Supercurrent structures utilizing mobil flux vortices

[57] ABSTRACT

A supercurrent logic structure of extended dimensions is capable of sustaining a plurality of trapped magnetic field vortices each of which supports one flux quantum. Such a vortex prefers to position itself in a region such that a local minimum of the sum of the magnetic energy plus the Josephson coupling energy is established. A variety of ways to create such preferred regions are disclosed. A vortex is moved from one such region to another in shift register fashion by applying a force thereto as, for example, by applying a local current or magnetic field near to the vortex.

Claims, 16 Drawing Figures

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PATENTED JUL 111972

3,676,718

SHEET 1 OF 4

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T. A. FULTON

ATTORNEY

PATENTED JUL 111972

3,676.718

SHEET 2 OF 4

FIG. 4A

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x

FIG. 4C

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PATENTED JUL 111972

3,676,718

SHEET 3 OF 4

FIG. 6

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PATENTED JUL 1T1972

3.676.718

SHEET U Of 4

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FIG. JOB

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3,676,718

SUPERCURRENT STRUCTURES UTILIZING MOBIL FLUX VORTICES

BACKGROUND OF THE INVENTION

This invention relates to weak-link supercurrent structures ⁵and, more particularly, to such structures capable of sustaining trapped magnetic field vortices.

In the early stages of the superconductive art the basic switching device was the classical cryotron a current controlled device capable of being switched between a supercon- ⁰ducting state and a normal conducting state. As the art progressed, more sophisticated switches such as the Josephson junction were developed. The Josephson junction, as well as the now well known SNS, point contact and bridge configura- j 5 tions, are characterized by the ability to sustain a supercurrent at zero voltage up to a certain maximum critical current J_r, and by a “normal” superconducting state at a finite voltage. Such devices are now described as “weak-link” devices. Switching between these states is typically effected by varying 20 an applied current above and below J_c or by fixing the applied current and varying a magnetic field which in turn changes J_c. The basic Josephson junction and its aforementioned properties are described in U.S. Pat. No. 3,281,609 issued to J. M. Rowell on Oct. 25, 1966 and assigned to the assignee hereof. 25 Improved forms of weak-link devices are disclosed in U.S. Pat.

No. 3,564,351 issued to D. E. McCumber on Feb. 16, 1971, also assigned to the assignee hereof. In addition, the superconductive totalizer or analog-to-digital converter disclosed in U.S. Pat. No. 3,450,735 issued on July 29, 1969 to M. D. Fiske is exemplary of the prior supercurrent art in which binary information is represented by a Josephson junction being in either its supercurrent-zero voltage state or its “normal” superconducting-finite voltage state.

It is an object of our invention, however, to represent logic information in a plurality of coupled weak-link devices, or in a plurality of coupled weak-link regions of an extended single junction device, which during operation remain in a supercur rent state.

4u

It is another object of our invention to represent such information by a plurality of trapped magnetic vortices capable of being controllably created or annihilated at preferred locations in a logic device.

It is another object of our invention to controllably move 45 such vortices in shift register fashion from one such preferred location to another.

SUMMARY OF THE INVENTION

These and other objects are accomplished in an illustrative embodiment of our invention, a weak-link supercurrent logic structure which is able to sustain one or more trapped magnetic field vortices. In an extended Josephson junction device which is large compared to the Josephson penetration depth (' Aj), such a vortex is induced by a spatial variation of the supercurrent J(x) in which a positive supercurrent flows through the oxide layer and into the contiguous superconductor to a depth A_t, the London penetration depth, then along the superconductor a distance of about 2λ₇, thence through the oxide again as a negative supercurrent into the opposite superconductor to a depth λ_£ and finally back to the point of beginning. Such a vortex supports a net magnetic flux of precisely Φ„ = 2.07 x IO¹⁵ Wb, the well-known flux quantum. Hereinafter, the term “vortex” shall define an entity which includes both the circulating supercurrent J(x) and the flux quantum Φ„ induced thereby.

