Fraunhofer Interference Research Articles

Supercurrent mediated by helical edge modes in bilayer graphene

Bilayer graphene encapsulated in tungsten diselenide can host a weak topological phase with pairs of helical edge states. The electrical tunability of this phase makes it an ideal platform to investigate unique topological effects at zero magnetic field, such as topological superconductivity. Here we couple the helical edges of such a heterostructure to a superconductor. The inversion of the bulk gap accompanied by helical states near zero displacement field leads to the suppression of the critical current in a Josephson geometry. Using superconducting quantum interferometry we observe an even-odd effect in the Fraunhofer interference pattern within the inverted gap phase. We show theoretically that this effect is a direct consequence of the emergence of helical modes that connect the two edges of the sample. The absence of such an effect at high displacement field, as well as in bare bilayer graphene junctions, supports this interpretation and demonstrates the topological nature of the inverted gap.

Diagnosing flux penetration condition of the Mo/Au bilayer transition-edge sensor

The magnetic-field-dependence critical current Ic(Ha) is measured for the Mo/Au bilayer transition-edge sensors. A model based on a surface barrier delaying the first penetration of magnetic flux into a flat superconducting strip, including both the geometrical and Bean–Livingston barrier, in combination with two Josephson junction models with different characteristic lengths, is found to ubiquitously fit the Ic(Ha) curves of devices with various geometry designs. The bulk penetration depth, London depairing current density, Josephson junction critical current, self-field coupling coefficient, and conditions of the first vortex entry are investigated throughout the superconducting transition. The evidences of Josephson effect are observed in both Fraunhofer interference pattern and Shapiro steps.

Critical Current Modulation in Josephson Junctions Contacted by Redundant Vias

We study the impact of redundant via placement on Fraunhofer interference patterns in superconductor–insulator–superconductor Josephson junctions with thin counter electrodes. By varying the number and location of contact vias to the counter electrode in otherwise equivalent junctions and studying the magnetic field dependence of the critical current, we observe a variety of unconventional features in the interference patterns, including a lifting of critical current minima and differences in node positions and side lobe amplitudes. We attribute these features to local changes in the Josephson phase gradient arising from the nonuniform magnetic thickness resulting from the vias. Our findings highlight the significant role that contact vias on thin counter electrodes play in the response of Josephson junctions to applied magnetic fields.

Focused ion beam fabrication of Janus bimetallic cylinders acting as drift tube Zernike phase plates for electron microscopy

Modern nanotechnology techniques offer new opportunities for fabricating structures and devices at the micrometer and sub-micrometer level. Here, we use focused ion beam techniques to realize micrometer-sized Janus bimetallic cylinders acting as drift tube devices, which are able to impart a controlled phase shift to an electron wave. The phase shift results from the presence of contact potentials in the cylinders, in a similar manner to the electrostatic Aharonov–Bohm effect in bimetallic wires. We use electron Fraunhofer interference to demonstrate that such bimetallic structures introduce phase shifts that can be tuned to desired values by varying the dimensions of the pillars, in particular their heights. Such devices are promising for electron beam shaping and for the realization of electrostatic Zernike phase plates (i.e., devices that are able to impart a constant phase shift between an unscattered and a scattered electron wave) in electron microscopy, in particular, cryo-electron microscopy.

Dual Fraunhofer interference and charge fluctuations in long quantum phase slip wires

Charge interference (Aharonov-Casher effect) in a long superconducting quantum phase slip wire is considered, and from this the ``dual'' Fraunhofer interference effect (dual to the critical current modulation of a short Josephson junction in an external magnetic field) is derived. The device that can be used to observe this effect is proposed. Furthermore, the impact of wire inhomogeneities, charge disorder, and noise on the phase slip amplitude is investigated. Although intrinsically protected against small fluctuations, the Aharonov-Casher interference resulting from jumps of random offset charges and quasiparticles can result in significant fluctuations of the measured current-voltage characteristics of the quantum phase slip wire, similar to the effects of Joule heating when averaged out over many fluctuations. Possible ways to identify and mitigate such disorder are discussed.

