Quantum Josephson junctions in topological insulators show Fraunhofer patterns in a field

Researchers at the University of Cologne and the Chinese Academy of Sciences have demonstrated a multiterminal Josephson effect in side-contacted topological insulator trijunctions, revealing key features of superconducting current flow. The work establishes experimental evidence for two-dimensional critical current contours and identifies bias regimes where current isolates to a single junction within the trijunction. Magnetic fields applied to these junctions produce Fraunhofer patterns and SQUID oscillations, reflecting flux buildup within the device loop. These results provide foundations for future investigations into Majorana zero modes, a component in some theoretical approaches to topological quantum computing.

Side-Contacted TI Trijunctions Enable Multiterminal Josephson Effects

Side-contacted topological insulator trijunctions exhibit deformations of their critical current contours when exposed to perpendicular magnetic fields, a phenomenon reflecting flux buildup within the device’s loop structure. This observation provides experimental validation of theoretical predictions regarding multiterminal Josephson effects in these novel superconducting circuits. A simple model is sufficient to explain the observed effect.

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Magnetic Fields Induce Patterns and SQUID Oscillations These deformations provide a visual confirmation of the trijunction’s magnetic response and are accurately modeled using a simplified approach, demonstrating that the observed effects are not simply a consequence of individual junction behavior. Output ONLY the corrected text

The researchers study the transport properties and find typical features of a two-dimensional critical current contour (CCC) as well as bias regimes in which only a single junction remains dissipationless. Researchers observed a periodicity of 5.5 millitesla in -like modulations of the critical current, a result consistent with the geometry of the junctions and the focusing of magnetic flux. This regularity confirms the effectiveness of the side-contacted fabrication technique used to create the devices.

The team’s experiments demonstrate that an in-plane magnetic field applied along the junction qualitatively aligns with predictions from a semiclassical single-junction model, while an out-of-plane field couples all three junctions through fluxoid quantization. The researchers observe pronounced non-convex shape deformations of the CCC under perpendicular magnetic fields that reflect the flux buildup in the loop formed by their trijunctions and provide a simple model sufficient to explain the observed effect.

The study builds on previous work with top-contacted topological insulator trijunctions, which have yet to yield clear signatures of Majorana zero modes, and offers a promising new platform for their investigation. The researchers emphasize the suitability of the side-contacted topological insulator platform for fabricating high-quality trijunctions where the superconducting current is carried by the topological surface state.

Magnetic Fields Induce Fraunhofer Patterns and SQUID Oscillations

These deformations provide a visual confirmation of the trijunction’s magnetic response and are accurately modeled using a simplified approach, demonstrating that the observed effects are not simply a consequence of individual junction behavior. The researchers pay particular attention to these features and study the effects of magnetic fields on single junctions within the trijunction, where, depending on the field direction, the supercurrents show patterns, SQUID oscillations, or a monotonic decay. The researchers find good agreement with semiclassical simulations for a single TI junction that take into account the top and bottom surface states.

Semiclassical Simulations Model TI Junction Magnetotransport

Semiclassical simulations accurately predict the behavior of superconducting current within these trijunctions, aligning with experimental data obtained from a single topological insulator (TI) junction, a finding that validates the model’s ability to capture key physical processes. These simulations account for electron behavior on both the top and bottom surfaces of the TI, an important consideration given the material’s unique electronic structure and its impact on supercurrent flow.

The agreement between simulation and experiment strengthens confidence in the understanding of current distribution within the complex device. Current partitioning in these configurations is governed by Kirchhoff’s laws and the relative resistances of each junction, effectively isolating supercurrent flow to a single pathway while the others are driven into a resistive state.

This selective dissipation is further influenced by Joule heating, which reduces the width of the current-carrying arms, and is visualized as star-like resistance drops originating from the critical current contour in higher-dimensional bias space. These deformations reflect the complex interplay between the applied field and the superconducting currents, providing a visual confirmation of the magnetic field’s impact on the CCC’s shape.

The simulations also accurately reproduce the distinct responses to magnetic fields observed experimentally, including patterns, SQUID oscillations, or a monotonic decay. A mixed magnetic field, a superposition of perpendicular and in-plane components, rapidly suppresses the zero-resistance state in the junctions.

Topological Insulators as Platforms for Majorana Zero Mode Studies

The multiterminal Josephson effect has been experimentally demonstrated in a side-contacted topological insulator trijunction, a configuration predicted to potentially host Majorana zero modes key for topological quantum computing. The work builds on theoretical predictions from Fu and Kane in 2008, which suggested that trijunctions of this type could support discrete vortices and isolated Majorana zero modes. The team’s model, validated by experimental data, provides a foundation for future investigations into the complex interplay between magnetic fields and supercurrents in these unique junctions.

The study also identified specific bias regimes within the trijunction where only a single junction remains dissipationless, effectively isolating current paths. The researchers note that “the data and simulation codes that support the findings of this article are openly available under the Zenodo repository with the identifier 10.5281/zenodo.23562455,” encouraging transparency and reproducibility within the scientific community.

Back-Gate Voltage Modulates Josephson Junction Critical Current

An unexpected increase in critical current within one junction of a topological insulator trijunction was observed when a negative back-gate voltage was applied. While junctions B and C exhibited the anticipated decrease in current with negative voltage, junction A displayed a broadening of its current-bias map. This behavior deviates from previous work where gate voltage was used to differentiate the contributions of top and bottom surface states, as the gating behavior in this instance proved more complex.

The team modeled the trijunction as a network of three Josephson junctions, accounting for magnetic flux threading the device’s effective area, similar to a conventional SQUID. This approach incorporated a -like reduction in the critical current of each junction due to the applied magnetic field, alongside the constraint imposed on phase differences by the total flux.

The simulations also account for the phase modulation imposed by the magnetic fields, using equations where the superconducting flux quantum is represented as Φ₀ = h/2e. The bulk-insulating nature of the material concentrates the supercurrent within the surface states, influencing the observed patterns. This is a key characteristic of the device, as the supercurrent is carried predominantly by these surface states, and the team’s ability to model this effect demonstrates a strong understanding of the underlying physics.

Specifically, the application of a perpendicular magnetic field induces pronounced non-convex deformations in the contour, reflecting the buildup of flux within the trijunction loop. This effect is captured by the model, which considers the effective junction length taking flux-focusing into account.

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