Once a vortex is created it prefers to position and distribute itself in a region so that a local minimum of the sum of the magnetic energy plus the Josephson coupling energy is 70 established. Where a plurality of such preferred locations are present in a single weak-link structure, it is possible to move the vortex from one such location to another by applying a force thereto as, for example, by applying a local current or magnetic field to a region near to the vortex. 75

A number of ways are hereinafter described to create such preferred locations including, for example: (1) creating regions in the structure at which J_c(x) = 0, e.g., by intentionally fabricating the oxide with gaps in it, thereby forming a structure having periodic oxide regions; a similar structure may also be fabricated utilizing discrete isolated junctions connected in parallel; (2) fabricating the oxide of a variable thickness to create regions of variable J_c(x) in a fashion similar to (1) above; (3) applying a local point source of magnetic field at periodic locations along the oxide layer; (4) applying a local current at periodic locations along the oxide layer to create a local magnetic field analogous to (3) above; and (5) fabricating the structure such that it has a variable’ self-inductance per unit length, e.g., in top view the width of the device undulates in a prescribed manner such that a vortex prefers to position itself about a region of minimum width.

In a similar fashion vortices and preferred locations can be created in other types of weak-link structures. As used herein, the term “weak-link structure” includes, but is not limited to, not only a structure having a single uniform weak-link region (e.g., structures (3), (4) and (5) supra) but also a structure having a plurality of smaller separated weak-link regions connected in parallel e.g., structures (1) and (2) supra).

BRIEF DESCRIPTION OF THE DRAWING

These and other objects of the invention, together with its various features and advantages, can be more easily understood from the following more detailed description taken in conjunction with the accompanying drawing, in which:

FIG. 1 is an end view of a typical Josephson junction;

FIG. 2, Parts A - E, indicate the gradual change in supercurrent spatial distribution as applied current is increased;

FIG. 3A shows schematically a trapped vortex having a supercurrent J(x) and a magnetic field B;

FIGS. 3B and 3C are graphs of the approximate distribution of vortex magnetic field in the junction of the devices of FIG.

FIGS. 4A-4C are end views of a Josephson junction structure in accordance with an illustrative embodiment of our invention in which a hole in the oxide creates a region where J_c

FIG. 5 is an isometric view of a second embodiment of our invention utilizing discrete Josephson junctions;

FIG. 6 is an end view of a third embodiment of our invention in which the oxide layer is of variable thickness;

FIG. 7A is an end view of a fourth embodiment of our invention utilizing point sources of magnetic field to create preferred vortex locations;

FIG. 7B is an en view of a fifth embodiment of our invention in which preferred locations are made to propagate;

FIG. 8 is an end view of a sixth embodiment of our invention utilizing current sources to create preferred vortex locations;

FIG. 9 is an isometric view of a seventh embodiment of our invention utilizing variable self-inductance to create preferred vortex locations;

FIG. 10A is a top view of a working example of our invention utilizing a pair of the devices of FIG. 5 connected in parallel; and

FIG. 10B is a schematic of FIG. 10A.

DETAILED DESCRIPTION

Before discussing in detail the various embodiments of our invention, it will be helpful to consider the spatial buildup of supercurrent in an SIS Josephson junction and the subsequent creation of a trapped magnetic field vortex. An SIS Josephson junction is depicted for the purposes of illustration only, it being understood that the following comments apply equally as well to other types of weak-link structures.

Turning then to fig. 1, there is shown an end view of an elongated Josephson junction structure 10 of length Ζ»λ₇, the Josephson penetration depth. The structure 10 is multilayered including an oxide layer 12 (e.g., PbO) formed between a pair

3,676,718 of superconductive layers 14 and 16 (e.g., Pb). A current source 18 is connected across the superconductors at he lefthand edge 19.

As the current from source 18 is increased, the supercurrent J(x) penetrates farther and farther into the device from left to 5 right until at some current 7 = /,, as shown in FIG. 2, Part A, the maximum supercurrent is at the left-hand edge (x = 0) and the distribution JJx) gradually decreases to zero at a distance Kj from the left-hand edge. Note that in FIG. 1, as well as in embodiments to be subsequently described, the supercurrent

The first term on the right-hand side of Equation (1) is £_m and the second is E₇, where μ₀ is the permeability of free space, B is the total magnetic field equal to B_r+ B_c, where is the magnetic field other than that of the vortex and B_v is the magnetic field associated with the vortex; V is volume, Φ„ is the flux quantum; J_c(x,y) is the critical supercurrent density in the junction (x,y) plane; and 4&gt;(x,y) is the spatially dependent phase difference between the wave-functions in the superconductors on either side of the junction.

