Session S16: Novel Effects in Josephson Junctions

Atomistic modeling of a superconductor–transition metal dichalcogenide–superconductor Josephson junction

Using an atomistic tight-binding model, we investigate the characteristics of a Josephson junction formed by monolayers of MoS₂ sandwiched between Pb superconducting electrodes. We derive and apply Green's function–based formulation to compute the Josephson current as well as the local density of states in the junction. Our analysis of diagonal and off-diagonal components of the local density of states reveals the presence of triplet superconducting correlations in the MoS₂ monolayers and spin-polarized subgap (Andreev bound) states. Our formulation can be extended to other systems where atomistic details and large scales are needed to obtain accurate modeling of Josephson junction physics.   

Artificial flat bands in frustrated Josephson junction arrays based on a superconductor/semiconductor hybrid platform

Epitaxial semiconductor-superconductor hybrid materials provide a novel highly-tunable platform to study exotic emergent quantum phenomena, taking advantage of gate-controlled density, ballistic transport, and non-sinusoidal current-phase relations. Recently, hybrid Josephson junction arrays have been used to study a gate-controlled superconductor-insulator transition (SIT), where Josephson coupling between Islands, E_J, can be tuned to be greater than or less than the charging energy of the island, E_C.

When applying a perpendicular magnetic field, frustration is introduced, leading to complex ground states, which depend on the geometry of the array. I will present data recorded in a two-dimensional Josephson junction array with dice lattice geometry, which is predicted to host flat bands when frustrated. I will discuss our recent effort to map out the phase diagram as a function of frustration. Commensurate values of frustration lead to the formation of vortex lattices, which are absent at incommensurate values of frustration. When frustrating the array with half a flux quantum per array plaquette, quantum interference localizes individual Cooper pairs on the array, corresponding to formation of a flat band system.   

Driving Josephson Junctions with Spin-Orbit Coupling

A common approach to drive Josephson junctions (JJs) out of equilibrium is to apply bias current. However, in planar Josephson junctions (JJs), which provide a suitable platform to realize topological superconductivity and the superconducting diode effect [1,2], we predict another mechanism due to the time-dependent spin-orbit coupling (SOC). Based on Al/InAs JJs, where the steady-state gate-control of SOC has already been demonstrated [1], we propose to instead consider time-dependent SOC. As a result, we show that both driving JJs as well as their switching from on to off state is possible even without any bias current. We explain the underlying dynamics in JJs and modified current-phase relations, as well as how they are connected to the time-dependent superconducting diode effect.

 

[1] M. C. Dartiailh et al., Phys. Rev. Lett. 126, 036802 (2021).

[2] M. Amudsen et al., arXiv:2210.03549, Rev. Mod. Phys (under review).

[3] D. Monroe, M. Alidoust, I. Žutić, Phys Rev. App. 18, L031001 (2022)   

KTaO3-based nanodevices

The KTaO₃ (KTO)-based two dimensional electron gas (2DEG) has recently raised interest in the field of oxide interfaces, due to its superconductivity that depends on the KTO interface orientation [1,2]. Here we report the creation of KTO-based Josephson Junctions and SQUIDs, using conductive atomic force microscope (c-AFM) lithography [3]. These devices reflect the underlying spin-orbit coupling of KTO 2DEG, as well as its high kinetic inductance. The development of nanodevices positions KTO as a promising future platform for applications in quantum information and spintronics.

[1] Liu, Changjiang, et al. Science 371.6530 (2021): 716-721.

[2] Chen, Zheng, et al. Physical Review Letters 126.2 (2021): 026802.

[3] Yu, Muqing, et al. Nano Lett. 22.15 (2022): 6062–6068   

Crossover of h/e and h/2e oscillations in chiral edge-channel Josephson junctions

Recently, several experiments reported that the magnetic field interference pattern of the quantum hall edge states mediated Josephson junctions can exhibit Fraunhofer oscillations with a periodicity of either h/e or h/2e. However, a unified understanding of such a phenomenon is still absent. In this work, we show that the competition between crossed Andreev reflections and local Andreev reflections results in the crossover between h/e and h/2e quantum oscillations in chiral edge-channel Josephson junctions. Our theory explains why recent experiments observed either h/e or h/2e oscillations in different samples. Furthermore, we predict a thermal-driven h/e to h/2e Fraunhofer oscillations crossover.   

