By measuring the Josephson emission of a diffusive Superconductor-Normal metal-Superconductor (SNS) junction at a finite temperature we reveal a non-trivial sensitivity of the supercurrent to microwave irradiation. We demonstrate that the harmonic content of the current-phase relation is modified due to the energy redistribution of quasiparticles in the normal wire induced by the electromagnetic field. The distortion originates from the phase-dependent out-of-equilibrium distribution function which is strongly affected by the ac-response of the spectral supercurrent. For phases close to $π$, transitions accross the Andreev gap are dynamically favored leading to a supercurrent reduction. This finding is supported by a comparison with the quasiclassical Green's function theory of superconductivity in diffusive SNS junctions under microwave irradiation.
In this work, we investigated the nonadiabatic transport properties of the one-dimensional time-dependent superconductor-normal metal-superconductor (SNS) Josephson junction biased by a current source and driven by a high-frequency-ac-gate-potential applied to the normal-metal layer. BCS superconductors are considered and treated with the time-dependent Bogoliubov-de Gennes equation. Using Floquet theory, we compute the transmission coefficients and the Wigner-Smith delay times as a function of the incident energy and find that they display resonances when one of the electron or hole Floquet w…
Irradiating a Josephson junction with microwaves can operate not only on the amplitude but also on the phase of the Josephson current. This requires breaking time inversion symmetry, which is achieved by introducing a phase lapse between the microwave components acting on the two† sides of the junction. General symmetry arguments and the solution of a specific single level quantum dot model show that this induces chirality in the Cooper pair dynamics, due to the topology of the Andreev bound state wavefunction. Another essential condition is to break electron-hole symmetry within the junction.…
We present transport measurements on long diffusive graphene-based Josephson junctions. Several junctions are made on a single-domain crystal of CVD graphene and feature the same contact width of ~9$μ$m but vary in length from 400 to 1000 nm. As the carrier density is tuned with the gate voltage, the critical current in the these junctions spans a range from a few nA up to more than $5μ$A, while the Thouless energy, ETh, covers almost two orders of magnitude. Over much of this range, the product of the critical current and the normal resistance IcRn is found to scale linearly with ETh, as expe…
Periodically driven systems exhibit resonance when the difference between an excited state energy and the ground state energy is an integer multiple of $\hbar$ times the driving frequency. On the other hand, when a superconducting phase difference is maintained between two superconductors, subgap states appear which carry a Josephson current. A driven Josephson junction therefore opens up an interesting avenue where the excitations due to applied driving affect the current flowing from one superconductor to the other. Motivated by this, we study charge transport in a superconductor-normal meta…
We consider a planar SIS-type Josephson junction between diffusive superconductors (S) through an insulating tunnel interface (I). We construct fully self-consistent perturbation theory with respect to the interface conductance. As a result, we find correction to the first Josephson harmonic and calculate the second Josephson harmonic. At arbitrary temperatures, we correct previous results for the nonsinusoidal current-phase relation in Josephson tunnel junctions, which were obtained with the help of conjectured form of solution. Our perturbation theory also describes the difference between th…
Motivated by experiments with current biased superconducting atomic point contacts the general problem of nonadiabatic transitions between adiabatic surfaces in presence of strong dissipation is studied. For a single channel device the supercurrent is determined by the diffusive motion of the superconducting phase difference on two Andreev levels. These surfaces are uncoupled only in the adiabatic limit of low to moderate transmissions, while for high transmissions curve crossings are important. Starting from a general master equation of the full density matrix an approximate time evolution eq…
We study the supercurrent in quasi-one-dimensional Josephson junctions with a weak link involving magnetism, either via magnetic impurities or via ferromagnetism. In the case of weak links longer than {\color{black}the magnetic pair-breaking} length, the Josephson effect is dominated by mesoscopic fluctuations. We establish the supercurrent-phase dependence $I(φ)$ along with statistics of its sample-dependent properties in junctions with transparent contacts between leads and link. High transparency gives rise to the inverse proximity effect, while the direct proximity effect is suppressed by …
