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arXiv:2506.08985 · Physical review. B./Physical review. B

Tuning the fundamental periodicity of the current-phase relation in multiterminal diffusive Josephson junctions

Venkat Chandrasekhar

Published Sep 3, 2025• 1 citation
arXivHTMLPDF

Abstract

Conventional superconductor/insulator/superconductor (SIS) Josephson junctions, devices where two superconductors are separated by a tunnel barrier are technologically important as elements in quantum circuits, particularly with their key role in superconducting qubits. An important characteristic of Josephson junctions is the relation between the supercurrent Is and the phase difference $ϕ$ between them. For SIS junctions, the current-phase relation is sinusioidal and 2$π$ periodic. Other types of Josephson junctions, where the material between the superconductors is a weak link or a normal metal (N) may have non-sinusoidal current-phase relations that are still 2$π$ periodic. We show here that a multi-terminal diffusive SNS Josephson junction with 4 superconducting contacts can show a current phase relation between two of the contacts that is a superposition of 2$π$ and 4$π$ periodic components whose relative strength is controlled by the phase difference between the other two contacts, becoming 2$π$ or 4$π$ periodic for certain values of this phase difference. This tunability might have applications in tailoring the Hamiltonians of superconducting quantum circuits.

DOI
10.1103/73rl-wmzw

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Conventional superconductor/insulator/superconductor (SIS) Josephson junctions, devices where two superconductors are separated by a tunnel barrier are technologically important as elements in quantum circuits, particularly with their key role in superconducting qubits. An important characteristic of Josephson junctions is the relation between the supercurrent Is and the phase difference ϕϕϕ between them. For SIS junctions, the current-phase relation is sinusioidal and 2πππ periodic. Other types of Josephson junctions, where the material between the superconductors is a weak link or a normal metal (N) may have non-sinusoidal current-phase relations that are still 2πππ periodic. We show here that a multi-terminal diffusive SNS Josephson junction with 4 superconducting contacts can show a current phase relation between two of the contacts that is a superposition of 2πππ and 4πππ periodic components whose relative strength is controlled by the phase difference between the other two contacts, becoming 2πππ or 4πππ periodic for certain values of this phase difference. This tunability might have applications in tailoring the Hamiltonians of superconducting quantum circuits.
Abstract Hybrid superconductor-semiconductor Josephson field-effect transistors (JoFETs) function as Josephson junctions with a gate-tunable critical current. Additionally, they can feature a non- sinusoidal current-phase relation (CPR) containing multiple harmonics of the superconducting phase difference, a so-far underutilized property. In this work, we exploit this multi-harmonicity to create a Josephson circuit element with an almost perfectly π-periodic CPR, indicative of a largely dominant charge-4e supercurrent transport. Such a Josephson element was recently proposed as the basic building block of a protected superconducting qubit. Here, it is realized using a superconducting quantum interference device (SQUID) with low-inductance aluminum arms and two nominally identical JoFETs. The latter are fabricated from a SiGe/Ge/SiGe quantum-well heterostructure embedding a high-mobility two-dimensional hole gas. By carefully adjusting the JoFET gate voltages and finely tuning the magnetic flux through the SQUID close to half a flux quantum, we achieve a regime where the sin(2φ) component accounts for more than 95 % of the total supercurrent. This result demonstrates a new promising route for the realization of superconducting qubits with enhanced coherence properties.
Controlling the current-phase relation (CPR) of Josephson elements is essential for tailoring the eigenstates of superconducting qubits, tuning the properties of parametric amplifiers, and designing nonreciprocal superconducting devices. Here, we introduce the hybrid Josephson rhombus, a highly tunable superconducting circuit containing four semiconductor-superconductor hybrid Josephson junctions embedded in a loop. Combining magnetic frustration with gate-voltage-controlled tuning of individual Josephson couplings provides deterministic control of the harmonic content of the rhombus CPR. We show that, for balanced Josephson couplings at full frustration, the hybrid rhombus displays a π -periodic cos ( 2 φ ) potential, indicating coherent charge- 4 e transport. Tuning away from the balanced configuration, we observe a superconducting diode effect with efficiency exceeding 25%. These results showcase the potential of hybrid Josephson rhombi as fundamental building blocks for noise-resilient qubits and quantum devices with custom transport properties.