Fraunhofer response and supercurrent spin switching in black phosphorus with strain and disorder

We develop theory models for both ballistic and disordered superconducting monolayer black phosphorus devices in the presence of magnetic exchange field and strain. The ballistic case is studied through a microscopic Bogoliubov-de Gennes formalism while for the disordered case we formulate a quasiclassical model. Utilizing the two models, we theoretically study the response of supercurrent to an externally applied magnetic field in two-dimensional black phosphorus Josephson junctions. Our results demonstrate that the response of the supercurrent to a perpendicular magnetic field in ballistic samples can deviate from the standard Fraunhofer interference pattern when the Fermi level and mechanical strain are varied. This finding suggests the combination of chemical potential and strain is an efficient external knob to control the current response in highly sensitive strain-effect transistors and superconducting quantum interference devices. We also study the supercurrent in a superconductor-ferromagnet-ferromagnet-superconductor junction where the magnetizations of the two adjacent magnetized regions are uniform with misaligned orientations. We show that the magnetization misalignment can control the excitation of harmonics higher than the first harmonic sin(phi) (in which phi is the phase difference between the superconductors) in supercurrent and constitutes a full spin switching current element. Finally, we discuss possible experimental implementations of our findings. We foresee our models and discussions could provide guidelines to experimentalists in designing devices and future investigations.

Supercurrent in Graphene Josephson Junctions with Narrow Trenches in the Quantum Hall Regime

ABSTRACTCoupling superconductors to quantum Hall edge states is the subject of intense investigation as part of the ongoing search for non-abelian excitations. Our group has previously observed supercurrents of hundreds of picoamperes in graphene Josephson junctions in the quantum Hall regime. One of the explanations of this phenomenon involves the coupling of an electron edge state on one side of the junction to a hole edge state on the opposite side. In our previous samples, these states are separated by several microns. Here, a narrow trench perpendicular to the contacts creates counterpropagating quantum Hall edge channels tens of nanometres from each other. Transport measurements demonstrate a change in the low-field Fraunhofer interference pattern for trench devices and show a supercurrent in both trench and reference junctions in the quantum Hall regime. The trench junctions show no enhancement of quantum Hall supercurrent and an unexpected supercurrent periodicity with applied field, suggesting the need for further optimization of device parameters.

Nb lateral Josephson junctions induced by a NiFe cross strip

We fabricated lateral junctions by crossing superconducting Nb strips in metallic contact with a ferromagnetic NiFe strip. Transport measurements on the Nb lateral junctions exhibit modulations of the critical current with a varying perpendicular magnetic field similar to a Fraunhofer interference pattern, which demonstrates the dc Josephson effect. The modulations of the critical current could be attributed to an effective weak link embedded in the Nb strip and formed a Josephson junction. Appearance of Shapiro steps on the current-voltage curves of these junctions when microwaves irradiation is applied proves the ac Josephson effect. The underlying physics of the effective weak link induced by the NiFe strip is discussed.

Nb Lateral Josephson Junction Induced by Inverse Proximity Effect With NiFe

We utilize the inverse proximity effect in superconductor-ferromagnet bilayer to generate lateral Josephson junctions. The weak link is created by a ferromagnetic NiFe strip across a superconductor Nb bridge due to the inverse proximity effect. The critical currents of the junctions were measured at different temperatures and magnetic fields. The junctions exhibit a modulation of the critical current in perpendicular magnetic field similar to a Fraunhofer interference pattern which proves the dc Josephson effect. The weak link region induced by the NiFe in Nb persists down to 2 K.

Pb–Graphene–Pb Josephson Junctions: Characterization in Magnetic Field

We fabricate superconductor-graphene-superconductor Josephson junctions with superconducting regions made of lead (Pb). The critical current through grapehene may be modulated by external magnetic field; the resulting Fraunhofer interference pattern shows several periods of oscillations, indicating that the junction is uniform. Deviations from the perfect Fraunhofer pattern are observed, and their cause is explained by a simulation that takes into account the sample design.

