The present-day experimental techniques [1] have stimulated a large variety of theoretical proposals to create new condensed matter physics by an appropriate combination of known materials. One particularly appealing assembly is a conventional superconductor with a semiconductor with strong spin-orbit properties, including its dependence on the chemical potential and magnetic field [2]. A major experimental and theoretical challenge is to disentangle the desired new physics from the, also mostly unknown, physical properties of the combination of these materials. Both of them are to be determined from electrical transport measurements [3], which are interpreted using existing theoretical concepts. I will discuss the results of a recent analysis of the properties of the voltage-carrying state of HgTe-based Josephson junctions to understand their normal state quantum transport properties, which carry over into observations in the superconducting state [4]. The results are expected to be relevant more generally.

[1] H. Heersche et al, Nature 446, 56 (2007).
[2] Liang Fu and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008).
[3] E. Bocquillon et al, Nature nanotechnology 12, 137 (2016).
[4] D. Breunig et al, Physical Review B 103, 165414 (2021).