About eight years ago a 22-year-old studentshowed his professor some calculations on quantum tunneling.

Now that professor tells us

How Josephsondiscovered his effect

Philip W. Anderson

The discovery of what we have ever 

since called the “Josephson effect” took 

 pl ace whil e I was vi si ti ng Cambri dg e,England, for a sabbatical year in 1961-

62. R ec e nt l y, wh e n I tr av e ll e d t o

Kyoto to accept the London Prize onBrian Josephson’s behalf, I put to-

gether s o m e r e m i ni s c e n ce s of t h at

 period, which may be more interestingthan a mere recapitulation of the bare

scientific facts. Lest I appear too cen-tral to this account, I should make it

clear that at least two other people

could have told a similar story from

t he ir ow n p oi nt s o f v ie w. T he y a re

Brian   Pippard, Josephson’s thesis ad-

visor   while the work was being done,

an d   David Shoenberg, director at thattime   of the Mond Laboratory in which

Josephson   was a  research student inexperimental physics and where I

served as nominal head of the solid-statetheory   group.

The discovery

Josephson had taken my course on

solid-state and many-body theory.

This was a disconcerting experience for 

a lecturer, I can assure you, because

Philip W. Anderson is at Bell TelephoneLaboratories, Murray Hill, N.J.

everything had to be right or he would

come up and explain it to me after 

class. Probably because of the course

and some of the things I said, he showedme his calculations within a day or two

afte r f i rs t making them. At f ir st he

followed directly some recent calcula-tions, by Morrel Cohen, Leo Falicov

and James Phillips,1  of the current by

the “tunneling Hamiltonian” method,

applied to two superconductors sepa-

rated by an insulat ing layer. But bythe time I saw the calculations he had

already worked out the rather sophisti-

cated formalism he later published in

which he kept track of particle charges.

By this time I knew Josephson well

enough that I would have acceptedanything else he said on faith. How-

ever, he himself seemed dubious, so I

spent an evening checking one of the

terms that make up the current. We

were all-Josephson, Pippard and my-self, as well as various other people

who also habitually sat at the Mond tea

table and participated in the discussions

of the next few weeks-very much puz-

zled by the meaning of the fact that

t h e c u r r e n t d e p e n d s o n t h e p h a s e .

(This is the famous  J   =  J 1  sin φ  rela-

tion-see box on page 24.) I think itwas residual uneasiness on this score

that caused the two Brians (Pippard 

Brian D. Josephson in 1969

PHYSICS TODAY / NOVEMBER 1970 2 3

 

The Josephson effect

Superconducting tunneling. Oxidise a strip of superconducting film (say lead)very lightly to a depth of 10-20 A; then evaporate a cross strip of lead film.Simply plot the current-voltage characteristic of the resulting “tunnel junction.”

Electrons can tunnel quantum mechanically directly from an energy level in onepiece of lead to an equal energy in the other.  At temperatures less than T c, thesuperconducting transition temperature, “normal” current does not flow verywell until we apply enough voltage to overcome the energy gap 2 ∆, becausethere are no single-particle levels in the gap.

Josephson effect. But Josephson showed that superconducting pairs of elec-trons can   also tunnel, almost equally well. The supercurrent is

J

 J

sin @

where J is comparable with the “normal” current at V 2~.

9  is the differencebetween the phases of the electron-pair “wave   functions” in the two supercon-

ductors on opposite sides of the insulating barrier of oxide. Later it was real-ized that the phases are coupled by an energy E El   cos @ that the minimumenergy is achieved by equal phases and zero current. But an external currentsource can drive the phases unequal. If the phases are time independent, adc supercurrent flows with no voltage drop. (See below.)

Superconductivity. The phenomenology of superconductivity can be sum-marized in terms of the phase

6

  of the pair wave functions. The superconduct-ing electrons (usually most of them) move   with a velocity v,,  which is given(except for a factor 2 in the vector-potential term) by the standard quantum-mechanical equation

If the phase is uniform, v,   is proportional   to the vector potential A, which givesthe standard London equation describing the Meissner effect of flux exclusion.The quantization of flux is just the requirement that @  be the phase of asingle-valued function, so it may change only by r  or going around a ring.We see from this equation that either a magnetic field A or a current

vs

  can lead

to a gradient ofc;

  either may be used in a Josephson interferometer.The time dependence of the phase is given by the “Josephson equation”

  v

 

which is just the Einstein equation relating frequency to the energy of a pair.This equation, together with the previous one, shows that a voltage can not bemaintained across a superconductor without accelerating the supercurrent.This equation, together with the Josephson-current equation, allows us tomeasure e/h from the relationship between voltage and the frequency of theac Josephson current that flows when we maintain a voltage across the junction.

