Magnetic Interference Patterns Research Articles

Beyond the effective length: How to analyze magnetic interference patterns of thin-film planar Josephson junctions with finite lateral dimensions

The magnetic-field-dependent critical current ${I}_{\text{c}}(B)$ of a Josephson junction is determined by the screening currents in its electrodes. In macroscopic junctions, a local vector potential drives the currents; however, in thin-film planar junctions, with electrodes of finite size and various shapes, they are governed by nonlocal electrodynamics. This complicates the extraction of parameters such as the geometry of the effective junction area, the effective junction length, and the critical current density distribution from the ${I}_{\text{c}}(B)$ interference patterns. Here, we provide a method to tackle this problem by simulating the phase differences that drive the shielding currents and use those to find ${I}_{\text{c}}(B)$. To this end, we extend the technique proposed by Clem [Phys. Rev. B 81, 144515 (2010)] to find ${I}_{\text{c}}(B)$ for Josephson junctions separating a superconducting strip of length $L$ and width $W$ with rectangular, ellipsoid, and rhomboid geometries. We find the periodicity of the interference pattern ($\mathrm{\ensuremath{\Delta}}B$) to have geometry-independent limits for $L\ensuremath{\gg}W$ and $L\ensuremath{\ll}W$. By fabricating elliptically shaped superconductor--normal-metal--superconductor junctions with various aspect ratios, we experimentally verify the $L/W$ dependence of $\mathrm{\ensuremath{\Delta}}B$. Finally, we incorporate these results to correctly extract the distribution of critical currents in the junction by the Fourier analysis of ${I}_{\text{c}}(B)$, which makes these results essential for the correct analysis of topological channels in thin-film planar Josephson junctions.

Anomalous periodicity of magnetic interference patterns in encapsulated graphene Josephson junctions

We investigate supercurrent interference patterns measured as a function of magnetic field in ballistic graphene Josephson junctions. At high doping, the expected $\Phi_{0}$-periodic "Fraunhofer" pattern is observed, indicating a uniform current distribution. Close to the Dirac point, we find anomalous interference patterns with an apparent 2$\Phi_{0}$ periodicity, similar to that predicted for topological Andreev bound states carrying a charge of $e$ instead of $2e$. This feature persists with increasing temperature, ruling out a non-sinusoidal current-phase relationship. It also persists in junctions in which sharp vacuum edges are eliminated. Our results indicate that the observed behavior may originate from an intrinsic property of ballistic graphene Josephson junctions, though the exact mechanism remains unclear.

Implementation of Full Spin-State Interferometer**Supported by the National Key Research and Development Program of China under Grant No 2016YFA0301501, and the National Natural Science Foundation of China under Grant Nos 61727819 and 91736208.

Matter-wave interferometers with spin quantum states are attractive in quantum manipulation and precision measurements. Here, five spatial interference patterns corresponding to the full spin states are observed in each run of the experiment, by the combination of the Majorana transition according to the exponential modulation of the magnetic field pulse decline curve and radio frequency coupling among multiple magnetic sub-states. Compared to the realization of two Majorana transitions, the interference fringe for the magnetic field insensitive state also has a higher contrast. After spatially overlapping the full magnetic sub-state interference patterns dozens of times in consecutive experimental measurements, clear fringes are still observed, indicating the great stability of the relative phases of different components. This indicates the potential to achieve an interferometer with multiple spin clocks.

Imaging local magnetic structure by polarized neutron holography

Neutrons, due to their intrinsic magnetic moment, are suitable scattering particles for measuring magnetic structures. Long-range magnetic structure is routinely measured, but the imaging of local magnetic structure around selected nuclei with holography methods is still an open field. The aim of this study was to provide a reconstruction method for polarized neutron holography which is capable to separate and reconstruct the three components of atomic magnetic moments around the probe nucleus. The computer model of the magnetic interference pattern and the proposed reconstruction was set up to demonstrate the viability of the idea and to find the optimal experimental conditions. The simulation showed that the experimental conditions, most importantly the neutron intensity can be implemented at existing neutron sources, however, an instrument optimized for this experiment is required.