Ta-based Josephson junctions using insulating ALD TaN tunnel barriers

Josephson junctions (JJs) are critical for superconducting quantum computing and sensing. The conventionally used Al/Al oxide JJs are susceptible to degradation at elevated temperatures. We introduce junctions employing superconducting α-phase tantalum (Ta) electrodes and insulating TaN tunnel barriers, fabricated on 300 mm diameter, high-resistivity silicon wafers using advanced processes including 193 nm optical lithography, atomic layer deposition (ALD) of TaN, and chemical mechanical planarization of Ta. We assessed critical current density, sub-gap resistance, and gap voltage for JJs sized 100 nm to 3 μm. We detail the temperature dependence of junctions from 50 mK to 3.8 K, demonstrate area scaling, as well as the scaling of critical current with ALD TaN thickness. We also report the across-wafer uniformity of junction resistance, measured at 300 K. Remarkable stability of JJ characteristics over three months of room temperature storage, and the behavior of JJ arrays and 2-junction SQUIDs are described. Our approach holds promise for thermally stable junctions on 300 mm wafers with consistent performance, marking an important step towards offering advanced qubit fabrication at 300 mm scale, in the near future, in a Quantum Foundry operated by a non-profit entity.   

Noise characteristics of the current biased super-semi Josephson junctions

Josephson junctions with a semiconductor weak link demonstrated high tunability suitable for applications in superconducting quantum devices. 

At the same time, the noise and dissipation characteristics of these Junctions remain unexplored. We present a theoretical study of 

the current-voltage characteristics and voltage noise of a semiconductor weak link shunted by a resistor. We calculate the effect of 

the resistor's Johnson thermal noise on the low-frequency voltage noise by performing a stochastic calculus in low frequency. 

We also evaluate the contribution to the noise from the fluctuations in the quasiparticle distribution on the Andreev bound states in the weak link.     

Characterizing Majorana bound states in extended disordered Josephson junctions

In this talk, we consider the emergence of Majorana bound states (MBS) in extended S-TI-S Josephson junctions between p+ip superconductors. In a single junction geometry, it has been shown that the cores of Josephson vortices can host MBS when an external magnetic field is present within the junction. Here, we present analytic and numerical studies of MBS dynamics in a single Josephson junction system formed by two finite-sized p+ip superconducting islands. We focus primarily on the interplay between flux and disorder in the system by first developing an effective 1D-model for the system before examining the spectrum for the full 2D-lattice model. We discuss potential implications of our results in experimentally relevant S-TI-S junction systems and the extension of this analysis to a tri-junction system, in which braiding of MBS can occur.   

Measurements of the current-phase relationship in SIS and SNS Josephson junctions

The current-phase relationship (CΦR) of Josephson junctions (JJs) is an important parameter for modeling the behavior of superconducting circuits such as those used for the voltage standard, SFQ digital logic, and quantum information. The CΦR for superconductor-insulator-superconductor (SIS) JJs is typically assumed to be perfectly sinusoidal although this can be inaccurate in certain cases. For JJs with normal-metal (N) barriers, called SNS junctions, the CΦR has been shown to have a ramp-like dependence, which can significantly affect the behavior of circuits using these JJs. For example, the use of  SNS JJs with niobium-doped silicon barriers significantly alters the operating margins of NIST voltage standard circuits and can affect the timing and margins of SFQ digital circuits. We will show extracted CΦR data for both SIS and SNS junctions measured at 4 K using a microwave resonator technique. The measurement circuit consists of a ~ 5 GHz niobium resonator terminated with an RF-SQUID. Using an on-chip flux line to vary the SQUID JJ phase φ and the junction inductance, L_j (φ) ~ [ d(CΦR)/ dφ ]^-1, the resonator frequency shifts depending on the derivative of the CΦR and is measured by monitoring the transmission (S₂₁) of the coupled microwave circuit.   

Majorana Bound States in the Diffraction Patterns of S-TI-S Lateral Josephson Junctions

In an extended superconductor-topological insulator-superconductor (S-TI-S) Josephson junction, localized Majorana bound states (MBS) are predicted to exist where the local phase difference across the junction is an odd-multiple of π. These states can induce a supercurrent with a 4π-periodic current-phase relation (CPR). In this talk, we present an extensive study of the critical current vs. magnetic field diffraction patterns of S-TI-S lateral Josephson junction devices, comparing measurements and simulations. The measurement exhibits distinct deviations from the usual Fraunhofer diffraction pattern of uniform extended Josephson junctions which include the lifting of odd-numbered nodes, features that signify the entry of Majorana states, and evidence for parity states and fluctuations.  We compare results from junctions with TI barriers of Bi₂Se₃ and Bi_0.8Sb_1.2Te₃ and non-TI graphene barriers.   

