In the OSTI Collections: Josephson Junctions
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| Article Acknowledgement: Dr. William N. Watson, Physicist DOE Office of Scientific and Technical Information |
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When a steady voltage gradient is applied along an ordinary conducting wire, electrons in the wire will flow in one direction to form a direct current. The strength of the current through the wire will equal the voltage difference between the wire’s two ends divided by the wire’s resistance to current. If, instead, the gradient is alternated back and forth along opposite directions, the current also alternates back and forth. From the way in which steady and alternating gradients set up direct and alternating currents, the voltages are called DC and AC voltages.
If one sets up currents in superconducting wires instead of in ordinary ones that resist current, the supercurrents can respond to the applied voltages quite differently. In the 1960s, Brian Josephson’s mathematical analysis of superconductors[Wikipedia] led him to predict that a particular type of circuit element would behave differently from ordinary conductors in several ways. First, in a circuit element made of two superconductors separated by a thin piece of “normal” nonsuperconducing material, a supercurrent set up in the superconductors will pass from one to the other through the separator, even if the separator material usually acts as an insulating barrier against normal electric current. Second, if a DC voltage is applied along this circuit element, the supercurrent will alternate instead of flowing in just one direction, as it would in an ordinary conducting element. Third, if an AC voltage that alternates at any one of a certain set of frequencies is applied on top of the DC voltage, a direct supercurrent will flow again. All three behaviors were later observed in experiments, after which it was realized that the first behavior had already been seen in earlier experiments but misattributed to breaches in the insulator; the insulator can actually conduct supercurrent in this case without being damaged.
Like any analysis of a quantum-physical system, Josephson’s analysis of these superconductor-barrier-superconductor junctions included two features; together, these features turn out to account for the phenomena he predicted. One is the set of forces that acts on the supercurrent’s electrons. The forces in these junctions include the resistive ones of the barrier and the forces from the DC or AC voltage gradients applied across the entire junction, but they don’t include any resistive force fields in the superconducting materials, since these become ineffective when the electrons condense into the superconducting state. The other important feature is the wave nature of the electrons. If electrons were nothing more than particles that each occupied a single point, their response to a DC voltage would always be to accelerate in the direction along which the voltage changes most with distance, and they’d respond to AC voltages by equally alternating accelerations. Electron waves, like other waves, do move somewhat like particles under a particular condition: when their accelerations are so small that their velocities barely change over distances of one wavelength. But in Josephson junctions, this condition is not met, and the electron wave’s response to the applied voltage gradients is very different from that of point particles.
The behavior of Josephson junctions is not only interesting but technically useful.[Wikipedia] Investigations of Josephson junctions and their uses are being sponsored by the US Department of Energy and other organizations around the world, as can be seen from the many reports found through various DoE data collections.
The alternating current produced by applying a DC voltage across a Josephson junction has an alternation frequency that’s directly proportional to the voltage. The current’s alternation stirs up waves of the same frequency in the electromagnetic field that surrounds it. Electromagnetic waves of any frequency can thus be produced if the right voltage can be applied to the junction.
As it happens, there are many different devices that can produce electromagnetic waves of most frequencies, from radio waves through visible light to gamma rays. But devices that can produce electromagnetic waves with frequencies around one terahertz (one trillion vibrations per second, or 1 THz), which is in the low-frequency infrared, high-frequency microwave range, have not been practical and economically viable, although terahertz waves’ interactions with matter would make such sources very useful. Two recent reports among several describe the use of a particular type of Josephson junction as a source of terahertz electromagnetic waves.
