systems requires a detailed study of both these effects. As a particular example we numerically study the effect of disorder on the stability of the many body zero mode in a Kitaev chain with local interactions. Our numerical procedure allows us to resolve the position-space and multi-particle structure of the zero modes, as well as providing estimates for the mean energy splitting between pairs of states of opposite fermion parity, over the full many body spectrum. We find that the parameter space of a clean system can be divided into regions where interaction induced decay transitions are suppressed (Region I) and where they are not (Region II). In Region I we observe that disorder has an adverse effect on the zero mode, which extends further into the bulk and is accompanied by an increased energy splitting between pairs of states of opposite parity. Conversely Region II sees a more intricate effect of disorder showing an enhancement of localization at the system’s end, accompanied by a reduction in the mean pairwise energy splitting.


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