Criticality in the Crossed Andreev Reflection of a Quantum Hall Edge
Vladislav D. Kurilovich, Leonid I. Glazman
DOI 10.1103/PhysRevX.13.031027 · Physical Review X
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Abstract
We develop a theory of the nonlocal transport of two counterpropagating ν=1 quantum Hall edges coupled via a narrow disordered superconductor. Contrary to the predictions developed for the clean case, the edge states proximitized in this way do not turn into a topological superconductor. Instead, they are naturally tuned to the critical point between trivial and topological phases. This occurs due to the competition between tunneling processes with and 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 appear as a topological one. Our results offer an interpretation of recent experiments [G.-H. Lee , Nat. Phys. 13, 693 (2017); O. Gül , Phys. Rev. X 12, 021057 (2022)].
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