In effect, a vortex “seeks out” regions in which this minimization can be accomplished. Once located in such region, a vortex will remain there until a force is applied to the vortex as described hereinafter.

is shown on the end face for the purpose of clarity only. In practice, the supercurrent would be interior to the device and generally located opposite the contacts of source 18. As the

Consequently, it is desirable to construct a device so that ³ vortices can distribute themselves to minimize E„ and/or to maximize E, (since its contribution to E is negative). Of course, trade-offs may be required since in a particular structure the position of a vortex in a particular region may, for ex20 ample, both decrease E_m and decrease Ej or conversely may both increase Ej and increase E„. In the latter cases, therefore, the relative magnitude of changes should be considered. Utilizing the above criteria, we have determined that preferred vortex locations may be created in a number of illus25 trative ways, to wit:

A. by fabricating a weak-link structure with one or more regions where J_c = 0, as by the use of discrete Josephson junctions;

B. by fabricating an oxide layer of a Josephson junction, for 30 example, to have a thickness which varies in the z-dimension along the layer;

C. by utilizing a uniform junction and point sources of magnetic field placed at periodic points along the junction to establish a field in opposition to B_r;

D. by utilizing locally applied currents to establish the field of (C) above;

E. by fabricating the weak-link structure to have a variable self-inductance per unit length.

Before describing each of the foregoing illustrative embodi40 ments, however, the determination of the separation between preferred locations will be discussed.

current is increased further, the point of maximum J(x) moves away from the left-hand edge and to the right, as shown in FIG. 2, Parts B and C. In fact, at I &gt; I₃ the supercurrent flows across the junction in both directions as represented by the positive and negative values of J₄(x) in FIG. 2, Part D.

At this point it should be noted that the spatial supercurrent distributions Λ(χ) to J₄(x) are fixed in space. At a current 1 = I_t &gt; If (FIG. 2, Part E), however, a limit is reached where the supercurrent distribution cannot adjust itself to carry additional current. Consequently, an incipient vortex is formed which propagates to the right at a velocity, and to a distance, determined by damping processes (e.g., single particle tunneling). Simultaneously, another vortex begins to form at the lefthand edge as described with reference to FIG. 2, Parts A - D. The process is repeated until other factors intervene, e.g., the applied current is reduced or a propagating vortex stops at a preferred location somewhere between the left and right-hand edges. Techniques for creating such preferred locations will be discussed hereinafter.

A schematic of an isolated vortex is shown in FIG. 3A, where it has been assumed that the vortex is stationary at some arbitrary preferred location designated 20. From point 20 where J(x) = 0 the supercurrent increases (positively and negatively) on either side thereof to a distance (typically about 100 μ. in SIS devices, but typically considerably shorter in SNS and other weak-link devices) so that the total length of the spatial distribution of J(x) extends over a length of about

2Xj. This current tunnels from one superconductor to the other through the oxide layer penetrating to a depth k_L, the London penetration depth (typically about 0.1 μ. is SIS devices). As shown, the lateral skin current flows in each superconductor parallel to the oxide layer 12 but in opposite directions thus forming a closed supercurrent loop centered at point 20. This current supports precisely one magnetic flux quantum Φ„ = 2.07 X 10~¹⁵ Wb which extends through the Oxide layer from one end face 19 to the other (not shown) closing upon itself through space. The magnetic field B_r associated with the vortex is related to Φ„ by the well-known relation that

Φο= J B„(x, y) dA, where A is the area bounded by J(x). For simplicity only, B_c is shown in FIG. 3A as consisting of a single closed flux line. In actuality, in the x-direction along the junction, B_v(x) is approximately Gaussian in shape as shown in FIG. 3B, whereas in the z-direction across the junction, B,.(z) is uniform in the oxide and decays exponentially to a distance of about K_L as shown in FIG. 3C.