One report, a patent entitled “Tunable terahertz radiation source”[DOepatents] issued to Los Alamos National Security, LLC, describes how large numbers of intrinsic Josephson junctions—that is, junctions formed in a compound by alternating plane layers of superconducting and “normal” materials rather than being fabricated separately from different materials—can, when spaced within one wavelength of each other, produce an intense terahertz wave. According to the patent,
| Whereas a single junction emits minuscule power, it has been discovered that, if many IJJs [intrinsic Josephson junctions] are co-located within a radiation wavelength, the IJJs may be synchronized in terms of the phase of their respective oscillation so that the total power emitted is proportional to the square of the number of junctions. This novel approach allows individual junctions to interact with one another so as to produce stimulated emission[Wikipedia], similar to the behavior of atomic oscillators in a laser[Wikipedia]. Under these conditions, it is possible to generate useful amounts of THz radiation on the order of milliwatts from a single stack comprising IJJs, scalable to about 1 W for an phased-array configuration of junction stacks, as opposed to <10 mW as in previous attempts. [Links added.--wnw] |
The patent focuses on a particular material, bismuth strontium calcium copper oxide[Wikipedia], that can be fabricated into stacks of suitable intrinsic Josephson junctions. A report[NLE] in Physical Review Applied, on Kyoto University researchers’ experiments with the same material connected in electrical circuits, describes details of how the distribution and strength of electric current at the connection points affects the existence and location of “hot spots” in the material, where its highest superconducting temperature is exceeded so that the junctions won’t superconduct. Such hot spots leave less of the material to function as a terahertz-wave emitter, so that the terahertz waves it radiates are less intense. The reported experiments indicate the size of the effect under various conditions.
Other reports describe the use of Josephson junctions as instruments for measuring the properties of subatomic particles.
Most of the matter in the universe has been found to be of a “dark” type, quite different from the visible kind seen with telescopes. The exact nature of this dark matter has yet to be discovered. Axions[Wikipedia], hypothetical particles whose existence is suggested (though not required) by certain features of the strong interactions among quarks and gluons[Wikipedia], have been investigated as a possible dark matter type. The known features of strong interactions imply mathematically that axions should have certain properties if they do exist. One of the mathematical implications is worked out in a report by Christian Beck of Queen Mary University of London entitled “Axion mass estimates from resonant Josephson junctions”[E-print Network], which shows that axions passing through the normal-material link between a Josephson junction’s superconductors should induce an oscillating current. The report describes optimum design conditions for Josephson junction experiments to detect axions, and notes that certain unexpected results of experiments already done for other purposes would be consistent with the existence of axions having a very small mass that’s most likely between 108 and 112 millionths of an electronvolt. For comparison, the mass of an electron, small as it is, is 511 thousand electron volts, so if the experimental results are in fact due to axions, their masses are about a fifth of a billionth of an electron mass—what a fifth of a milligram is to a ton.
While axions may or may not exist given our current evidence, the existence of neutrons has long been established. However, people have only measured neutrons’ physical properties (like everything else) to a finite precision. One of these properties is how the positive and negative electric charges of the neutron’s constituent quarks are distributed, and in particular whether the centers of the positive and negative charges’ distribution are separated. If there is any such separation, it’s known to be very small, but the known laws of particle interactions give some reasons to suspect that it might not be exactly zero.[Wikipedia] One of the numerous experiments being undertaken to measure this separation, expressed as a quantity called an electric dipole moment[Wikipedia], involves the use of devices called SQUIDs (for “superconducting quantum interference devices”)[Wikipedia], which are based on pairs of Josephson junctions connected in parallel. This experiment, to be conducted at the Spallation Neutron Source at Oak Ridge National Lab, is outlined in a Los Alamos National Lab slide presentation entitled “nEDM at SNS”[SciTech Connect]. Another set of slides, “SQUID applications in the SNS nEDM Experiment”[SciTech Connect], sketches details of the design and use of SQUIDs in the experiment, in which neutrons are to react with the nuclei of helium-3 atoms within ambient electric and magnetic fields. The SQUIDs’ role is not to measure the neutron’s electric dipole moment directly, but to measure very small magnetic fields that are related to it because of the way the experiment is set up.
