Criticality in the crossed Andreev reflection of a quantum Hall edge

We develop a theory of the non-local transport of two counter-propagating ν = 1 quantum Hall edges coupled via a narrow disordered superconductor. The system is self-tuned to the critical point between trivial and topological phases by the competition between tunneling processes with or without particle-hole conversion. The critical conductance is a random, sample-specific quantity with a zero average and unusual bias dependence. The negative values of conductance are relatively stable against variations of the carrier density, which may make the critical state to appear as a topological one. Our theory provides an interpretation of recent experiments [Nature Physics 13, 693 (2017), Phys. Rev. X 12, 021057] and has important ramifications for an ongoing search for Majorana zero modes.