A vortex once created as previously described will prefer to position and distribute itself in a region such that a local minimum (not necessarily an absolute minimum) of the sum E of the magnetic energy E_m plus the Josephson coupling energy Ej is created, i.e., a minimum of E=E_m + Ej given by 70

PREFERRED LOCATION SPACING ₄₅ In a uniform extended junction (e.g., FIGS. 3A, 7A, 8) in ⁰ order to support flux vortices the appropriate separation of adjacent preferred locations is about 2Kj. On the other hand, in a nonuniform junction (e.g., FIGS. 4C, 5, 6) the appropriate separation S is determined as follows: given an ex50 tended structure having arbitrary spacing S between tentatively selected preferred locations, but otherwise having a fixed geometry, one can readily calculate numerically in a wellknown fashion the extent and precise form of a supercurrent distribution J(x,y) which will support a single quantum of flux

Φ»; i-β., the form of a vortex in such a structure can be determined. This calculation is performed by utilizing Josephson’s equations (see, for example, Physical Review, 41, 2,047 (1970) by C. S. Owen and D. J. Scalapino), as they relate the spatial variation of φ(χ,γ) to magnetic fields, in conjunction ^w&gt;th Maxwell’s equations relating the supercurrent flow to the magnetic field distribution.

Having thus chosen an arbitrary S and calculated the vortex shape, one compares the two. If the vortex dimension in the xdirection is substantially larger than the spacing S, the calculation is iterated for a smaller S until a value of S is determined which is substantially equal to the vortex dimension in the xdirection. Conversely, if a value S were initially chosen to be too large, it is possible that more than one vortex could exist within a region of length S, a possibility which can readily be checked by numerical calculation. If so, a smaller S should be chosen until, again, it matches the vortex dimension in the xdirection. Precise equality is not, however, required as long as r Φο f S is chosen to confine a single vortex.

E= I pJFdV—— I J_c (x, y) ^cos &lt;Ρ(χ&gt; y) dxdy. To a first approximation, the preceding criterion is

J an space 2π J plane or junction 75 equivalent to satisfying the relationship

3,676,718 (e.g., negative contribu- 30 0). One way of effecting this

LI_c = &lt;b„ (2) where L is the self-inductance of a typical supercurrent loop which supports a single flux quantum Φ_ο and I_e is the net critical current of a region of the device of length S.

EMBODIMENT A: REGIONS WHERE J_c=0

One way to create a region where J_c = 0 is to form the oxide layer 12, as shown in FIG. 4A, with a hole 22 therein extending between the superconductors. Accordingly, the supercurrent J(x) centers itself on the hole with current flowing in opposite directions on either side thereof. The flux Φ_ο (not shown) is directed into the page and is substantially confined in the hole 22.

To appreciate qualitatively the reason that the vortex prefers to “sit” on the hole it must be recognized that the right hand term (Ej) of Equation (1) would be a maximum if cos φ equaled unity (φ = 0, 2ττ) everywhere in the junction. However, the presence of a magnetic field B(y) in the y-direction, for example, either from an external source or the vortex it- 20 self, causes φ to vary spatially in the Λ-direction because the derivative άφ/dx is proportional to B(y). Consequently, the presence of a vortex alone dictates that φ cannot be zero everywhere in the x-dimension. In fact, with reference again to FIG. 3A, cos φ = 1 at points 21 and 23, the extreme edges of 25 J(x) and cos φ = —1 at the center 20. At intermediate points cos φ takes on values between +1 and —1. Since φ varies with x, it follows that cos φ does also. To increase Ej it would be desirable to reduce the contribution of the regions corresponding to values of cos φ tions of regions where cos φ result is to locate the center of the vortex at a point where J_e = 0 since Ej involves the product of J_c(x,y)cos φ (x,y). Consequently, the negative contributions to Ej are eliminated, Ej is increased and, as desired, E is decreased.