Both neutrons and helium-3 atoms have magnetic fields of their own, and both also have angular momentum, or spin, around the symmetry axis of their magnetic fields. Such objects, behaving as gyroscopes, tend to be reoriented when a torque is exerted on them by an ambient magnetic field. Because of the differences in their magnetism, the reorientation rates are different for neutrons and helium-3. Any electric dipole moment in the neutron will also affect its reorientation rate if the ambient magnetic field is accompanied by an ambient electric field, with the rate being larger or smaller as the electric field has the same or opposite direction to the magnetic field, as indicated in Figure 1. Neutrons and helium-3 nuclei also tend to react with each other and turn into pairs of hydrogen nuclei—one of ordinary hydrogen and one of tritium. The reaction rate depends on how close the neutron and helium-3 spins are to having the same orientation, so in a combination of electric and magnetic fields, the neutron-helium reaction rate will increase and decrease as the two spins periodically come in and out of alignment.
The role of the SQUIDs in this experiment is to measure the magnetic field of the helium-3 atoms so the atoms’ reorientation rate can be determined. This information, combined with data on the strength and direction of the ambient electric field and on how frequently the neutron-helium reaction rate rises and falls, can be used to calculate the neutron’s electric dipole moment.
The SQUID’s sensitivity to small changes in magnetic field is directly related to its being a pair of Josephson junctions connected in parallel, through which the supercurrents in each junction act as waves. A supercurrent wave through the SQUID is split in two to pass through the two parallel junctions, and the two waves are then reunited beyond them. If the waves from the two junctions are in phase, the waves will reinforce each other and a supercurrent will pass through the SQUID. If the waves are of equal strength but completely out of phase, they will cancel each other and no current will pass. The waves’ phases will be affected by any magnetic field between the junctions, with even slight changes in the field strength producing sizeable changes in the waves’ phase difference and the resulting supercurrents. SQUID-based magnetometers are thus very sensitive and well suited for experiments in which very small differences in magnetic fields have to be distinguished.
 | Figure 1. The frequencies vn and v3 with which the orientation of neutrons and helium-3 nuclei undergo complete rotations in the presence of an ambient electric and magnetic fields E and B0 depend on the neutron and helium-3’s electric and magnetic properties, and particularly, if the neutron’s electric dipole moment dn is not zero, on whether the fields E and B0 are parallel (top) or antiparallel (bottom). The frequency with which neutrons and helium-3 nuclei cycle in and out of alignment and back is the difference vn - v3; since the rate of the reaction n + 3He $arrow ->$ p + 3H depends on this alignment, vn - v3 is also the frequency with which the reaction rate goes through a cycle of maximum to minimum to maximum again. The use of SQUIDs—circuit elements comprising pairs of Josephson junctions connected in parallel—to detect changes in the orientation of helium-3 nuclei is an important part of an experiment designed to relate the orientation to the reaction rate and so measure dn. (From “nEDM at SNS”[SciTech Connect], p. 8 of 35.)
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A common theme of the aforementioned reports is the use of Josephson junctions to perform some particular function, either affecting or being affected by their environment in certain ways. In a different kind of use, one wants to determine one or more physical properties of a certain material, and appropriate conditions for determining those properties are provided by making the material part of a Josephson junction.
Researchers at Duke University and North Carolina State University reported how they used such a method to determine thermal properties of graphene within 1 kelvin of absolute zero[Wikipedia] in the journal Physical Review Letters (“Phonon Bottleneck in Graphene-Based Josephson Junctions at Millikelvin Temperatures”[DoE PAGES]). Determining how electrons in graphene lose thermal energy by generating vibrations in the graphene’s lattice of carbon atoms is relatively easy when the graphene is part of a high-temperature electric circuit, but at low temperatures, the electrons would tend to heat the graphene’s metal contacts rather than set up lattice vibrations (phonons) in the graphene itself. The researchers suppressed this contact heating by using superconducting contacts, and found that the rate of energy transfer between electrons and phonons in the graphene is proportional to the cube of the absolute temperature, which is consistent with other measurements and with theory.