Tracking Majorana Bound States in Superconductor-Topological Insulator-Superconductor Josephson junctions by transport measurements

Josephson junctions with a Superconductor-Topological Insulator-Superconductor (S-TI-S) geometry are expected to host Majorana Bound States (MBS) under certain conditions. In an external magnetic field, the MBS will be localized in Josephson vortices where the phase difference is an odd multiple of π. We describe and present progress on two experiments designed to test the interaction of pairs of Majorana states. In one experiment, we contrast the critical current diffraction patterns of two junction geometries - one geometry in which we proximitize only the top surface of the TI which creates localized MBS paired with delocalized Majorana extended states, with another geometry of junctions in which we proximitize both surfaces of the TI creating localized MBS pairs on the two surfaces. In the second experiment, we use a small field coil to apply a local magnetic field to the junction which tunes the distance between a pair of localized MBS. This can be detected as a modification of the critical current diffraction pattern and affects the hybridization of the Majorana states.   

Designing exciton-condensate Josephson junction in graphene heterostructure

Exciton condensation have been robustly realized in several 2D-material heterostructures, specifically graphene quantum hall bilayers. This work proposes a realistic setup of exciton-condensate Josephson junction and a measurement ansatz in such systems.The junction mimics the S-I-S structure of the ordinary Josephson junction, where the insulating barrier is a layer-polarized quantum Hall state controlled by external gating. We estimate the strength of Josephson coupling as a function of junction width, which reveals its high range of tunability. Finally, we propose a capacitive measurement ansatz of the Josephson frequency.   

Dynamical Stabilization of Supercurrents in a Graphene-Based Josephson Network

Josephson networks are a promising platform for harboring synthetic topological phases of matter and Floquet states. These networks have hosted Cooper multiplets–coherent transport of four or more electrons through splitting of Cooper pairs and subsequent Andreev reflections. In this talk, we demonstrate multi-junction dynamical supercurrents emerging from an engineered Josephson network. The device features three superconducting electrodes connected through graphene to a superconducting island. The dynamical supercurrents include features similar to Cooper quartets, which are robust to elevated temperatures and exhibit the expected Shapiro step quantization under microwave drive. Additionally, we observe an unexpected supercurrent mediated between adjacent contacts through the superconducting island. These experimental results are substantiated by demonstrations of dynamical stabilization in the RCSJ model of the device.   

Floquet theory of multi-level Landau-Zener transitions in topologically trivial Josephson junctions

We study multi-level Landau-Zener (LZ) transitions in periodically driven quantum systems, both numerically and analytically using Floquet theory. In the high frequency regime, we perform a nondegenerate Floquet perturbation theory and calculate transition probabilities between the different adiabatic states. In the low frequency regime, we employ a degenerate Floquet perturbation theory that treats Floquet resonances systematically. We apply our results to investigate multi-modal scattering in ac Josephson junctions hosting topologically trivial high-transparency modes. A single pair of high-transparency modes has been shown to mimic the 4π - periodicity in the current-phase relation and missing Shapiro steps expected of topological Majorana modes. We find that transitions between multiple pairs of high-transparency modes can result in additional structure in the current-phase relation with various periodic patterns.   

Towards RF spectroscopy of Andreev bound states in an InAs-Al 2DEG

Hybrid superconducting-semiconducting heterostructures provide a promising platform for investigating topological superconductivity via the proximity effect. Planar multi-terminal Josephson junctions (JJs) [1] are predicted to host zero-energy Andreev bound states (ABSs). In this regard, we present the characterization of conventional two-terminal JJs in an InAs two-dimensional electron gas (2DEG) with epitaxially grown Al. By applying an external magnetic flux, we can tune the superconducting phase difference in a superconducting quantum interference device (SQUID). We further implement a gated InAs-Al JJ in a coplanar waveguide (CPW) resonator [2] to perform microwave spectroscopy of ABSs for studying unconventional superconductivity in such JJs.

 

[1] N. Pankratov et al., Phys. Rev. X 10, 031051 (2020)

[2] W.M. Strickland et al., Phys. Rev. Applied 19, 034021 (2023)