Josephson penetration depth. The Josephson current can itself   cause a mag-netic field that modulates @ The resulting coupling leads to a modified kind of Meissner effect with a long   characteristic length

hJ

Junctions larger than

XJ  behave like bulk superconductors in some ways.

 pap er to   Physics Letters,2  which was

and Josephson) to decide to send the

 ju st th en st ar ti ng pu bl ic at io ns , ra th er than to  Physical Review Letters.

Earlier in my course I had made

some remarks about broken symmetry,

and later we discussed how brokensymmetry made this peculiar behavior 

of the current possible. Josephson has

always given me much more credit for 

these remarks than my understanding

at the time deserved. Apart from these

ideas about broken symmetry and some

very minor points acknowledged ex-

 plicitly in that  Physics Letters  paper, Iw a n t t o e m p h a s i z e t h a t t h e w h o l e

achievement, from the conception to

the explicit calculation to the publica-tion, was completely Josephson’s.

I hope it was no coincidence thatthese developments occurred in the

thoughtful and stimulating atmosphere

characteristic of the Cavendish. But

the specific achievement was Joseph-

son’s own; this young man of 22 con-

ceived this entire thing and carried it

Two things about that original paper 

through to a successful conclusion.

have always struck me as remarkable.

The first one is that, from the originalidea of a dc supercurrent, he should im-

mediately make the all-important leap

not only to the ac supercurrent but

also to the mathematics of how to syn-

chronize it with an external ac signal.Furthermore, he explained how to ob-

serve the effect in exactly the way that

Sidney Shapiro did nearly two years

later,3  and so predicted what is nowthe standard method for measuring e/h.

The second remarkable thing was the

initial response of our excellent patent

lawyer at Bell Telephone Laboratories

when John Rowell and I consulted him;in his opinion Josephson’s paper was

so complete that no one else was ever 

going to be very successful in patentingany substantial aspect of the Josephson

effect.

Let me then complete the history.At this point I have to start looking

at things from my own point of view,

which was that I was extremely en-

thusiastic about what Josephson had

done and eager to work on it, I be-

lieve I was probably the most en-thusiastic evangelist for the effect that

he had. Therefore this narrative will

now begin to sound like a description

of what I did with the Josephson effect,But of course at the same time other 

lines of development were being fol-

lowed, lines I had nothing to do with.

After a few more discussions at theCavendish, which did not carry us

much further than what had been pub-lished in the first paper, I returned home

to Bell Labs. There I mentioned to

Rowe11 my conviction that Josephsonwas right. Rowe11 admitted to me that

he had, from time to time, seen sug-

gestive things in his tunnel junctions,

and a few months later he called me

in to look at his experimental resultson a new batch of tunnel junctions.

He thought he might actually be seeingthe Josephson effect. In thinking atthat time about the results of Rowell’s

measurements the penny finally dropped

for me, and the only two remainingessential components of the phenom-

enon became clear.The first of these is that

J

sin

implied a coupling energy between thetwo superconductors of  E E co s   ‘

The value of E is a very vital point;

it must be larger than the noise energy

in the circuit, which is why our experi-ments with low-resistance junctions

w o r k e d a n d p r e v i o u s a t t e m p t s b yJosephson and others with higher re-sistance junctions, and thus smaller J

and E had not been successful. Thesecond new idea was the Josephson

 pe ne tr at io n de pt h.

Looking back, I assume that many

workers m u st h av e ob s er v ed t he

coupling-energy effect previously, butthe point is that this effect   is not easy

to distinguish from a tunnel junction

shorted across the layer separating the

two metals. We were able to see theeffect because three conditions were

satisfied: First, we knew what to look 

for; second , we unders tood what wesaw. Both of these were the result of our contact with Josephson. The third

condition was that we were confident of 

Rowell’s skills in making good, clean,reliable, tunnel junctions.

