Demonstration of the Nonlocal Josephson Effect in Andreev Molecules.

We perform switching current measurements of planar Josephson junctions (JJs) coupled by a common superconducting electrode with independent control over the two superconducting phase differences. We observe an anomalous phase shift in the current-phase relation of a JJ as a function of gate voltage or phase difference in the second JJ. This demonstrates the nonlocal Josephson effect, and the implementation of a φ0-junction which is tunable both electrostatically and magnetically. The anomalous phase shift is larger for shorter distances between the JJs and vanishes for distances much longer than the superconducting coherence length. Results are consistent with the hybridization of Andreev bound states, leading to the formation of an Andreev molecule. Our devices constitute a realization of a tunable superconducting phase source and could enable new coupling schemes for hybrid quantum devices.

Al-Ge-Al Nanowire Heterostructure: From Single-Hole Quantum Dot to Josephson Effect.

Superconductor-semiconductor-superconductor heterostructures are attractive for both fundamental studies of quantum phenomena in low-dimensional hybrid systems as well as for future high-performance low power dissipating nanoelectronic and quantum devices. In this work, ultrascaled monolithic Al-Ge-Al nanowire heterostructures featuring monocrystalline Al leads and abrupt metal-semiconductor interfaces are used to probe the low-temperature transport in intrinsic Ge (i-Ge) quantum dots. In particular, demonstrating the ability to tune the Ge quantum dot device from completely insulating, through a single-hole-filling quantum dot regime, to a supercurrent regime, resembling a Josephson field effect transistor with a maximum critical current of 10 nA at a temperature of 390 mK. The realization of a Josephson field-effect transistor with high junction transparency provides a mechanism to study sub-gap transport mediated by Andreev states. The presented results reveal a promising intrinsic Ge-based architecture for hybrid superconductor-semiconductor devices for the study of Majorana zero modes and key components of quantum computing such as gatemons or gate tunable superconducting quantum interference devices.

Shadow Epitaxy for In Situ Growth of Generic Semiconductor/Superconductor Hybrids.

Uniform, defect-free crystal interfaces and surfaces are crucial ingredients for realizing high-performance nanoscale devices. A pertinent example is that advances in gate-tunable and topological superconductivity using semiconductor/superconductor electronic devices are currently built on the hard proximity-induced superconducting gap obtained from epitaxial indium arsenide/aluminum heterostructures. Fabrication of devices requires selective etch processes; these exist only for InAs/Al hybrids, precluding the use of other, potentially superior material combinations. This work introduces a crystal growth platform-based on 3D structuring of growth substrates-which enables synthesis of semiconductor nanowire hybrids with in situ patterned superconductor shells. The platform eliminates the need for etching, thereby enabling full freedom in the choice of hybrid constituents. All of the most frequently used superconducting hybrid device architectures are realized and characterized. These devices exhibit increased yield and electrostatic stability compared to etched devices, and evidence of ballistic superconductivity is observed. In addition to aluminum, hybrid structures based on tantalum, niobium, and vanadium are presented.

Josephson Effect in a Few-Hole Quantum Dot.

A Ge-Si core-shell nanowire is used to realize a Josephson field-effect transistor with highly transparent contacts to superconducting leads. By changing the electric field, access to two distinct regimes, not combined before in a single device, is gained: in the accumulation mode the device is highly transparent and the supercurrent is carried by multiple subbands, while near depletion, the supercurrent is carried by single-particle levels of a strongly coupled quantum dot operating in the few-hole regime. These results establish Ge-Si nanowires as an important platform for hybrid superconductor-semiconductor physics and Majorana fermions.

Interaction-induced zero-energy pinning and quantum dot formation in Majorana nanowires.

Majorana modes emerge in non-trivial topological phases at the edges of specific materials such as proximitized semiconducting nanowires under an external magnetic field. Ideally, they are non-local states that are charge-neutral superpositions of electrons and holes. However, in nanowires of realistic length their wave functions overlap and acquire a finite charge that makes them susceptible to interactions, specifically with the image charges that arise in the electrostatic environment. Considering a realistic three-dimensional model of the dielectric surroundings, here we show that, under certain circumstances, these interactions lead to a suppression of the Majorana oscillations predicted by simpler theoretical models, and to the formation of low-energy quantum-dot states that interact with the Majorana modes. Both features are observed in recent experiments on the detection of Majoranas and could thus help to properly characterize them.

Andreev spectrum and supercurrents in nanowire-based SNS junctions containing Majorana bound states.

Hybrid superconductor-semiconductor nanowires with Rashba spin-orbit coupling are arguably becoming the leading platform for the search of Majorana bound states (MBSs) in engineered topological superconductors. We perform a systematic numerical study of the low-energy Andreev spectrum and supercurrents in short and long superconductor-normal-superconductor junctions made of nanowires with strong Rashba spin-orbit coupling, where an external Zeeman field is applied perpendicular to the spin-orbit axis. In particular, we investigate the detailed evolution of the Andreev bound states from the trivial into the topological phase and their relation with the emergence of MBSs. Due to the finite length, the system hosts four MBSs, two at the inner part of the junction and two at the outer one. They hybridize and give rise to a finite energy splitting at a superconducting phase difference of π, a well-visible effect that can be traced back to the evolution of the energy spectrum with the Zeeman field: from the trivial phase with Andreev bound states into the topological phase with MBSs. Similarly, we carry out a detailed study of supercurrents for short and long junctions from the trivial to the topological phases. The supercurrent, calculated from the Andreev spectrum, is 2π-periodic in the trivial and topological phases. In the latter it exhibits a clear sawtooth profile at a phase difference of π when the energy splitting is negligible, signalling a strong dependence of current-phase curves on the length of the superconducting regions. Effects of temperature, scalar disorder and reduction of normal transmission on supercurrents are also discussed. Further, we identify the individual contribution of MBSs. In short junctions the MBSs determine the current-phase curves, while in long junctions the spectrum above the gap (quasi-continuum) introduces an important contribution.

On-Chip Andreev Devices: Hard Superconducting Gap and Quantum Transport in Ballistic Nb-In0.75 Ga0.25 As-Quantum-Well-Nb Josephson Junctions.

A superconducting hard gap in hybrid superconductor-semiconductor devices has been found to be necessary to access topological superconductivity that hosts Majorana modes (non-Abelian excitation). This requires the formation of homogeneous and barrier-free interfaces between the superconductor and semiconductor. Here, a new platform is reported for topological superconductivity based on hybrid Nb-In0.75 Ga0.25 As-quantum-well-Nb that results in hard superconducting gap detection in symmetric, planar, and ballistic Josephson junctions. It is shown that with careful etching, sputtered Nb films can make high-quality and transparent contacts to the In0.75 Ga0.25 As quantum well, and the differential resistance and critical current measurements of these devices are discussed as a function of temperature and magnetic field. It is demonstrated that proximity-induced superconductivity in the In0.75 Ga0.25 As-quantum-well 2D electron gas results in the detection of a hard gap in four out of seven junctions on a chip with critical current values of up to 0.2 µA and transmission probabilities of >0.96. The results, together with the large g-factor and Rashba spin-orbit coupling in In0.75 Ga0.25 As quantum wells, which indeed can be tuned by the indium composition, suggest that the Nb-In0.75 Ga0.25 As-Nb system can be an excellent candidate to achieve topological phase and to realize hybrid topological superconducting devices.