There is an on-going effort to engineer a one-dimensional topological superconductor. Such a superconductor is expected to host Majorana zero modes at its ends; the exotic properties of these excitations might be useful for the development of a fault-tolerant quantum computer. A recent theory predicts that topological superconductivity may arise in a structure combining quantum Hall and conventional superconducting states. It led to active experimental attempts of bringing the two states together. We note, however, that the prediction focuses on the idealized “clean” case whereas, in practice, only strongly disordered superconductors are compatible with high magnetic fields needed for the quantum Hall effect. Does topological superconductivity survive the presence of disorder? In this thesis defense, I will present our theory of nonlocal transport of two counter-propagating quantum Hall edge states coupled via a narrow disordered superconductor. In contrast to the clean-case predictions, we find that the coupled edge states do not turn into a topological superconductor. Instead, the disorder naturally tunes them to the critical point between trivial insulating and topological phases. The criticality manifests itself in a random character of the conductance and its unusual bias dependence, which we quantify. Our results for the transport properties of the critical state are not restricted to the quantum Hall-superconductor structure; they are universal and apply to other realizations of Majorana wires.
Thesis committee: Leonid Glazman (advisor), Steven Girvin, Meng Cheng, Michel Devoret