We present a full microscopic theory based on the SU(2) covariant formulation of the quasiclassical formalism to describe the Josephson current through an extended superconductor-normal metal- superconductor (SNS) diffusive junction with an intrinsic spin-orbit coupling (SOC) in the presence of a spin-splitting field h. We demonstrate that the ground state of the junction corresponds to a finite intrinsic phase difference 0 < ϕ0 < 2π between the superconductor electrodes provided that both, h and the SOC-induced SU(2) Lorentz force are finite. In the particular case of a Rashba SOC we present …
In this paper, the spin transfer torque (STT) and the exchange coupling of the Josephson junctions containing interesting cases of diffusive/ballistic-triplet/singlet ferromagnetic superconductor materials together with diffusive Josephson junction of the form S$_{1}$/F$_{1}$/I$_1$/N/I$_2$/F$_2$ with I being insulating barrier are investigated. Using the Nazarov quantum circuit theory, it is found that for the diffusive FS$_1$/N/FS$_2$ structure the only emerged torque in normal direction to the plane of the exchange fields of F$_1$ and F$_2$ results in antiparallel/parallel or vice versa para…
The energy of an Andreev bound state in a clean normal metal in contact with two superconductors disperses with the difference $Δϕ$ in the superconducting phase between the superconductors in much the same way as the energies of electrons in a one-dimensional crystal disperse with the crystal momentum $k$ of the electrons. A normal metal with $n$ superconductors maps on to a $n-1$ dimensional crystal, each dimension corresponding to the phase difference $ϕ_i$ between a specific pair of superconductors. The resulting band structure as a function of the phase differences $\{Δϕ_i\}$ has been prop…
Josephson transport in YBa${}_{2}$Cu${}_{3}$O${}_{7}$ weak links created by focused-helium-ion-beam irradiation: Analysis based on diffusive-SNS-junction model
National Institute of Advanced Industrial Science and Technology（日本产业技术综合研究所）
The superconducting proximity effect leads to strong modifications of the local density of states in diffusive or chaotic cavity Josephson junctions, which displays a phase-dependent energy gap around the Fermi energy. The so-called minigap of the order of the Thouless energy $E_{\mathrm{Th}}$ is related to the inverse dwell time in the diffusive region in the limit $E_{\mathrm{Th}}\llΔ$, where $Δ$ is the superconducting energy gap. In the opposite limit of a large Thouless energy $E_{\mathrm{Th}}\ggΔ$, a small new feature has recently attracted attention, namely, the appearance of a further s…
We perform extensive analysis of graphene Josephson junctions embedded in microwave circuits. By comparing a diffusive junction at 15 mK with a ballistic one at 15 mK and 1 K, we are able to reconstruct the current-phase relation.
Divergence at low bias and down-mixing of the current noise in a diffusive superconductor-normal metal-superconductor junction
我们目前的电流噪声测量在一个长的扩散超导正常金属超导结在低电压制度，其中运输可以部分地描述在相干多Andreev反射。我们发现，当电压降低时，电流噪声表现出强烈的发散性以及一个宽峰。我们把这个峰归因于交流约瑟夫森电流和结本身噪声之间的混合。我们表明，结噪声对应于一个非线性电阻4kBT=R，R V = I V和没有可调参数的热噪声。
Bijunctions are three-terminal Josephson junctions where three superconductors are connected by a single weak link made of a metallic region or of quantum dots. Biasing two of the superconductors with commensurate voltages yields Andreev resonances that produce d.c. Josephson currents made of correlated Cooper pairs. For instance with applied voltages (0, V,-V), quartets formed by two entangled Cooper pairs are emitted by one reservoir towards the two others. Theory involving non-equilibrium Green's functions reveal the microsopic mechanism at play, e.g. multiple coherent Andreev reflections t…
A mesoscopic hybrid Normal/ Superconducting (NS) ring is characterized by a dense Andreev spectrum with a flux dependent minigap. We measure the linear response to a high frequency flux, in a wide frequency range, with a multimode superconducting resonator. We find that the current response contains, beside the well known dissipation-less Josephson contribution, a large dissipative component. At high frequency compared to the minigap and low temperature we find that the dissipation is due to transitions above the minigap. In contrast, at lower frequency there is range of temperature for which …
We solve Dirac-Bogoliubov-De-Gennes (DBdG) equation in a superconductor-normal graphene superconductor (SGS) junction with Corbino disk structure to investigate the Josephson current through this junction. We find that the critical current $I_c$ has a nonzero value at Dirac point in which the concentration of the carriers is zero. We show this nonzero critical current depends on the system geometry and it decreases monotonically to zero by increasing the ratio of the outer to inner radii of the Corbino disk ($R_2/R_1$), while in the limit of $R_2/R_1 \rightarrow 1$ it scales like a diffusive C…
Graphene on silicon carbide (SiC) has proved to be highly successful in Hall conductance quantization for its homogeneity at the centimetre scale. Robust Josephson coupling has been measured in co-planar diffusive Al/monololayer graphene/Al junctions. Graphene on SiC substrates is a concrete candidate to provide scalability of hybrid Josephson graphene/superconductor devices, giving also promise of ballistic propagation.