After we understood these theoreti-cal ideas we changed the title of our 

 paper 4  from “Possible . . .” to “Probable

Observation of the Josephson Effect.”

Publication

The story of the publication of thesevarious ideas is complicated. I soon

learned that the two ideas I have  just

mentioned had both been discovered

and written out by Josephson several

m on th s e ar li er . T he h is to ry o f ho wthey  w e r e p u b l i s h e d i s a k i n d o f  

“Alphonse-Gaston” story.

24 PHYSICS TODAY / NOVEMBER 1970

 

 

The first time they were written downwas in August 1962. Josephson sub-mitted, in support of an application for a research fellowship at Trinity College,Cambridge, a “fellowship thesis” thatcontained the first really full, account of the general nature and the physicalmeaning of the Josephson effect. This

 paper also contained the generalizationto nontunneling situations, which I  later called “weak superconductivity,” Onecopy of this thesis remains, I believe,in the Trinity College library; one copyJosephson kept, and for some reason a

 photostat copy turned up in Chicago.Later on, after we did the experiments,I received a copy also. But the firstthree copies represented what Joseph-son felt to be adequate publication.Perhaps I am not being quite fair, be-cause most of these ideas were includedin Josephson’s remarks at the LT8 con-ference in London, September 1962, ina rather famous debate with JohnBardeen.

I had reproduced some of theseresults but, knowing after the factabout Josephson’s thesis, I did not wantto call too much attention to my ownwork of several months later. There-fore I published by own full version 5

in the notes of the Ravello Summer School of May 1963, which took almosttwo years to appear in print.

 Neither of these two roughly equiva-lent papers is widely quoted, to saythe least. That is a pity, because to-gether they contain many things thathad to be rediscovered later. I find inmy file of letters from Josephson thatwe discussed the possibility of a joint

 paper, but this seems not to have comeoff.

Significance

This is enough reminiscence; whathas turned out to be the significanceof Josephson’s discovery? I think twoanalogies may help to show how im-

 portant it is. Imagine, for one, that wehad developed a purely theoretical geo-

 physical model of the earth that pre-dicted the existence of a magnetic field,

 but imagine in addition that no one hadyet invented the compass! I like thatanalogy because it shows up both as- pects   of the importance of a measuringinstrument-and the Josephson effect isfirst and foremost a measuring instru-ment. The measuring instrument is im-

 portant because, first, it verifies thetheory, and second, it suggests a host of 

 practical uses.The second analogy for the signifi-

cance of the Josephson effect is some-what deeper. Suppose we understoodthe wave nature of light theoretically,and had even developed the laser, butno one had ever invented a way to getthe light beam out without completelymessing up the laser oscillations. Thatis, suppose no one had invented slits,

half-silvered mirrors and all the other  paraphernalia of interference experi-ments. We should then be in the samefrustrating position that we were in withregard to superconductivity beforeJosephson. Then we had a theory andsources of coherent radiation, but nomeasuring instruments or gadgets toverify the theory and make use of thecoherence.

In 1962 we had already postulatedthat superconductivity consisted of acoherence of the de Broglic waves repre-senting pairs of electrons inside thesuperconductor. Prior to Josephson, the

 phase of these macroscopic waves wasthought to be

-

  unmeasurable in prin-ciple, by the same   kind of speciousreasoning that has been used to provesuch things as the nonexistence of ferro-electricity. In principle the phase varieswith magnetic field and current in spaceaccording to the equations

velocity of superelectrons v

= i v - y

and in time according to the Einstein-Josephson equation

hω  = energy

1 0 0

1 0

 

5

B

 

1.0

0.1

That is,

h

  =p

e

where p.   is the chemical potential.It was not yet entirely clear at the

time that these two equations are equiv-alent to our theoretical understanding of superconductivity. The second equa-tion predicts zero resistance in the ab-sense of acceleration /dt),  and thefirst leads to the Meissner effect and toflux quantization.

The four equations in the box on page24 tell us all we ever need to knowabout the Josephson effect and most of what we need to know about super-conductivity. The first two equationsgive us a way of comparing the phasesof two weakly coupled bits of super-conductor, if they are so weaklycoupled that they do not seriously per-turb one another.