Ordinary electrical currents and supercurrents can both be described in terms of the flow of negatively charged electrons through a material. But if the set of possible electron motions in the material has certain characteristics, the currents may be more conveniently analyzed as the flow of “holes”—possible electron states that no electrons happen to be in. Holes of this type are analogous to bubbles in a liquid, which are spaces that aren’t occupied by liquid molecules. One can think of the bubbles either as empty spaces whose locations change according to how the surrounding liquid molecules accelerate due to forces applied to them, or as things in themselves that respond to the forces by being accelerated in the opposite direction. Similarly, electronic holes act like things whose acceleration by electromagnetic forces is opposite to that of the electrons, as though the holes were particles themselves that had positive charge instead of having electrons’ negative charge.
As with other superconductors, some of the supercurrent states of iron-based superconducting compounds[Wikipedia] can be most conveniently described in terms of electron motion, others in terms of hole motion. While it’s clear that holes behave like particles whose electric charge is opposite to that of electrons, it’s not so clear whether the mathematical functions that describe supercurrent waves have opposite signs for hole and electron supercurrents—different experiments have provided apparently conflicting evidence. To guide further experiments that could resolve the question, a Physical Review B paper from Argonne National Laboratory describes a theoretical analysis of Josephson junctions between a “same sign” (or “s”) superconductor and an “opposite sign” (or “s±”) superconductor if both materials were “maximally dirty”, i.e. having a maximal number of defects[Wikipedia] in their atoms’ arrangements. The analysis is reported in “Phase diagram of Josephson junction between s and s± superconductors in the dirty limit”[DoE PAGES].
As with any kind of electronic device, the predictability of a Josephson junction’s output for a given intentional input depends on how much the device is disturbed by additional influences. Predictability is particularly important for devices used to represent 1s and 0s for information processing, since such disturbances (or “noise” [Wikipedia]) can unintentionally introduce errors into a signal or calculation, changing 1s to 0s or vice versa. Predictable response is even more important for devices that use the quantum-physical properties of matter as qubits that each represent both 1 and 0 simultaneously—something that Josephson junctions’ effect on supercurrent waves give them the potential to do.
Different researchers have investigated various ways in which Josephson junctions, and electronic circuits based on them, might be affected by noise. One such investigation, by researchers at RMIT University (the Royal Melbourne Institute of Technology), is reported in “Atomic delocalisation as a microscopic origin of two-level defects in Josephson junctions”[E-print Network], which addresses how a Josephson junction might be subject to noise that’s generated, not by an outside source, but by the junction itself.
If a circuit element is made of a “dirty” material with defects in its atomic arrangement, the material itself can generate noise in the circuit. Defects resulting from impurity atoms in an otherwise orderly atomic lattice can be taken care of, as the authors indicate, by appropriate manufacturing methods or circuit designs. But defects can occur even in a pure material, if the atoms that it’s supposed to contain are irregularly spaced. The question these researchers address is whether a Josephson junction with no impurities in the composition of its barrier layer could still generate noise.
The report examines the particular case of an aluminum oxide barrier, and presents a mathematical model of two kinds of defects out of the many possible ones in its atomic arrangement. If the aluminum atoms were equally and appropriately spaced throughout, each oxygen atom would occupy a single position halfway between pairs of aluminum atoms to make a defect-free arrangement. But aluminum oxide can be amorphous, with some aluminum atoms further apart or closer together. When two aluminum atoms are too far apart, an oxygen atom between them is likely to be bound closer to one aluminum than the other. If the aluminum atoms are too close together, an intermediate oxygen will likely be equidistant from both, but off to one side or another from the straight line between the aluminums. In each of these situations, the oxygen atoms won’t just stay in one of the possible positions, but will tend to oscillate between them, at frequencies comparable to those of the circuits they are part of, and thus produce noise that could affect the circuits’ operation. Although the model presented includes just these two defect types, the aluminum oxide properties calculated from it are equivalent to those seen in experiments, thus demonstrating that such defects can arise even in pure aluminum oxide. The authors expect that more realistic models derived from “[m]ore sophisticated modeling techniques such as molecular mechanics and density functional methods” will “guide future fabrication and design of superconducting circuits, leading to lower levels of noise and greater control over their quantum properties.”
A new type of Josephson junction has been found to conduct supercurrents with a new, potentially useful property whose nature is directly related to how supercurrents form.
