In a standard Josephson junction the current is zero when the phase difference between superconducting leads is zero. This condition is protected by parity and time-reversal symmetries. However, the combined presence of spin–orbit coupling and magnetic field breaks these symmetries and can lead to a finite supercurrent even when the phase difference is zero. This is the so called anomalous Josephson effect—the hallmark effect of superconducting spintronics—which can be characterized by the corresponding anomalous phase shift. Here we report the observation of a tunable anomalous Josephson effect in InAs/Al Josephson junctions measured via a superconducting quantum interference device. By gate controlling the density of InAs, we are able to tune the spin–orbit coupling in the Josephson junction. This gives us the ability to tune the anomalous phase, and opens new opportunities for superconducting spintronics, and new possibilities for realizing and characterizing topological superconductivity. The anomalous Josephson effect can be regarded as the hall-mark effect of superconducting spintronics. Here, the authors report the observation of a tunable anomalous Josephson effect in InAs/Al Josephson junctions measured via a superconducting quantum interference device.

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Gate controlled anomalous phase shift in Al/InAs Josephson junctions.

WTe2 is a layered transitional-metal dichalcogenide (TMD) with a number of intriguing topological properties Recently, WTe2 has been predicted to be a higher-order topological insulator (HOTI) with topologically protected hinge states along the edges The gapless nature of WTe2 complicates the observation of one-dimensional (1D) topological states in transport due to their small contribution relative to the bulk Here, we study the behavior of the Josephson effect in magnetic field to distinguish edge from bulk transport The Josephson effect in few-layer WTe2 reveals 1D states residing on the edges and steps Moreover, our data demonstrates a combination of Josephson transport properties observed solely in another HOTI-bismuth, including Josephson transport over micrometer distances, extreme robustness in a magnetic field, and nonsinusoidal current-phase relation (CPR) Our observations strongly suggest the topological origin of the 1D states and that few-layer WTe2 is a HOTI

One-Dimensional Edge Transport in Few-Layer WTe2.

We investigate the critical current I_{C} of ballistic Josephson junctions made of encapsulated graphene-boron-nitride heterostructures. We observe a crossover from the short to the long junction regimes as the length of the device increases. In long ballistic junctions, I_{C} is found to scale as ∝exp(-k_{B}T/δE). The extracted energies δE are independent of the carrier density and proportional to the level spacing of the ballistic cavity. As T→0 the critical current of a long (or short) junction saturates at a level determined by the product of δE (or Δ) and the number of the junction's transversal modes.

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Ballistic Graphene Josephson Junctions from the Short to the Long Junction Regimes: Part II- Critical current scaling of the Short and Long Junctions.

Starting from the basic definitions of Chern-Simons current, it is possible to calculate its values with a quantum machine learning approach, the so-called supersymmetric support Dirac machine. The related supercurrent is generated from the coupling between three states of the quantum flux of a modified Wilson loop of Cooper pairs. We adopt the Holo-Hilbert spectrum, in frequency modulation, to visualize the network as the coupling of convolutional neuron network in a superstatistic theory where the theory of superconductors is applied. According to this approach, it is possible to calculate the number of carbon atoms in the spinor network of a graphene wormhole. A supercurrent of Cooper pairs is produced as graviphoton states by using the Holo-Hilbert spectral analysis.

https://www.mdpi.com/2073-8994/12/5/774/pdf

Chern-Simons Current of Left and Right Chiral Superspace in Graphene Wormhole

In a standard Josephson junction the current is zero when the phase difference between the superconducting leads is zero. This condition is protected by parity and time-reversal symmetries. However, the combined presence of spin-orbit coupling and magnetic field breaks these symmetries and can lead to a finite supercurrent even when the phase difference is zero. This is the so called anomalous Josephson effect -- the hallmark effect of superconducting spintronics --and can be characterized by the corresponding anomalous phase shift ($\phi_0$). We report the observation of a tunable anomalous Josephson effect in InAs/Al Josephson junctions measured via a superconducting quantum interference device (SQUID). By gate controlling the density of InAs we are able to tune the spin-orbit coupling of the Josephson junction by more than one order of magnitude. This gives us the ability to tune $\phi_0$, and opens several new opportunities for superconducting spintronics, and new possibilities for realizing and characterizing topological superconductivity.

/pdf/gate-controlled-anomalous-phase-shift-in-al-inas-josephson-123hy0m0dn.pdf

Gate Controlled Anomalous Phase Shift in Al/InAs Josephson Junctions

The superconducting proximity effect in graphene can be used to create Josephson junctions with critical currents that can be tuned using local field-effect gates. These junctions have the potential to add functionality to existing technologies; for example, superconducting quantum interference device (SQUID) magnetometers with adaptive dynamic range and superconducting qubits with fast electrical control. Here, we present measurements of graphene-based superconducting quantum interference devices incorporating ballistic Josephson junctions that can be controlled individually. We investigate the magnetic field response of the SQUIDs as the junctions are gated and as the device is tuned between symmetric and asymmetric configurations. We find a highest transfer function 300 lV/U0, which compares favorably with conventional, low temperature DC SQUIDs. With low noise readout electronics and optimised geometries, devices based on ballistic graphene Josephson junctions have the potential to match the sensitivity of traditional SQUIDs while also providing additional functionality.

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Graphene-based tunable SQUIDs

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Ziad Melhem

Papers

Graphene-based tunable SQUIDs

Superconducting quantum interference devices with graphene junctions.