Consider now that the hole is made wider as shown at 24 in FIG. 4B. Since no supercurrent can flow in the hole, the distribution J(x) accommodates the hole by increasing its density in the extreme regions at 26 and 28. Note that the device of FIG. 4B is beginning to resemble two discrete junctions, one on either side the hole 24. Ultimately, as shown in FIG. 4C, a structure having a plurality of such holes 24 between discrete oxide regions 30 will support a plurality of vortices, one centered on each hole. As discussed previously, the oxide regions are separated by a distance S calculated to satisfy equation (2). Therefore, a single flux quantum is induced by each supercurrent loop 32 flowing between adjacent oxide regions 30. Note also that supercurrent from adjacent vortices may flow through a common junction in opposite directions, thereby producing substantially total cancellation of the supercurrent therein. Thus, adjacent loops 32.1 and 32.2 flow through common junction 30.2 producing substantially total cancellation. The loop, therefore, in effect extends between junctions 30.1 and 30.3 and supports two vortices, one centered at point 24.1 and one at point 24.2.

Instead of utilizing holes in an otherwise uniform junction structure to create preferred vortex locations, it is possible as shown in FIG. 5 to utilize a discrete junction configuration which satisfies Equation (2). In this case the “hole” is created by fabricating a U-shaped superconductor 40 on the end portions of which are formed discrete oxide layers 42 and 44. Subsequently superconductor 46 is deposited to join the oxide layers, thereby forming a pair of Josephson SIS junctions electrically connected in parallel. Current source 48 causes a supercurrent J(x) to flow in path shown by the dashed line. This supercurrent supports a magnetic field B_v which threads the hole 50 formed by U-shaped superconductor 40 and superconductor 46. The use of this type of device in a shift register will be described hereinafter with reference to FIGS. 10A and 10B.

EMBODIMENT B: VARIABLE INSULATOR THICKNESS

Recognizing that thick insulator regions (e.g., about 20 A. thick) also produce regions where J_e = 0 (since electron pair tunneling is effectively prevented), it follows that a structure such as shown in FIG. 6 will support a plurality of trapped vortices. More specifically, an insulator, such as oxide layer 12, is fabricated with a plurality of thin oxide regions 62, each capable of carrying a supercurrent, separated from one another by thick oxide regions 60 in each of which J_e = 0. As before the thin oxide regions 62 are spaced from one another by a distance S calculated to satisfy Equation (2). Accordingly, a single vortex prefers to center itself On a thick oxide region 60 with the supercurrent J(x) flowing through adjacent thin oxide regions (i.e., the operative junctions).

EMBODIMENT C: POINT SOURCES OF MAGNETIC FIELD

In FIG. 7A there is shown a cross-sectional view of a twostage Josephson shift register in accordance with an illustrative embodiment of our invention in which a substantially uniform oxide layer 59 is sandwiched between a pair of elongated superconductive layers 63 and 64. Vortices are created by means of current source 61 connected across the superconductors 62 and 64 at the left-hand edge 57. Illustratively, a pair of preferred vortex locations 66 and 68 are established by directing at each of these locations an external magnetic field B„₍ generated by point sources 70 and 72. The magnetic sense of B_exl is made to be opposite of that of B_v thereby reducing the total field B = B_elt + B_e. Since E_m is thereby reduced, vortices distribute themselves around points 66 and 68 so that local minima of Equation (1) are created. Since FIG. 7A depicts a uniform junction, joints 66 and 68 are separated by about 2\j to satisfy Equation (2).

In order to cause the vortices to propagate to the right, a current source 74 is selectively connectable by means 52, switches 75 and 77 to points 52 and 54 intermediate each vortex location. With switch 77 closed a current I₂ flows across the junction in a region adjacent to the right-hand side of supercurrent loop J₂(x). The current I₂ flows in the same direction as J₂(x) does in region 69. As a result, J₂(x) will shift to the right (toward I₂). At the extreme right-hand end the vortex is detected by utilization device 76, typically a weaklink double junction magnetometer, (or alternatively a voltmeter) connected across the right-hand end of superconductors 63 and 64. Note that both vortices may be moved 45 together by closing switches 75 and 77 simultaneously. In addition, adjacent vortices can be moved simultaneously if /, is sufficiently large (thus J, “pushes” J₂ to the right). Care should be exercised, however, since too much control current I, may drive the junctions into a finite-voltage state. 50 Moreover, whereas control current flows between preferred vortex locations, as at point „ it should be made to flow much nearer to the preferred vortex location it is designated to control than to the adjacent vortex location, e.g., since /, is designated to control J,, point 52 should be closer to vortex lo55 cation 66 than location 68.