Electrons can move within a conducting material only in certain ways, which are determined by their interactions with each other and with the conductor’s ions[Wikipedia]. When a material becomes superconducting, the interactions apparently allow electrons to bind into pairs, which has a great deal to do with why the material loses its resistance to the flow of the electrons through it. The reason involves the spin, or angular momentum, of the electron pairs.
While individual electrons have a spin of one half unit (the unit being h $sup bar$, i.e. Planck’s constant h[Wikipedia] divided by 2pi), bound electron pairs can have a spin of either zero units or one unit. With respect to any given direction in space, a half-unit spin can have either of two possible orientations, clockwise or counterclockwise, in a plane perpendicular to that direction. A zero-unit spin has only one “orientation” along any direction, neither clockwise nor counterclockwise, while a one-unit spin has one of three basic orientations—clockwise, counterclockwise, or in a plane that includes the given direction. (An interesting quantum-physical feature of such particles is that there are no intermediate spin orientations; whatever direction one chooses, a half-unit spin can only be perpendicular to it and a one-unit spin can only be perpendicular or parallel to it. The introductions of two earlier articles in this series have briefly discussed this feature of particles’ spins[OSTI] and the related property of particles’ magnetic moments[OSTI], which are aligned parallel or antiparallel to the particles’ spin axes.)
As it turns out, the spin of any simple or composite particle affects whether or not the particle can or cannot move in the same way as another particle of the same type at the same time. If the particle’s spin is only half an h $sup bar$, it can’t. But if the spin is a whole number of units, the particle’s state of motion not only can be the same as that of other identical particles, but is most likely to be the same as others if the particles’ motion is at low enough energy. This latter situation is the case for bound pairs of electrons in superconductors. The pairs tend to get into a state in which they all move identically, with an energy so far below that of any possible motion for unbound electrons that the pairs will practically never collide energetically enough with the material’s ions to knock even one electron out of the supercurrent into a different state. Because of this, the supercurrent isn’t affected by resistive forces from the material.
Superconducting electron pairs with zero spin have been the most studied, but pairs with one unit of spin, and the corresponding triplet of basic spin orientations[Wikipedia], are found in Josephson junctions whose middle segments can exhibit ferromagnetism, the type of strong magnetism seen in iron[Wikipedia]. Electron pairs with a nonzero spin also have a nonzero magnetic moment along their spin axis. The possibility that supercurrents with particular magnetic orientations might be useful has led to ferromagnetic Josephson junctions’ being examined experimentally, as University of Cambridge researchers note in a paper published in Nature Communications. Two other papers, one by a group at Michigan State University and another by the same researchers together with colleagues at Michigan State and the National Institute of Standards and Technology (NIST), describe particular experiments that addressed how spin-triplet supercurrents depend on the area of the junction and how the strength of the current can be optimized through control of the magnetic field in the junction’s ferromagnetic section.
The Michigan State group’s experiments, reported in the Physical Review B paper “Area-dependence of spin-triplet supercurrent in ferromagnetic Josephson junctions”[DoE PAGES], showed that while the critical (maximum possible) supercurrents in their ferromagnetic junctions were directly proportional to each junction’s area once the junctions had been magnetized, whether the same proportionality existed before the junction was ever magnetized depended on whether the junction’s base was a thick layer of niobium or a thinner layer in which niobium was alternated with other materials. The thinner layers did exhibit a direct linear proportionality between critical supercurrent and junction area before being magnetized, but supercurrents in junctions based on the thicker pure-niobium layers maxed out less than linearly with area.