The straightforward way to verify theJosephson effect is simply by observingthe superconducting tunnel current be-tween   two bits of superconductor. Itis important that the junction really bea tunnel junction. Josephson’s theory

 predicts a certain magnitude for thetunnel current. We began4  by makingthis observation, which is simple the-oretically but not very elegant experi-

 

- 5   0 5 1 0 1 5 20

FIELD (GAUSS)

Single-slit interference pattern shows dependence of Josephson current in a lead-lead-

oxide-lead junction on magnetic field at 1.3 K. From reference 6. Figure 1

 

mentally. A more convincing verifica-tion6  is the observation of the single-slitinterference pattern caused   by a small,steady change in the magnetic field near the sample. The change in magneticfield gives a linear variation of  phaseacross the sample in the   same   way thatchanging the angle of observation acrossa slit gives a linear change in phaseacross the slit.

Figure 1 shows an observation of this pattern, made by Rowell in 1963 withthe best junctions he was at that timeable to produce.6 The extremely deepminima attest to the high uniformity of his junctions. The original observa-tions of this effect, made by Rowell inDecember 1962, were comparativelycrude. He simply observed the changesin the tunneling current on a recorder while he slid a bar magnet along thesurface of a table towards the sample,Again from my file of correspondencewith Josephson I note that he also hadsuggested this observation before he hadany way of knowing that we were in the

 process of carrying it out.In principle the next thing to do is

the two-slit experiment. This was con-ceived and carried out7  in many fasci-nating versions by the group of RobertJaklevic, James Mercereau,   Arnold Sil-ver and John Lambe   at the Ford Lab-oratories. Figure 2 shows their two-slit pattern, obtained as a function of v  s, which is proportional to the currentthrough one arm of a loop containinga pair of junctions. In addition theyobserved the pattern in three other ways-as a function of the magneticfield alone, as a function of the vector 

 potential in the absence of a field andas a function of the velocity of thesuperelectrons imparted through rota-tion.

The Anal coup verifying the Joseph-son effect was carried ou t3  by SidneyShapiro, of the A. D. Little Co, actually

 before the two-slit experiments weredone. Shapiro applied an external acsignal to the junction and observed the

 points  of synchronization with the in-ternal ac  supercurrent. Figure 3 showsthe results of a similar experiment car-ried out later 8  with a thin-film bridge by Ali Dayem   and myself; this geome-try greatly enhances the coupling toexternal rf fields.

I do not think one should underesti-mate the impact of the Josephson dis-covery on our understanding of super-fluidity and superconductivity. Oneexample of great importance is in thestudy of dissipative phenomena. Theidea and the experimental verification of flux and vortex quantization, and theJosephson frequency condition, alreadyexisted in the literature. It was thedirect tangibility given them by the ex-

 perimental access that made us putthem together in the two phenomena,seemingly diverse, of high-field super-

conducting magnets and dissipation insuperfluid helium.9 In each case thekey  to what is going on in the dissipativeeffects is the Josephson frequency con-dition and the idea of phase slippage   byvortex motion.

Applications

We have now reached the third stageof the application of Josephson’s dis-covery, after a zeroth stage consisting of his predictions, a first stage of verifica-tion and a second stage of generaliza-tion and conceptualization. This thirdstage is practical application, which of course means scientific application inother fields as well.

At present by far the most famousapplication is the measurement   of h/e,as suggested by Josephson himself veryearly and as carried out 10   by DonaldLangenberg, Barry Taylor and WilliamParker of the University of Pennsylva-nia. The story of this measurement istoo well known to bear repetition; Ishould say only that, from the first, allof us in the field have felt that it wasonly a matter of time before the mostaccurate standard of voltage measure-ment became the comparison with fre-quency   via Josephson’s equation. Thisrole is analogous to that of Iight inter-ferometry in length measurements.

We can assume that  h/me  and 4mne

two more constants that can also bemeasured by Josephson experiments,will also fall to sufficiently ingenious andcareful experimentalists. The experi-ment for h m in particular, is veryclean; one has only to count and to mea-sure an area. Parker has already donethis experiment to an accuracy of 10-4.I see no reason why the major portion of our system of units should not be basi-cally defined in the future by two kinds

of interferometry-Josephson interferom-etry   and light intcrfcrometry.

