The conventional description of transport through the interface between a normal conductor and a superconductor reduces the system to a one-dimensional problem treating Andreev reflection based on a zero-dimensional Sharvin-type point-contact model, and effectively neglects all considerations of device geometry. While this has been successful in systems where conductance in the normal material is in the diffusive transport regime, such an oversimplification of the problem fails in other transport regimes. In particular, when transport is ballistic as in a typical semiconductor-superconductor hybrid structure, geometrical effects are inherently important, and a proper description must consider a one-dimensional contact injecting into a two-dimensional ballistic cavity. We present a study of this regime and explore the bias-voltage dependence of Andreev transport in a cavity-type device comprised of a high-mobility HgTe quantum well side-contacted by one superconducting and one normal contact, each creating a one-dimensional interface. The enhanced conductance from Andreev transport features two finite-bias conductance peaks, observed at energies within the energy gap of the superconductor. Interestingly, these two peaks respond differently to the application of a perpendicular-to-plane magnetic field. Using a semiclassical model for the quantum transport within the cavity, we are able to attribute each peak to a different class of ballistic trajectories. One class is dominated by normal reflection, and its interference condition is independent of magnetic field, whereas the other one contains retroreflected Andreev processes at the superconductor interface. These create closed trajectories that are strongly suppressed by magnetic field due to Aharonov-Bohm and Doppler shift effects.

A superconductor, when exposed to a spin-exchange field, can exhibit spatial modulation of its order parameter, commonly referred to as the Fulde–Ferrell–Larkin–Ovchinnikov state. Such a state can be induced by controlling the spin-splitting field in Josephson junction devices, allowing access to a wide range of the phase diagram. Here we demonstrate that a Fulde–Ferrell–Larkin–Ovchinnikov state can be induced in Josephson junctions based on the two-dimensional dilute magnetic topological insulator (Hg,Mn)Te. We do this by observing the dependence of the critical current on the magnetic field and temperature. The substitution of Mn dopants induces an enhanced Zeeman effect, which can be controlled with high precision by using a small external magnetic field. We observe multiple re-entrant behaviours of the critical current as a response to an in-plane magnetic field, which we assign to transitions between ground states with a phase shifted by π. This will enable the study of the Fulde–Ferrell–Larkin–Ovchinnikov state in much more accessible experimental conditions.