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| Figure 2. Atomic force microscopy pictures of base layers for Josephson junctions used in the experiments reported in “Area-dependence of spin-triplet supercurrent in ferromagnetic Josephson junctions”[DoE PAGES]. (a) A niobium base layer 150 nanometers thick. (b) A niobium-aluminum-niobium-gold multilayer stack 87.4 nanometers thick. |
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| Figure 3. Schematic diagram of Josephson junction samples described in “Optimization of Spin-Triplet Supercurrent in Ferromagnetic Josephson Junctions”[DoE PAGES]. The cobalt/ruthenium/cobalt sandwich in the middle of the junction functions as a synthetic antiferromagnet whose response to an externally applied magnetic field affects the flow of supercurrent, thus demonstrating that an external magnetic field can be used to control the amount of supercurrent in the junction. |
The combined Michigan State-NIST group and the University of Cambridge group each examined control of the triplet supercurrent in different types of Josephson junction. The Cambridge group’s paper, “Reversible control of spin-polarized supercurrents in ferromagnetic Josephson junctions”[E-print Network], shows that, in a junction whose ferromagnetic section consists of a cobalt layer sandwiched between two Permalloy layers, the size of the critical supercurrent can be controlled by the net misalignment of the different layers’ magnetic fields, and that when the magnetic fields in the Permalloy are aligned with the field in the cobalt, the supercurrent is zero. The Michigan State-NIST paper “Optimization of Spin-Triplet Supercurrent in Ferromagnetic Josephson Junctions”[DoE PAGES], published in Physical Review Letters, describes experiments on Josephson junctions with a different type of ferromagnetic sandwich made of ruthenium between two layers of cobalt. This combination served as a synthetic antiferromagnet, or material whose own magnetic fields oppose each other[Wikipedia], since the cobalt layers’ magnetic fields were locked into antiparallel directions by a strong exchange field mediated by the ruthenium. When these junctions were magnetized by applying a large ambient field,
| … contrary to expectations, the critical current, Ic, increases up to a factor of 20 relative to its value in the as-grown state. This seemingly counter-intuitive result can be understood by considering a unique property of the SAF [synthetic antiferromagnet]: when the large magnetizing field Happ is applied, the Co magnetizations ‘‘scissor’’ towards Happ. When the field is removed, the Co magnetizations relax back to directions perpendicular to Happ. This SAF ‘‘spin-flop’’ transition was predicted and first demonstrated over a decade ago … . |
The authors note that this “confirms the theoretical prediction that the spin-triplet supercurrent is maximum when the magnetizations of the adjacent ferromagnetic layers inside the junctions are aligned perpendicular to each other”.
Findings like these show that spin-triplet supercurrents can not only be made, but controlled, and suggest that even more effective ways to do both might remain to be discovered.
The interrelatedness of physical phenomena is evident from the way the research reports described in this article together mention several items that have been discussed in earlier “In the OSTI Collections” articles on quite different subjects. As mentioned above, spin angular momentum and the magnetic moments of particles were discussed in a recent article about neutrinos and a much earlier article on progress toward making quantum computers, respectively. The latter article also mentioned the use of SQUIDs to represent qubits. Devices to manipulate terahertz waves, as opposed to producing them, were discussed in an earlier article about metamaterials. Evidence for the existence for “dark matter” in the universe was described in an article about dark matter and dark energy. Other properties of neutrons besides their electric dipole moment are being examined in experiments conducted at neutron sources, as a more recent article mentioned, while graphene was the subject of the article immediately preceding it. And certain points of existing theory about how electrons become immune to resistive forces and form supercurrents were described in an article about materials that superconduct up to relatively high critical temperatures.
Wikipedia
- Josephson effect: The effect; Applications
- Stimulated emission
- Laser
- Bismuth strontium calcium copper oxide
- Axion
- Strong interaction
- Neutron electric dipole moment: Theory
- Electric dipole moment
- SQUID [superconducting quantum interference device]
- Kelvin
- Iron-based superconductor
- Crystallographic defect
- Noise (electronics)
- Ion
- Planck constant
- Triplet state
- Ferromagnetism
- Antiferromagnetism
- Los Alamos National Security, LLC
- Kyoto University [English]
- Queen Mary University of London
- Oak Ridge National Lab: Spallation Neutron Source
- Los Alamos National Laboratory
- Duke University
- North Carolina State University
- Argonne National Laboratory
- RMIT University (the Royal Melbourne Institute of Technology)
- University of Cambridge
- Michigan State University
- National Institute of Standards and Technology
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