Topological transconductance quantization in a four-terminal Josephson junction

Recently we predicted that the Andreev bound-state spectrum of four-terminal Josephson junctions may possess topologically protected zero-energy Weyl singularities, which manifest themselves in a quantized transconductance in units of 4e2/h when two of the terminals are voltage biased [R.-P. Riwar, M. Houzet, J. S. Meyer, and Y. V. Nazarov, Nature Commun. 7, 11167 (2016)2041-172310.1038/ncomms11167]. Here, using the Landauer-Büttiker scattering theory, we compute numerically the currents flowing through such a structure in order to assess the conditions for observing this effect. We show that the voltage below which the transconductance becomes quantized is determined by the interplay of nonadiabatic transitions between Andreev bound states and inelastic relaxation processes. We demonstrate that the topological quantization of the transconductance can be observed at voltages of the order of 10-2Δ/e,Δ being the the superconducting gap in the leads.QN/Nazarov Grou