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arXiv:2212.06866 · Physical Review Letters

Diode Effects in Current-Biased Josephson Junctions

Jacob F. Steiner, Larissa Melischek, Martina Trahms, Katharina J. Franke, Felix von Oppen

Published Apr 27, 2023• 57 citations
arXivHTMLPDF

Abstract

Current-biased Josephson junctions exhibit hysteretic transitions between dissipative and superconducting states as characterized by switching and retrapping currents. Here, we develop a theory for diodelike effects in the switching and retrapping currents of weakly damped Josephson junctions. We find that while the diodelike behavior of switching currents is rooted in asymmetric current-phase relations, nonreciprocal retrapping currents originate in asymmetric quasiparticle currents. These different origins also imply distinctly different symmetry requirements. We illustrate our results by a microscopic model for junctions involving a single magnetic atom. Our theory provides significant guidance in identifying the microscopic origin of nonreciprocities in Josephson junctions.

DOI
10.1103/physrevlett.130.177002

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Current-biased Josephson junctions exhibit hysteretic transitions between dissipative and superconducting states as characterized by switching and retrapping currents. Here, we develop a theory for diodelike effects in the switching and retrapping currents of weakly damped Josephson junctions. We find that while the diodelike behavior of switching currents is rooted in asymmetric current-phase relations, nonreciprocal retrapping currents originate in asymmetric quasiparticle currents. These different origins also imply distinctly different symmetry requirements. We illustrate our results by a microscopic model for junctions involving a single magnetic atom. Our theory provides significant guidance in identifying the microscopic origin of nonreciprocities in Josephson junctions.
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Hysteresis and retrapping are hallmarks of underdamped Josephson dynamics, yet they have remained elusive in atomic Josephson junctions. Here, we introduce a velocity-sweep protocol to demonstrate these phenomena in the underdamped regime of an atomic Josephson junction. Specifically, using classical-field simulations of a two-dimensional bosonic superfluid, we show hysteresis in the velocity-imbalance characteristics and determine the retrapping current. The dynamics are quantitatively captured by the resistively and capacitively shunted junction (RCSJ) model. We show that hysteresis originates from persistent phase slips below the critical current, with the associated dissipation mediated by vortex-antivortex pair nucleation at the weak link. The retrapping current follows the Stewart-McCumber scaling of underdamped junctions, establishing a common phase-dynamical framework for atomic and superconducting Josephson junctions.
Josephson junctions enable dissipation-less electrical current through metals and insulators below a critical current. Despite being central to quantum technology based on superconducting quantum bits and fundamental research into self-conjugate quasiparticles, the spatial distribution of super current flow at the junction and its predicted evolution with current bias and external magnetic field remain experimentally elusive. Revealing the hidden current flow, featureless in electrical resistance, helps understanding unconventional phenomena such as the nonreciprocal critical current, i.e., Josephson diode effect. Here we introduce a platform to visualize super current flow at the nanoscale. Utilizing a scanning magnetometer based on nitrogen vacancy centers in diamond, we uncover competing ground states electrically switchable within the zero-resistance regime. The competition results from the superconducting phase re-configuration induced by the Josephson current and kinetic inductance of thin-film superconductors. We further identify a new mechanism for the Josephson diode effect involving the Josephson current-induced phase. The nanoscale super current flow emerges as a new experimental observable for elucidating unconventional superconductivity, and optimizing quantum computation and energy-efficient devices. Diract imaging of supercurrent flow at a Josephson junction has been inaccessible in experiment. Here, using nanoscale magnetometry, the authors find large kinetic inductance of thin film superconductors can lead to competing Josephson vortex states hidden below the critical current, and also provide a new route towards the Josephson diode effect.
Deep theoretical understanding of the electrical response of Josephson junctions is indispensable regarding both recent discoveries of new kinds of superconductivity and technological advances such as superconducting quantum computers. Here, we study the microscopic theory of the dc current-biased I-V characteristics of Josephson tunnel junctions. We derive an analytical formula of the I-V characteristics of generic junctions. We identify subharmonics of the I-V characteristics and their underlying mechanism as the feedback effect of intrinsic ac currents generated by voltage pulses in the past. We apply our theory to analytically solve the Werthamer equation and describe various dc current-biased I-V characteristics as a function of softening of the superconducting gap. Strikingly, we identify voltage staircases of the I-V characteristics in a genuine Josephson junction without ac current bias or qubit dynamics. Our general analytical formalism opens new avenues for a microscopic understanding of I-V characteristics of Josephson junctions that have been limited to phenomenological models so far.
We propose a many-body mechanism for a strong Josephson diode effect (JDE) in an interacting nanoscale SQUID formed by two parallel quantum dots coupled to superconducting leads. Unlike conventional diode behavior, where nonreciprocity originates from a skewed current-phase relation within a single, continuously evolving ground state, the JDE reported here is \emph{branch selected}: the positive and negative critical currents are optimized on different many-body branches across the 000-πππ phase boundary, yielding a substantial enhancement of the diode efficiency. We further show that a \emph{nonlocal} Cooper-pair tunneling channel, which binds the two electrons on different arms, is essential: it reshapes the 000-πππ boundary and produces a pronounced ``diode band'' in parameter space, in sharp contrast to the fragile hotspot obtained when only local Cooper-pair transfer is available. While the key physics is captured by an effective model in the superconducting atomic limit, our conclusions remain robust for realistic finite-gap devices, as demonstrated within a generalized atomic-limit framework.
We propose a Josephson diode mechanism in which nonreciprocity arises not from a conventional asymmetric Andreev spectrum but from nonequilibrium occupation of the current-carrying states engineered by attached reservoirs. We realize this mechanism in a double-quantum-dot junction, where a phase-textured nonlocal reservoir acts as a quantum Zeno selector: rapid dissipation freezes out the bright state directly coupled to the jump operator LLL, while preserving an orthogonal dark Andreev channel whose supercurrent remains comparable to that of the lossless junction. In the infinite-gap limit, the steady-state current factorizes as Iss=IAPγI_{\rm ss}=I_A P_γIss​=IA​Pγ​, so that even when the Andreev current IAI_AIA​ is strictly reciprocal, the phase asymmetry of PγP_γPγ​ alone can produce a Josephson diode effect through reservoir engineering. We further show that local Coulomb repulsion can drive the system toward a nearly ideal diode regime via a dark-pair resonance. Using Keldysh-Lindblad calculations, we demonstrate that our results remain robust for realistic junctions with a finite superconducting gap and dissipation.