Supercurrent and Andreev bound states in multi-terminal Josephson junctions

Abstract

A Josephson junction (JJ) is known as a weak link connecting two superconductors, in which the non-dissipative supercurrent flows. More than two superconductors also can form a single composite JJ, called a “multi-terminal JJ”, by being connected through a common weak link. The supercurrent in multi-terminal JJs may depend on multiple superconducting phase differences defined across the junction. The multi-phase-dependence of the supercurrent is attributed to the sub-gap quasiparticle bound states, called Andreev bound states (ABSs), which carry the supercurrent across the junction. First, we investigate the supercurrent of three- and four-terminal JJs fabricated on hybrid two-dimensional Al/InAs (superconductor/semiconductor) heterostructures. The critical current of an N-terminaljunction is given as a (N-1)-dimensional hypersurface of the DC bias currents, which can be reduced to a set of critical current contours (CCCs) in low dimensional space. Non-trivial modifications of the geometry of the CCCs in response to magnetic field, electrical gating and phase biasing can be understood in the presence of the multi-phase-dependent ABSs. Second, we demonstrate the multi-phase-dependent ABSs in three-terminal JJs by tunneling spectroscopy measurements. Multi-loop superconducting quantum interference devices (SQUIDs) are realized to detect the multi-phase-dependence. The ABS energy spectrum mimics electronic band structure in solid, which makes multi-terminal JJs provide a new platform to study band topology in higher dimensional parameter space. Moreover, spin-splitting of ABS energies induced by the multi-phase and gapless energy spectrum facilitated by the presence of a discrete vortex, a nonzero winding of the superconducting phases, are investigated.