Edge effects in the magnetic interference pattern of a ballistic SNS junction

We investigate the Josephson critical current $I_c(\Phi)$ of a wide superconductor-normal metal-superconductor (SNS) junction as a function of the magnetic flux $\Phi$ threading it. Electronic trajectories reflected from the side edges alter the function $I_c(\Phi)$ as compared to the conventional Fraunhofer-type dependence. At weak magnetic fields, $B\lesssim \Phi_0/d^2$, the edge effect lifts zeros in $I_c(\Phi)$ and gradually shifts the minima of that function toward half-integer multiples of the flux quantum. At $B>\Phi_0/d^2$, the edge effect leads to an accelerated decay of the critical current $I_c(\Phi)$ with increasing $\Phi$. At larger fields, eventually, the system is expected to cross into a regime of "classical" mesoscopic fluctuations that is specific for wide ballistic SNS junctions with rough edges.

Signature of gate-tunable magnetism in graphene grafted with Pt-porphyrins

Inducing magnetism in graphene holds great promises, such as controlling the exchange interaction with a gate electrode and generating exotic magnetic phases. Coating graphene with magnetic molecules or atoms has so far mostly lead to decreased graphene mobility. In the present work, we show that Pt-porphyrins adsorbed on graphene lead to an enhanced mobility and to gate-dependent magnetism. We report that porphyrins can be donor or acceptor, depending on graphene s initial doping. The porphyrins transfer charge and ionize around the charged impurities on graphene, decreasing the graphene doping and increasing its mobility. In addition, ionized porphyrins carry a magnetic moment. Using the sensitivity of mesoscopic transport to magnetism, in particular the superconducting proximity effect and conductance fluctuations, we explore the magnetic order induced in graphene by the interacting magnetic moments of the ionized porphyrins. Among the signatures of magnetism, we find two-terminal-magnetoresistance fluctuations with an odd component, a tell-tale sign of time reversal symmetry breaking at zero field, that does not exist in uncoated graphene sample. When graphene is connected to superconducting electrodes, the induced magnetism leads to a gate-voltage-dependent suppression of the supercurrent, modified magnetic interference patterns, and gate-voltage-dependent magnetic hysteresis. The magnetic signatures are greatest for long superconductor graphene superconductor junctions and for samples with the highest initial doping, compatible with a greater number of ionized and thus magnetic porphyrins. Our findings suggest that long-range magnetism is induced through graphene by the ionized porphyrins magnetic moment. This magnetic interaction is controlled by the density of carriers in graphene, a tunability that could be exploited in spintronic applications.

Broken time-reversal symmetry in a SQUID based on chiral superconducting Sr2RuO4

Unconventional superconductors involve not only gauge-symmetry breaking but also orbital- and spin-symmetry breaking. Superconducting Sr2RuO4 is known as a spin-triplet chiral p-wave and a topological superconductor with broken time-reversal symmetry (BTRS). Kerr-effect and muon-spin-rotation (pSR) measurements have shown that the bulk superconducting state of Sr2RuO4 features BTRS in the orbital part; hence, it is called the chiral state. BTRS in the response of superconducting junctions or SQUIDs would appear as the shifts of magnetic interference patterns. However, it is problematic to distinguish whether the shift originates in the residual magnetic field (trapped vortex) or the effects of BTRS. Here, we show that the magnetic interference patterns of a SQUID based on Sr2RuO4 are explicitly asymmetric with respect to the direction of both the bias current and the applied magnetic field; namely, there is no inversion symmetry. This indicates that the superconducting state of Sr2RuO4 undoubtedly breaks the time-reversal symmetry of the SQUID.

Electrostatic tailoring of magnetic interference in quantum point contact ballistic Josephson junctions

The magnetoelectrostatic tailoring of the supercurrent in quantum point contact ballistic Josephson junctions is demonstrated. An etched InAs-based heterostructure is laterally contacted to superconducting niobium leads, and the existence of two etched side gates permits, in combination with the application of a perpendicular magnetic field, continuous modification of the magnetic interference pattern by depleting the weak link. For wider junctions the supercurrent presents a Fraunhofer-like interference pattern with periodicity $h/2e$, whereas by shrinking electrostatically the weak link, the periodicity evolves continuously to a monotonic decay. These devices represent tunable structures that might lead to the study of the elusive Majorana fermions.