A similar embodiment is shown in FIG. 7B. The sequential application of point sources of magnetic field generated by control sources M1-M3, ΜΓ-Μ3' and Ml'’-M3, causes the preferred vortex locations, and thus the vortices themselves to propagate. For example, with only M1-M3 ON, the preferred locations are designated by an x at locations P1-P3, respectively. If now ΜΓ-Μ3' are also turned ON (and then M1-M3 turned OFF), the preferred location moves to the right to in¢5 termediate positions Pl'-P3'. Consequently, vortices originally centered at P1-P3 move to Pl'-P3', respectively. Similarly, activation of Ml-M3'' causes vortices to move to the left to Pl-P3'', respectively. This form of control can be applied equally as well to the other embodiments of our inven7θ tion.

EMBODIMENT D: CURRENT SOURCES TO GENERATE

As discussed above with reference to Embodiment C, FIG. 75 7A, point sources of magnetic field B_exl applied at periodic io3,676,718

Since Equation (2) dictates that ΕΙ=Φ_α, s to a first approximation is given by cations along the oxide layer define preferred vortex locations provided the sense of B_ert is opposite to that of B_e in the oxide. In FIG. 8, the point sources 70 and 72 of FIG. 7A have been replaced by local current sources 80 and 82, respectively. The resultant current flow in oxide layer 59 from sources 80 and 82 generates at each preferred location a local magnetic field B„,. Tee operation and structure of this embodiment are otherwise identical to that of FIG. 7A. In addition, however, an alternate form of vortex source means is shown. Current source 61, instead of being connected across superconductors 63 and 64, is connected across an inductor 65 which is positioned to produce a magnetic field at point 66 near to the lefthand end and in the plane of the junction. This field in turn induces a circulating supercurrent J(x). Either of these source means may be used interchangeably with each ofthe embodiments of our invention.

EMBODIMENT E: VARIABLE SELF-INDUCTANCE

In FIG. 9 there is shown an illustrative embodiment of our 20 invention comprising a first portion 84, where J_c(x,y) is uniform and nonzero, and a second laterally contiguous portion 86 where J_r(x,y) = 0 and the self-inductance per unit length is variable. The self-inductance per unit length L(x) of the combined portions is therefore also variable.

More specifically, portion 84 illustratively comprises a uniform Josephson junction having an oxide layer 91.1 of uniform thickness sandwiched between superconductive layers 93.1 and 95.1. Portion 86 is similarly constructed except that oxide layer 91.2 is thicker in order that J_c be made zero therein. In addition, the width of portion 86 is made variable as measured in a direction (y-axis) normal to the direction of vortex propagation (x-axis). To produce a variable L(x) at least one edge 90 parallel to the direction of propagation is made to have an undulating, preferably periodic, shape. As shown in FIG. 9, edge 90 illustratively has a square wave shape. A current source 92 connected across superconductors 93.1 and 95.1 creates a supercurrent flow across the junction and generates trapped vortices as previ- ‘ ously described. These vortices prefer to position themselves at points 96 of minimum width (i.e., in the notches). As before, current from control source 94 is applied to regions 89 intermediate preferred vortex locations 96 to shift the vortices to the right, selectively or simultaneously, depending on the manner in which switches 87 are closed. Of course, the device of FIG. 9 may also be symmetrical by fabricating on one end face 88, a structure which is a substantial mirror image of portion 86.

In order for this embodiment to operate effectively in trapping vortices in the notches 90.2, it is important that the notch separation s be properly chosen. In devices in which the undulations take on complicated shapes, a proper s would be calculated by numerical analysis to satisfy Equation (2). However, the embodiment of FIG. 9 utilizes a simplified undulating shape, a square wave, in which the maximum width (y-dimension) is 2m·, the minimum width (in a notch 90.2) is h·, the width of a notch is r and the notches are separated from one another by a distance r. In this structure the self-inductance 60 per unit length L in the notches 90.2 is given by

L Mo (2λ_Δ 4~d)/w (J) where μ_ο is the permeability of free space, K_L is the London penetration depth and d is the oxide thickness in portion 86. In « the wide sections 90.1 the inductance per unit length is onehalf Equation (3).

