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Register a new userThe multi-terminal Josephson effect
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Added by
Vladimir Manucharyan
Publication date
2018
fields
Physics
and research's language is
English
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Establishment of phase-coherence and a non-dissipative (super)current between two weakly coupled superconductors, known as the Josephson effect, plays a foundational role in basic physics and applications to metrology, precision sensing, high-speed digital electronics, and quantum computing. The junction ranges from planar insulating oxides to single atoms, molecules, semiconductor nanowires, and generally to any finite-size coherent conductor. Recently, junctions of more than two superconducting terminals gained broad attention in the context of braiding of Majorana fermions in the solid state for fault-tolerant quantum computing, and accessing physics and topology in dimensions higher than three. Here we report the first observation of Josephson effect in 3- and 4-terminal junctions, fabricated in a top-down fashion from a semiconductor/superconductor (InAs/Al) epitaxial two-dimensional heterostructure. Due to interactions, the critical current of an N-terminal junction becomes the boundary of an (N-1)-dimensional manifold of simultaneously allowed supercurrents. The measured shapes of such manifolds are explained by the scattering theory of mesoscopic superconductivity, and they can be remarkably sensitive to the junctions symmetry class. Furthermore, we observed a notably high-order (up to 8) multiple Andreev reflections simultaneously across every terminals pair, which verifies the multi-terminal nature of normal scattering and a high interface quality in our devices. Given the previously shown gate-control of carrier density and evidence of spin-orbit scattering in InAs/Al heterostructures, and device compatibility with other 2D materials, the multi-terminal Josephson effect reported here can become a testbed for physics and applications of topological superconductivity.
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We investigate the Andreev-bound-state (ABS) spectra of three-terminal Josephson junctions which consist of 1D topological superconductors (TSCs) harboring multiple zero-energy edge Majorana bound states (MBSs) protected by chiral symmetry. Our theoretical analysis relies on the exact numerical diagonalization of the Bogoliubov-de Gennes (BdG) Hamiltonian describing the three interfaced TSCs, complemented by an effective low-energy description solely based on the coupling of the interfacial MBSs arising before the leads get contacted. Considering the 2D synthetic space spanned by the two independent superconducting phase differences, we demonstrate that the ABS spectra may contain either point or line nodes, and identify $mathbb{Z}_2$ topological invariants to classify them. We show that the resulting type of nodes depends on the number of preexisting interfacial MBSs, with nodal lines necessarily appearing when two TSCs harbor an unequal number of MBSs. Specifically, the precise number of interfacial MBSs determines the periodicity of the spectrum under $2pi$-slidings of the phase differences and, as a result, also controls the shape of the nodal lines in synthetic space. When chiral symmetry is preserved, the lines are open and coincide with high-symmetry lines of synthetic space, while when it is violated the lines can also transform into loops and chains. The nodal spectra are robust by virtue of the inherent particle-hole symmetry of the BdG Hamiltonian, and give rise to distinctive experimental signatures that we identify.
When a Josephson junction is exposed to microwave radiation, it undergoes the inverse AC Josephson effect - the phase of the junction locks to the drive frequency. As a result, the I-V curves of the junction acquire Shapiro steps of quantized voltage. If the junction has three or more superconducting contacts, coupling between different pairs of terminals must be taken into account and the state of the junction evolves in a phase space of higher dimensionality. Here, we study the multi-terminal inverse AC Josephson effect in a graphene sample with three superconducting terminals. We observe robust fractional Shapiro steps and correlated switching events, which can only be explained by considering the device as a completely connected Josephson network. We successfully simulate the observed behaviors using a modified two-dimensional RCSJ model. Our results suggest multi-terminal Josephson junctions are a playground to study highly-connected nonlinear networks with novel topologies.
Josephson junctions based on three-dimensional topological insulators offer intriguing possibilities to realize unconventional $p$-wave pairing and Majorana modes. Here, we provide a detailed study of the effect of a uniform magnetization in the normal region: We show how the interplay between the spin-momentum locking of the topological insulator and an in-plane magnetization parallel to the direction of phase bias leads to an asymmetry of the Andreev spectrum with respect to transverse momenta. If sufficiently large, this asymmetry induces a transition from a regime of gapless, counterpropagating Majorana modes to a regime with unprotected modes that are unidirectional at small transverse momenta. Intriguingly, the magnetization-induced asymmetry of the Andreev spectrum also gives rise to a Josephson Hall effect, that is, the appearance of a transverse Josephson current. The amplitude and current phase relation of the Josephson Hall current are studied in detail. In particular, we show how magnetic control and gating of the normal region can enable sizable Josephson Hall currents compared to the longitudinal Josephson current. Finally, we also propose in-plane magnetic fields as an alternative to the magnetization in the normal region and discuss how the planar Josephson Hall effect could be observed in experiments.
Topological Josephson junctions (JJs), which contain Majorana bound states, are expected to exhibit 4$pi$-periodic current-phase relation, thereby resulting in doubled Shapiro steps under microwave irradiation. We performed numerical calculations of dynamical properties of topological JJs using a modified resistively and capacitively shunted junction model and extensively investigated the progressive evolution of Shapiro steps as a function of the junction parameters and microwave power and frequency. Our calculation results indicate that the suppression of odd-integer Shapiro steps, i.e., evidence of the fractional ac Josephson effect, is enhanced significantly by the increase in the junction capacitance and IcRn product as well as the decrease in the microwave frequency even for the same portion of the 4$pi$-periodic supercurrent. Our study provides the optimal conditions for observing the fractional ac Josephson effect; furthermore, our new model can be used to precisely quantify the topological supercurrent from the experimental data of topological JJs.
We discuss the response of an rf-SQUID formed by anomalous Josephson junctions embedded in a superconducting ring with a non-negligible inductance. We demonstrate that a properly sweeping in-plane magnetic field can cause both the total flux and the current circulating in the device to modulate and to behave hysteretically. The bistable response of the system is analyzed as a function of the anomalous phase shift at different values of the screening parameter, in order to highlight the parameter range within which a hysteretic behavior can be observed. The magnetic flux piercing the SQUID ring is demonstrated to further modulate the hysteretical response of the system. Moreover, we show that the anomalous phase shift can be conveniently determined through the measurement of the out-of-plane magnetic field at which the device switches to the voltage state and the number of trapped flux quanta changes. Finally, we compare the response of two different device configurations, namely, a SQUID including only one or two anomalous junctions. In view of these results, the proposed device can be effectively used to detect and measure the anomalous Josephson effect.
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