Magnetic interference patterns in long disordered Josephson junctions

We study a diffusive superconductor - normal metal - superconductor (SNS) junction in an external magnetic field. In the limit of a long junction, we find that the form of the dependence of the Josephson current on the field and on the length of the junction depends on the ratio between the junction width and the length associated with the magnetic field. A certain critical ratio between these two length scales separates two different regimes. In narrow junctions, the critical current exhibits a pure decay as a function of the junction length or of the magnetic field. In wide junctions, the critical current exhibits damped oscillations as a function of the same parameters. This damped oscillating behavior differs from the Fraunhofer pattern typical for short or tunnel junctions. In wide and long junctions, superconducting pair correlations and supercurrent are localized along the edges of the junction.

Non-Fraunhofer patterns of the anharmonic Josephson current influenced by strong interfacial pair breaking

In the junctions with a strong Josephson coupling and a pronounced interfacial pair breaking, the magnetic interference patterns of the Josephson current are shown to differ substantially from the standard Fraunhofer shape. The Fraunhofer pattern occurs, when Josephson couplings are weak. The narrow peak of the critical current, centered at the zero magnetic field, and the suppressed hills at finite field values are the characteristic features of the non-Fraunhofer magnetic field modulation of the critical current, obtained in this paper.

Magnetic interference pattern in planar SNS Josephson junctions

We study the Josephson current through a ballistic normal metal layer of thickness $D$, on which two superconducting electrodes are deposited within a distance $L$ of each other. In the presence of an (in-layer) magnetic field, we find that the oscillations of the critical current ${I}_{c}(\ensuremath{\Phi})$ with the magnetic flux $\ensuremath{\Phi}$ are significantly different from an ordinary magnetic interference pattern. Depending on the ratio $L∕D$ and temperature, ${I}_{c}(\ensuremath{\Phi})$ oscillations can have a period smaller than flux quantum ${\ensuremath{\Phi}}_{0}$, nonzero minima, and damping rate much smaller than $1∕\ensuremath{\Phi}$. A similar anomalous magnetic interference pattern was recently observed experimentally.

Magnetic Interference Patterns and Vortices in Diffusive SNS Junctions

We study theoretically the electronic and transport properties of a diffusive superconductor-normal metal-superconductor junction in the presence of a perpendicular magnetic field. We show that the field dependence of the critical current crosses over from the well-known Fraunhofer pattern in wide junctions to a monotonic decay when the width of the normal wire is smaller than the magnetic length xi(H)=square root Phi(0)/H, where H is the magnetic field and Phi(0) the flux quantum. We demonstrate that this behavior is a direct consequence of the magnetic vortex structure appearing in the normal region and predict how this structure is manifested in the local density of states.

Helical Vortex Phase in the NoncentrosymmetricCePt3Si

We consider the role of magnetic fields on the broken inversion superconductor CePt3Si. We show that the upper critical field for a field along the c axis exhibits a much weaker paramagnetic effect than for a field applied perpendicular to the c axis. The in-plane paramagnetic effect is strongly reduced by the appearance of helical structure in the order parameter. We find that, to get good agreement between theory and recent experimental measurements of H(c2), this helical structure is required. We propose a Josephson junction experiment that can be used to detect this helical order. In particular, we predict that the Josephson current will exhibit a magnetic interference pattern for a magnetic field applied perpendicular to the junction normal. We also discuss unusual magnetic effects associated with the helical order.

Theory of anomalous magnetic interference pattern in mesoscopic superconducting/normal/superconducting Josephson junctions

The magnetic interference pattern in mesoscopic SNS Josephson junctions is sensitive to the scattering in the normal part of the system. In this paper we investigate it, generalizing Ishii's formula for current-phase dependence to the case of normal scattering at NS boundaries in an SNS junction of finite width. The resulting flattening of the first diffraction peak is consistent with experimental data for S-2DEG-S mesoscopic junctions.