When j is properly chosen, a vortex will position itself in the center of a notch 90.2 and extend on either side thereof. The supercurrent flow I of the vortex is, with a factor of about 2, 70 equal to (the approximation arises because ψ(χ,γ) depends on position in the notch so that sin φ * 1 in the entire notch).

Moreover, the supercurrents on the average will circulate around a loop of approximately length r centered in a notch so that the loop inductance is approximately μ„(2λ_Δ + d)s/w. 75 s=(\'²\Jcfio (2λ/, + d)/

That the vortices prefer to sit in the notches, which are points of high self-inductance per unit length, can be understood by reference to the E_mterrn of Equation (1). More specifically, the magnetic field of the vortex, which is mainly concentrated in a notch, has a value B,. = μ₀Ι/π, where μ„ is the permeability of free space, I is the supercurrent associated with the vortex and »· is the width of the structure in a notch. Since w is smaller in a notch, B, is larger thereby disadvantageously increasing the value of B² in the Em term However, the spatial extent of the vortex in the x-direction is smaller in a notch which more than compensates for the larger B² contribution. Another way of viewing this principle is to recognize that the magnetic energy Em is approximately equal to Φ_ο I. In the notches a higher self-inductance prevails so that the current I required to support Φ„ is smaller.

EXAMPLE

A two-loop, three-junction shift register 100 as shown in FIG. 10A has been successfully constructed and operated as follows.

On a rectangular glass substrate 102 there was evaporated a rectangular Sn film 104 filling the central portion ofthe substrate to serve as a superconducting ground plane. Both the Sn and glass were then covered with an evaporated germanium film (not shown) to electrically insulate the ground plane. The region of the ground plane forms the surface on which were evaporated the thin films which form the actual shift register.

On the ground plane 104 there was next deposited an evaporated Sn film 106 having an elongated central member 106a, three equally spaced (by a distance of about 3 mm) appendages 106 (b-d) on one side thereof, and five appendages 106 (e-i) on the other side thereof. Thereafter the surface of the Sn film 106 was oxidized in a glow discharge of oxygen Subsequently, evaporated Sn strips 107, 108 and 109 were deposited so that strip 108 coupled members 106e and 106/, strip 109 coupled members 106Λ and 106; and strip 107 coupled members 1066, 106c and 106d. Josephson junctions were thus formed at the regions of overlap between film 106 and strips 107, 108 and 109. The configuration of the junctions and the loops 113 and 114 were adapted to satisfy Equation (2). In a final evaporation, silver shunts 110, 111 and 112 were deposited in parallel with each of the junctions.

In FIG. 10B the pattern of the films 106 to 109 of FIG 10A is shown schematically. The circles E, F and G designate the three junctions which, together with the two large right-hand . loops 113 and 114 comprise a two-stage shift register (using structures of the type shown in FIG. 5). The other junctions, designated A, D, K and L comprise two separate double-junction interferometers (magnetometers) which were used to monitor the magnetic flux contained in the loops 113 and 114 of the shift register. More specifically, the junction pair A-D comprises a magnetometer to monitor loop 113 and junction pair K-L comprises a magnetometer to monitor loop 114. The two magnetometer loops are designated 115 and 116. Current leads were attached at the various numbered points number 1

In our structure the Sn films were of the order of 1,000 A. thick and the Ge film was about 10,000 A. thick. The ground plane was about 1 cm by ½ cm and the upper films 106-109 were about 0.2 mm wide and a few mm long. The dimensions otthe various loops were about 1-3 mm by 1-3 mm.

The entire structure was cooled in liquid He below the superconducting transition of Sn, and was shielded from the earth’s magnetic field by well-known mu-metal. Sn was chosen because oxidation thereof is relatively easy. In practice Pb Nb or Ta which are superconducting at 4.2° K. may also be used.

