Josephson junctions hosting Majorana fermions have been predicted to exhibit a 4π periodic current phase relation. One experimental consequence of this periodicity is the disappearance of odd steps in Shapiro steps experiments. Experimentally, missing odd Shapiro steps have been observed in a number of materials systems with strong spin-orbit coupling and have been interpreted in the context of topological superconductivity. Here we report on missing odd steps in topologically trivial Josephson junctions fabricated on InAs quantum wells. We ascribe our observations to the high transparency of our junctions allowing Landau-Zener transitions. The probability of these processes is shown to be independent of the drive frequency. We analyze our results using a bi-modal transparency distribution which demonstrates that only few modes carrying 4π periodic current are sufficient to describe the disappearance of odd steps. Our findings highlight the elaborate circumstances that have to be considered in the investigation of the 4π Josephson junctions in relationship to topological superconductivity.

The critical current response to an applied out-of-plane magnetic field in a Josephson junction provides insight into the uniformity of its current distribution. In Josephson junctions with semiconducting weak links, the carrier density, and therefore the overall current distribution, can be modified electrostatically via metallic gates. Here, we show local control of the current distribution in an epitaxial Al-InAs Josephson junction equipped with five minigates. We demonstrate that not only can the junction width be electrostatically defined but also the current profile can be locally adjusted to form superconducting quantum interference devices. Our studies show enhanced edge conduction in such long junctions, which can be eliminated by minigates to create a uniform current distribution.

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In the presence of a 4π-periodic contribution to the current phase relation, for example in topological Josephson junctions, odd Shapiro steps are expected to be missing. While missing odd Shapiro steps have been observed in several material systems and interpreted in the context of topological superconductivity, they have also been observed in topologically trivial junctions. Here, we study the evolution of such trivial missing odd Shapiro steps in Al−InAs junctions in the presence of an in-plane magnetic field B θ . We find that the odd steps reappear at a crossover B θ value, exhibiting an in-plane field angle anisotropy that depends on spin−orbit coupling effects. We interpret this behavior by theoretically analyzing the Andreev bound state spectrum and the transitions induced by the nonadiabatic dynamics of the junction and attribute the observed anisotropy to mode-to-mode coupling. Our results highlight the complex phenomenology of missing Shapiro steps and the underlying current phase relations in planar Josephson junctions designed to realize Majorana states.

Voltage-tunable superconductor-semiconductor devices offer a unique platform to realize dynamic tunability in superconducting quantum circuits. By galvanically connecting a gated InAs-Al Josephson junction to a coplanar waveguide resonator, we demonstrate the use of a wide-range gate-tunable superconducting element. We show that the resonant frequency is controlled via a gate-tunable Josephson inductance and that the non-linearity of the voltage-controlled InAs-Al junction is nondissipative as is the case with conventional Al-AlOx junctions. As the gate voltage is decreased, the inductive participation of the junction increases up to 44%, resulting in the resonant frequency being tuned by over 2 GHz. Utilizing the wide tunability of the device, we demonstrate that two resonant modes can be adjusted such that they strongly hybridize, exhibiting an avoided level crossing with a coupling strength of 51 MHz. Implementing such voltage-tunable resonators is the first step toward realizing wafer-scale continuous voltage control in superconducting circuits for qubit-qubit coupling, quantum-limited amplifiers, and quantum memory platforms.

Transparent contact interfaces in superconductor–graphene hybrid systems are critical for realizing superconducting quantum applications. Here, we examine the effect of the edge contact fabrication process on the transparency of the superconducting aluminum–graphene junction. We show significant improvement in the transparency of our superconductor–graphene junctions by promoting the chemical component of the edge contact etch process. Our results compare favorably with state-of-the-art graphene Josephson junctions. The findings of our study contribute to advancing the fabrication knowledge of edge-contacted superconductor–graphene junctions.

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