Josephson elements are cornerstones of cryogenic classical and quantum superconducting technology, owing to their nonlinearity. Two important types of Josephson elements are often considered distinct: the tunnel junction (superconductor-insulator-superconductor, SIS) and the normal weak link (superconductor-normalsuperconductor, SNS) referring to any non-superconducting and non-insulating central region. SNS junctions and SIS junctions have appeared in related technological and basic science contexts over the last decade. In this perspective article, we review correspondences between SISIS junctions and SNS junctions in limiting regimes, in which a single, general energy-phase relationship describes the systems. We show how this insight helped to connect recent bodies of theoretical and experimental work in both systems. We conclude by describing a few important differences that also impact their use in applied contexts.
Abstract The progressive miniaturization of superconducting quantum interference devices (SQUIDs) used, e.g. for magnetic imaging on the nanoscale or for the detection of the magnetic states of individual magnetic nanoparticles causes increasing problems in realizing a proper flux-bias scheme for reading out the device. To overcome the problem, a multi-terminal, multi-junction layout has been proposed and realized recently for the SQUID-on-tip configuration, which uses constriction-type Josephson junctions (JJ). This geometry is also interesting for SQUIDs based on overdamped superconductor—normal metal—superconductor (SNS) JJ. We fabricated four-terminal, four-junction SQUIDs based on a trilayer Nb/HfTi/Nb process and study their static and dynamic transport properties in close comparison with numerical simulations based on the resistively and capacitively shunted junction model. Simulations and measurements are in very good agreement. However, there are large differences to the transport properties of conventional two-junction SQUIDs, including unusual phase-locked and chaotic dynamic states which we describe in detail. We further extract the current-phase relation of our SNS junctions, which turns out to be purely sinusoidal within the experimental error bars.
We study a 0-$\ensuremath{\pi}$ dc superconducting quantum interference device (SQUID) with asymmetric inductances and critical currents of the two Josephson junctions (JJs). By considering such a dc SQUID as a black box with two terminals, we calculate its effective current-phase relation ${I}_{s}(\ensuremath{\psi})$ and the Josephson energy $U(\ensuremath{\psi})$, where $\ensuremath{\psi}$ is the Josephson phase across the terminals. We show that there is a domain of parameters where the black box has the properties of a $\ensuremath{\varphi}$ JJ with degenerate ground state phases $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The $\ensuremath{\varphi}$ domain is rather large, so one can easily construct a $\ensuremath{\varphi}$ JJ experimentally. We derive the current phase relation and show that it can be tuned in situ by applying an external magnetic flux resulting in a continuous transition between the systems with static solutions $\ensuremath{\psi}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi},\phantom{\rule{0.16em}{0ex}}\ensuremath{\psi}={\ensuremath{\varphi}}_{0} ({\ensuremath{\varphi}}_{0}\ensuremath{\ne}0,\ensuremath{\pi})$ and even $\ensuremath{\psi}={\ensuremath{\varphi}}_{0}\ifmmode\pm\else\textpm\fi{}\ensuremath{\varphi}$. The dependence of ${\ensuremath{\varphi}}_{0}$ on applied magnetic flux is not $2\ensuremath{\pi}$ (one flux quantum) periodic.
A superconducting condensate is characterized by the emergence of macroscopic and collective order, established between its constituent electrons. The degree of correlation at a given spatial position is a complex scalar: it is characterized both by an amplitude (proportional to the minimal energy to generate a fundamental excitation) and a complex phase. Through its gradient, the latter enables the flow of the condensate, demonstrating the quantum fingerprint of superconductivity. Superconductors exhibit strong coupling to electromagnetic fields, so that phase-dependent dissipationless transport through “weak link” circuital elements is easily manipulated by applying voltage or magnetic flux bias to superconducting terminals and loops, respectively. For these reasons, superconducting electronics is nowadays a core technology to enable robust access and manipulation of the fundamental degrees of freedom in quantum devices, from ultrasensitive electromagnetic sensors to superconducting qubits. In this work, we explore different designs of micro-magnetometers based on superconducting interferometers. Differently from conventional designs based on Superconductor, Insulator, Superconductor (SIS) tunnel junctions, here the core elements are nanoscale diffusive metal wires acting as superconducting weak links. These consist in circuital dishomogeneities that can be fabricated over scales much smaller than typical superconductor coherence lengths, typically yielding unique response properties. On the other hand, their intrinsic transparency is usually associated with strong supercurrent concentration, which can severely limit their practicality due to superconducting depairing and thermal-driven hysteresis upon switching to the dissipative regime. In this thesis we demonstrate how a judicious use of nanofabricated designs makes it possible to counter these drawbacks and achieve complete phase polarization in interferometers based on diffusive weak links. The resulting micro-magnetometers are characterized by extremely high magnetic responsivity.