(4)

IK

3,676,718

The I-V curves of the two magnetometers were displayed on an oscilloscope by applying current and measuring voltage between leads 7 and 8 and between leads 9 and 10 for the magnetometers A-D and K-L, respectively. The critical supercurrents of these magnetometers depend upon the magnetic field linking the loops 115 and 116. Since any flux supported in, say, the register loop 113 requires a current flowing around that loop, and in particular through the portion BC, some flux from that loop will also link the A-D magnetometer loop 115. Thus, the critical supercurrent of magnetometer A-D is affected by any flux present in the register loop 113, and one may observe changes in this flux as changes in the critical supercurrent of the magnetometer.

In the structure built the self-inductance of each register loop 113 and 114 was about 2xl0-ⁿH, and of each magnetometer loop 115 and 116 about 4xlO-ⁿH. The critical supercurrents of the magnetometers were about 50 μΑ, depending on temperature and other factors. The coupling between the magnetometer loops and the register loops was about 0.2, i.e., one-fifth of the flux trapped in a register loop linked a ^0 magnetometer loop.

The critical current of each register junction E, F and G was inferred from operational behavior to be in the approximate range 100-500μΑ.

In operation, with both magnetometer 1-V curves displayed on an oscilloscope so that their critical currents could be monitored, current was passed through leads 1-2, starting with zero current and gradually increasing. At a current, typically of the order of 100-200μΑ, a sudden change in the critical current of the magnetometer A-D was noted. No corresponding change was noted in the critical current of the magnetometer 116. We concluded therefore that a flux quantum (i.e., vortex) entered the register loop 113.

A subsequent decrease of the current in leads 1-2 to zero produced no change — the flux quantum remained in the register loop 113. A negative current of sufficient magnitude, again about 100 μΑ applied to leads 1-2, however, caused the flux quantum to be annihilated in the register loop 113. A still larger negative current introduced a flux quantum of the opposite sign in loop 113. (Note that if a clockwise current can be made to give a positive flux quantum, the same size current counterclockwise will produce a negative flux quantum.)

Similarly current made to flow into lead 5 and out of lead 6 produced analogous results, i.e., a flux quantum entered the 45 register loop 114 but not the register loop 113.

When current was applied to leads 3-4, a different result was observed; namely, that a sufficiently large current caused flux to suddenly appear in both loops 113 and 114, i.e., a positive flux was placed in the upper loop 113 and negative flux in ₅₀ gions near to each'of sdd pre?ekcted7ortices and i‘ the loop 114. If there had been a positive flux quantum in the loop 114 initially, this would have cancelled out the negative flux quantum resulting from application of the current to leads 3-4. Consequently, applying current to leads 3-4 caused in effect the transfer of a flux quantum from the loop 113 to loop 55 114. Thus, a two-stage shift register was demonstrated.

In principle, if the critical currents of the register junctions are all the Same and are properly chosen, then the loops can hold only, one, zero, or minus one flux quantum. Application of larger currents to leads 1-2 than that required to produce 60 one flux quantum would have the effect of driving flux into the next loop (by “passing it along”). Illustratively, a flux quantum is transferred from one register loop to another in a time corresponding to the inverse of the Josephson plasma frequency, i.e., about 10 picoseconds.

The purpose of the silver shunts 110, 111 and 112 will now be discussed. If current is applied to, say, leads 1-2, at the moment when the flux enters the register loop 113 a voltage pulse is developed across the junction E (which is the mechanism for causing currents to flow around the loop). The existence of 70 the pulse at the same time as the current is applied to the leads 1-2 means energy is given to the circuit which is partially the Vi LF magnetic energy due to creatine a current flowing around the loop 113 and partly a charging of the junction capacitance. This latter charging causes LC oscillations which can have the effect of allowing a second flux quantum to enter loop 113 or of transferring the flux down into the adjoining loop 114. The purpose of the shunts is to damp these oscillations (by providing low resistance in parallel to the junction capacitance).

It is to be understood that the above-described arrangements are merely illustrative of the many possible specific embodiments which can be devised to represent application of the principles of the invention. Numerous and varied other arrangements can be devised in accordance with these principles by those skilled in the art without departing from the spirit and scope of the invention. More particularly while the preceding embodiments relate specifically to the propagation of vortices in one-dimension, it is possible to move such vortices in more than one dimension, e.g., in two dimensions in a plane.