Charge transport across 45° asymmetrical grain boundary fabricated in YBa 2Cu 3O 7− x films grown by the liquid phase epitaxy

We report on the electrical transport properties of 45° asymmetrical grain boundaries (GB's) fabricated in YBa 2Cu 3O 7− x films grown by the liquid phase epitaxy (LPE). In total, about 15 samples have been studied. Similar to previous results obtained on bicrystals grown by various physical deposition (PVD) methods we found strong scattering of zero magnetic field critical current density. In striking contrast to PVD grown bicrystals selected LPE grown bicrystals demonstrate regular magnetic interference patterns suggesting better quality of the GB in LPE bicrystals compared to PVD samples.

Transport properties of bicrystal Josephson junctions in Y-Ba-Cu-O films grown by liquid phase epitaxy

We studied charge transport across 24/spl deg/, 36/spl deg/, 45/spl deg/ symmetrical and 45/spl deg/ asymmetrical grain boundaries (GB's) in YBCO bicrystals grown by liquid phase epitaxy (LPE). We show that transport properties of symmetrical GB's are similar to those in bicrystals formed by various physical vapour deposition (PVD) methods while for 45/spl deg/ asymmetrical GB's, a difference between transport properties of LPE and PVD bicrystals has been found. In particular, in contrast to PVD bicrystals, selected LPE samples demonstrate regular magnetic interference patterns. In an agreement with transmission electron microscopy data, this result suggests better quality of 45/spl deg/ asymmetrical GB's in LPE films.

Critical currents in Josephson junctions with d+i s symmetry

The magnetic interference pattern and the spontaneous flux in unconventional Josephson junctions of superconductors with d+i s symmetry are calculated for different reduced junction lengths. The asymmetry in the field-modulated diffraction pattern exists for lengths as long as L=10 λ J. This is a time-reversal broken symmetry state. We present the evolution of the overlap critical current as a function of the crystal orientation for the fractional vortex and antivortex that are spontaneously formed near the junction center.

Magnetic interference patterns in Josephson junctions withd+issymmetry

The magnetic interference pattern and the spontaneous flux in unconventional Josephson junctions of superconductors with $d+is$ symmetry are calculated for different reduced junction lengths and the relative factor of the d- and s-wave components. This is a time-reversal broken symmetry state. We study the stability of the fractional vortex and antivortex which are spontaneously formed and examine their evolution as we change the length and the relative factor of d- and s-wave components. Asymmetry in the field-modulated diffraction pattern exists for lengths as long as $L=10{\ensuremath{\lambda}}_{J}.$

Coherent transport and nonlocality in mesoscopic SNS junctions: anomalous magnetic interference patterns

We show that in ballistic mesoscopic SNS junctions the period of critical current versus magnetic flux dependence (magnetic interference pattern), Ic(Φ), changes continuously and nonmonotonically from Φ0to 2 Φ0as the length-to-width ratio of the junction grows, or temperature drops. In diffusive mesoscopic junctions the change is even more drastic, with the first zero of Ic(Φ) appearing at 3 Φ0. The effect is a manifestation of nonlocal relation between the supercurrent density and superfluid velocity in the normal part of the system, with the characteristic scale ξT=ℏvF/2 πkBT(ballistic limit) orξT=ℏD/2 πkBT(diffusive limit), the normal metal coherence length, and arises due to restriction of the quasiparticle phase space near the lateral boundaries of the junction. It explains the 2 Φ0-periodicity recently observed by Heida et al. [Phys. Rev. B57, R5618 (1998)]. We obtained explicit analytical expressions for the magnetic interference pattern for a junction with an arbitrary length-to-width ratio. Experiments are proposed to directly observe the Φ0→ 2 Φ0- and Φ0→ 3 Φ0-transitions.

Asymmetric Magnetic Interference Patterns in 0-πJosephson Junctions

We examine the magnetic interference patterns of Josephson junctions with a region of 0 and of $\ensuremath{\pi}$ phase shift. Such junctions have recently been realized as $c$-axis YBCO-Pb junctions with a single twin boundary in YBCO. We show that in general the junction generates self-fields which introduces an asymmetry in the critical current under reversal of the magnetic field. Numerical calculations of these asymmetries indicate that they account well for unexplained features observed in single twin boundary junctions.