The hybrid combination of low dimensional semiconductors with superconductors offers a versatile ground for novel device concepts, such as supercurrent transistors, sources of spin-entangled electrons or nano-SQUIDS.
From a more basic point of view, these hybrid systems are interesting melting pots where various fundamental effects in condensed matter physics coexist. For example, when a quantum dot (QD) is coupled to a superconducting electrode (S) two very distinct phenomena compete. On one hand, superconductivity arises from the collective behaviour of a large number of electrons, while QDs usually act as quantum box with just a few electrons. In a superconductor the electrons feel a net attractive interaction that binds them into Cooper pairs, while electrons in a QD strongly repel each other. The underlying physics behind such hybrid device ultimately relies on the physics of the Anderson model where the standard metallic host is replaced by a superconducting one, namely the physics of a (quantum) magnetic impurity in a superconductor.
Magnetic impurities can profoundly modify the state of a metal. Well below the Kondo temperature, the impurity is fully screened by quasiparticle exchange and the ground state is a Kondo singlet. In a superconductor, however, no quasiparticles are available below the superconducting gap, hence Kondo screening is incomplete. In general, a quantum impurity in a superconductor is a complex system where two many-body states, a magnetic doublet and a singlet, compete in becoming the GS. As a result, the system undergoes a
quantum phase transition (QPT) when the superconduting gap is of the order of the Kondo temperature. A characteristic feature is the the emergence of sub-gap bound states, the so-called Yu-Shiba-Rusinov (YRS) states. Across the QPT the GS switches fermion parity and spin. Accordingly, YRS states crossing zero energy also signal a parity-changing QPT.
Experimentally, parity crossings are marked by zero bias anomalies (ZBA)s in transport though the QD. Interestingly, ZBAs in similar hybrid devices based on semiconducting nanowires with strong spin-orbit coupling are a strong signature of emergent Majorana bound states.
The study of all these coexisting phenomena in hybrid nanostructures is one of the most exciting and challenging topics in modern condensed matter physics.