Influence of the domain walls on the Josephson effect in Sr2RuO4

A detailed theoretical interpretation of the Josephson interference experiment between Sr2RuO4 and Pb reported by Kidwingira et al (2006 Science 314 1267) is given. Assuming chiral p-wave pairing symmetry, a Ginzburg–Landau theory is derived in order to investigate the structure of domain walls between chiral domains. It turns out that anisotropy effects of the Fermi surface and the orientation of the domain walls are essential for their internal structure. Introducing a simple model for a Josephson junction, the effect of domain walls intersecting the interface between Sr2RuO4 and Pb is discussed. It is shown that characteristic deviations of the Fraunhofer interference pattern for the critical Josephson current as a function of the magnetic field occurs in qualitative agreement with the experimental finding. Moreover, the model is also able to account for peculiar hysteresis effects observed in the experiment.

Linear momentum quantization in periodic structures II

Fraunhofer interference of a single particle by a periodic array of scatterers, usually treated with a wave picture, can be fully explained on the basis of linear momentum quantization, as pointed out in a previous study by Van Vliet (1967) [4]. This analysis is now extended to scattering (or passing through slits) involving a finite number N of equidistantly spaced entities comprising the interferometer. The usual intensity probability distribution for W ( sin θ ) is obtained, noting that total momentum is conserved (as in the Compton effect), while the interferometer is treated as a quantum object—rather than a classical measuring apparatus, as perceived in the Copenhagen interpretation. Various aspects of the ‘orthodox view’ are examined and renounced.

Planar S-(S/F)-S Josephson junctions induced by the inverse proximity effect

We present a utilization of the inverse proximity effect in superconductor-ferromagnet (S-F) bilayer to generate lateral Josephson junctions. The weak link is created by a Pd0.95Fe0.05 strip across a Nb bridge. Close to TC and in perpendicular magnetic field the junctions exhibit a modulation of the critical current IC(B) similar to a Fraunhofer interference pattern which proves the dc Josephson effect. The structure contains three weak links (two different areas) in series which result in the observation of two periods scalable with the areas penetrated by magnetic flux. Measurements of Shapiro steps prove the presence of the ac Josephson effect.

Temporal Talbot effect in interference of matter waves from arrays of Bose–Einstein condensates and transition to Fraunhofer diffraction

We consider interference patterns produced by coherent arrays of Bose–Einstein condensates during their one-dimensional expansion. Several characteristic pattern structures are distinguished depending on value of the evolution time. Transformation of Talbot “collapse–revival” behavior to Fraunhofer interference fringes is studied in detail.

All YBa2Cu3O7−δ trilayer junctions with YBa2Cu3O7−δ wiring layers

We have fabricated all YBa2Cu3O7−δ (YBaCuO) trilayer junctions with YBaCuO wiring layers using CeO2 insulating layers. The trilayer junctions consist of YBaCuO/PrBa2Cu3O7−δ (PrBaCuO)/YBaCuO structures on (100) MgO substrate. Both YBaCuO wiring layer and base-YBaCuO electrode have the critical temperature Tc of ⩾87 K. A 5×5-μm2 junction with a PrBaCuO barrier thickness of 25 nm shows a resistively-shunted-junction (RSJ)-like current–voltage (I–V) characteristic with a critical current density Jc of 1.7×102 A/cm2 and a critical current×normal resistance (IcRn) product of 0.40 mV, and no contact resistance at 4.2 K. The magnetic field dependence of Ic for the junction shows a Fraunhofer interference pattern with a modulation period of 3.5 mT, which is in good agreement with the value estimated from the junction size of 5 μm. In addition, the YBaCuO wiring layers have no structures in the I–V characteristics due to grain–boundary junctions. These facts confirm that the observed Josephson properties come from the YBaCuO/PrBaCuO/YBaCuO trilayer structure.