We demonstrate that in sufficiently long diffusive superconducting-normal-superconducting ($SNS$) junctions dc Josephson current is exponentially suppressed by electron-electron interactions down to zero temperature. This suppression is caused by the effect of {\it Cooper pair dephasing} which occurs in the normal metal and defines a new fundamental length scale $L_φ$ in the problem. Provided the temperature length exceeds $L_φ$ this dephasing length can be conveniently extracted from equilibrium measurements of the Josephson current.
We study Josephson junctions with weak links consisting of two parallel disordered arms with magnetic properties -- ferromagnetic, half-metallic or normal with magnetic impurities. In the case of long links, the Josephson effect is dominated by mesoscopic fluctuations. In this regime, the system realises a $φ_0$ junction with sample-dependent $φ_0$ and critical current. Cooper pair splitting between the two arms plays a major role and leads to $2Φ_0$ periodicity of the current as a function of flux between the arms. We calculate the current and its flux and polarization dependence for the thre…
We have probed the superconducting proximity effect through long high-quality monocrystalline Ag nanowires, by realizing Josephson junctions of different lengths, with different superconducting materials. Thanks to the high number of junctions probed, both the contact resistance and electron diffusion constant could be determined, enabling a comparison of the measured critical current to theoretical expectation, over the entire regime from short to long diffusive junction. Although the length dependence of the critical current is as expected, the amplitude of the $R_{N}I_c$ product is smaller …
We present tunnel spectroscopy experiments on the proximity effect in lateral superconductor-normal metal-superconductor (SNS) Josephson junctions. Our weak link is embedded into a superconducting (S) ring allowing phase biasing of the Josephson junction by an external magnetic field. We explore the temperature and phase dependence of both the induced mini-gap and the modification of the density of states in the normal (N) metal. Our results agree with a model based on the quasiclassical theory in the diffusive limit. The device presents an advanced version of the superconducting quantum inter…
We calculate the phase, the temperature and the junction length dependence of the supercurrent for ballistic graphene Josephson-junctions. For low temperatures we find non-sinusoidal dependence of the supercurrent on the superconductor phase difference for both short and long junctions. The skewness, which characterizes the deviation of the current-phase relation from a simple sinusoidal one, shows a linear dependence on the critical current for small currents. We discuss the similarities and differences with respect to the classical theory of Josephson junctions, where the weak link is formed…
We report transport measurements on Josephson junctions consisting of Bi2Te3 topological insulator (TI) thin films contacted by superconducting Nb electrodes. For a device with junction length L = 134 nm, the critical supercurrent Ic can be modulated by an electrical gate which tunes the carrier type and density of the TI film. Ic can reach a minimum when the TI is near the charge neutrality regime with the Fermi energy lying close to the Dirac point of the surface state. In the p-type regime the Josephson current can be well described by a short ballistic junction model. In the n-type regime …
We discuss the statistics of heat current between two superconductors at different temperatures connected by a generic weak link. As the electronic heat in superconductors is carried by Bogoliubov quasiparticles, the heat transport fluctuations follow the Levitov--Lesovik relation. We identify the energy-dependent quasiparticle transmission probabilities and discuss the resulting probability density and fluctuation relations of the heat current. We consider multichannel junctions, and find that heat transport in diffusive junctions is unique in that its statistics is independent of the phase d…
We report the observation of a current-phase relation dominated by the second Josephson harmonic in superconductor-ferromagnet-superconductor junctions. The exotic current-phase relation is realized in the vicinity of a temperature-controlled 0-to-$π$ junction transition, at which the first Josephson harmonic vanishes. Direct current-phase relation measurements, as well as Josephson interferometry, non-vanishing supercurrent and half-integer Shapiro steps at the 0-$π$ transition self-consistently point to an intrinsic second harmonic term, making it possible to rule out common alternative orig…
We have theoretically studied the supercurrent profiles in three-dimensional normal metal and ferromagnetic Josephson configurations, where the magnitude of the superconducting gaps in the superconducting leads are unequal, i.e., $Δ_1\neq Δ_2$, creating asymmetric $S_1NS_2$ and $S_1FS_2$ systems. Our results reveal that by increasing the ratio of the superconducting gaps $Δ_2/Δ_1$, the critical supercurrent in a ballistic $S_1NS_2$ system can be enhanced by more than $100\%$, and reaches a saturation point, or decays away, depending on the junction thickness, magnetization strength, and chemic…
