A mechanism of $\frac{e^2}{2h}$ conductance plateau without 1D chiral Majorana fermions

Abstract: We address the question about the origin of the $\frac12 \frac{e^2}{h}$ conductance plateau observed in a recent experiment on an integer quantum Hall (IQH) film covered by a superconducting (SC) film. Since 1-dimensional (1D) chiral Majorana fermions on the edge of the above device can give rise to the half quantized plateau, such a plateau was regarded as a smoking-gun evidence for the chiral Majorana fermions. However, in this paper we give another mechanism for the $\frac12 \frac{e^2}{h}$ conductance plateau. We find the $\frac12 \frac{e^2}{h}$ conductance plateau to be a general feature of a good electric contact between the IQH film and SC film, and cannot distinguish the existence or the non-existence of 1D chiral Majorana fermions. We also find that the contact conductance between SC and an IQH edge channel has a non-Ohmic form $\sigma_\text{SC-Hall} \propto V^2$ in $k_BT \ll eV$ limit, if the SC and IQH bulks are fully gapped.