Cost-effective experiments on the diffraction and interference of light

Experiments on the Fraunhofer diffraction and interference of light using computer-interfaced apparatus and data logging software are now available from suppliers of educational scientific equipment, and are a very useful tool for the teaching of these fundamental aspects of light. Clearly, however, cost imposes limits on the number of sets of apparatus which can be made available for student use. An alternative experimental arrangement is presented here, which results in a considerable cost saving by reducing the number of sensors and other apparatus required, while giving excellent quantitative results for comparison with theory.

He scattering from compact clusters and from diffusion-limited aggregates on surfaces: observable signatures of structure

The angular intensity distribution of He beams scattered from compact clusters and from diffusion limited aggregates, epitaxially grown on metal surfaces, is investigated theoretically. The purpose is two-fold: to distinguish compact cluster structures from diffusion limited aggregates, and to find observable signatures that can characterize the compact clusters at the atomic level of detail. To simplify the collision dynamics, the study is carried out in the framework of the sudden approximation, which assumes that momentum changes perpendicular to the surface are large compared with momentum transfer due to surface corrugation. The diffusion limited aggregates on which the scattering calculations were done, were generated by kinetic Monte Carlo simulations. It is demonstrated, by focusing on the example of compact Pt heptamers, that signatures of structure of compact clusters may indeed be extracted from the scattering distribution. These signatures enable both an experimental distinction between diffusion limited aggregates and compact clusters, and a determination of the cluster structure. The characteristics comprising the signatures are, to varying degrees, the rainbow, Fraunhofer, specular and constructive interference peaks, all seen in the intensity distribution. It is also shown, how the distribution of adsorbate heights above the metal surface can be obtained by an analysis of the specular peak attenuation. The results contribute to establishing He scattering as a powerful tool in the investigation of surface disorder and epitaxial growth on surfaces, alongside with STM.

Graphical representations of Fraunhofer interference and diffraction

Traditional textbook presentations of Fraunhofer interference and diffraction are usually limited to a few discrete examples of one, two, and sometimes more sources, in which the analysis yields graphs of intensity versus distance y on a screen that is at a large distance D in the x direction from the sources. This paper presents two separate sets of graphical representations that can assist students and teachers in improving their understanding of the Fraunhofer phenomena. The polar intensity plots stress the angular nature of the interference phenomena, and stress the fact that the phenomena need not be limited to a narrow angular range around the forward direction. The three-dimensional plots illustrate the unity of diffraction and interference by examining the patterns when one makes a continuous variation of the geometrical parameters that characterize the sources.

Anisotropic Josephson effect in all (103)-oriented YBa2Cu3O7−δ /PrBa2Cu3O7−δ′/YBa2Cu3O7−δ junctions

We report a demonstration of the anisotropic Josephson effect in all (103)-oriented junctions consisting of YBa2Cu3O7−δ /PrBa2Cu3O7−δ′/YBa2Cu3O7−δ film sandwiches. The junction shows a resistively shunted junction-like current-voltage characteristics with hysteresis and clear Shapiro steps under the microwave radiation. Depending on the direction of external magnetic field H, the junction exhibits anisotropic Fraunhofer interference patterns with different critical magnetic fields Hc0 and periods in the oscillation of critical current. The agreement between experimental and expected values by the Owen–Scalapino analysis for anisotropic Hc0 confirms that this anisotropic property comes from the anisotropy in the magnetic penetration depth of (103)-oriented YBaCuO films.

Dissipation mechanism in a high-Tc granular superconductor: Applicability of a phase-slip model.

The magnetoresistance and I-V characteristics for the 110-K phase of a polycrystalline Bi-Pb-Sr-Ca-Cu-O superconductor are reported. The Josephson-junction model of Ambegaokar and Halperin fits well to the data and yields the temperature and field dependence of the phase-slip activation energy ${\mathit{U}}_{0}$. The field dependence of ${\mathit{U}}_{0}$ is explained by Fraunhofer interference under magnetic field within weak links originated from the sample microstructure. We suggest that this model may have general applicability to dissipation in both granular and single-crystal materials.