Perhaps even more important will bethe role of the effect in ultrasensitiveelectromagnetic (and, with liquid he-lium, gravitational) measuretnents. The

 pioneering work of Jaklevic,   Mercereauand their coworkers has been followed

 by the development, at the Mond   Labo-ratory at Cambridge, of the SLUG  pico-voltmeter by John Clarke.11  This in-strument can measure voltages such asthose that arise from the resistance of a10-nanometer (100-angstrom)   copper film normal to its area from one super-conductor to another. I have no ideawhat further plans for ultrasensitivemeasurements are on the drawing board.But it is a bit frightening to realize thatClarke’s voltmeter was a success be-cause he deliberately reduced the sen-sitivity to make the instrument easier tohandle!

A third promising direction is in thedetection and demodulation of high-frequency radiation, pioneered at BellLabs by Dayem, Shapiro, Mike Grimesand Paul Richards.12 So far the naturalconvenience of the ac Josephson effectas a direct frequency-to-voltage con-verter (the relation is directly linear)has not been fully exploited, but great

 promise exists.The use of the Josephson effect as  a

high-frequency generator has been dis-cussed widely, but I have a faint per-sonal prejudice against such a use. Itappears to me to be a crude applicationfor this delicate effect. Of course Ihope I shall be proved wrong and the acgenerator will turn out to be highlyvaluable in the region behveen the mi-crowave and the infrared frequencies.

Perhaps the wildest application yet isat the General Electric research labora-

DRIFT CURRENT (mA)

Interference and diffraction effects in two thin tin films separated by an oxide layer,vacuum deposited on a quartz substrate in such a way as to give two junctions con-nected in parallel. This experimental trace of Josephson current versus drift currentat 3.7 K shows the two-slit pattern. Maximum current is 1.5 mA. Zero offset arisesfrom a static applied field. Figure 2

 

4  8  12 16VOLTAGE (MICROVOLTS)

Effect of an external ac signal. These are current-voltage characteristics for a thin-film bridge of indium subjected to a 4.26-GHz external signal. The steps in the char-acteristic curves are induced at voltages V = nhv/2me. Fractions in color are valuesof n/m. The separate curves are for different power levels. From A. H. Davem. J.J. Wiegand, Phys. Rev. 155, 419 (1967).

tories at Schenectady, where Ivar Gia-ever 13   has a light-sensitive Josephson

 junct ion that can be switched on with

light.An application I have been advocat-

ing for many years would involve using

Josephson junctions for the control andmovement of single quantized vortex

lines as computer elements, rather likethe recent “bubble” devices developed

at Bell Labs. Rough calculations indi-

cate great advantages in size and speed,

 but so far no real work has been done on

such systems. The technology is chal-

lenging, to say the least.With these last speculative comments

References

1. M. H. Cohen , L. M. Falicov, J. C.Phillips, Phys. Rev. Lett. 8, 316  (1962).

2. B. D. Josephson, Phys. Lett. 1, 251(1962).

3. S.  Shapiro, Phys. Rev. Lett. 11, 80(1963).

4. P. W. Anderson, J. M. Rowell, Phys.Rev. Lett. 10,  230 (1963).

5. P. W. Anderson, in  Lectures on the Many-Body Problem, E. R.  Caianello,ed.,   Academic, New York, 1964.

6. J. M. Rowell, Phys. Rev. Lett.   11, 200(1963).

7. R. L. Jaklevic, J. Lambe,   J. E. Mer-cereau,   A. H. Silver, Phys. Rev. Lett.12: 159 (1964)  and 12, 274 ( 1964);Phys. Rev. 140, A1628  (1965),   an dother papers  by  members of the samegroup.

Figure 3

I have tried to convey the impressionthat the Josephson effect is not a closed

subject but still very much open-ended.

The technology as well as the science of the future is likely to depend greatly on

macroscopic quantum interference of 

matter waves, the discovery and exploi-tation of which we owe in large part to

Brian Josephson.

* * *

This article was adapted from a talk pre- sented at the Twelf th International Confer-ence on Low Temperature Physics, 4-10September 1970, and will also appear inthe Proceedings of that conference.

8. P. W. Anderson, Ali  H. Dayem,   Phys.Rev. Lett.   13, 195 (1964).

9. Y.  B. Kim, C. F. Hempstead,  A. R.Strnad, Phys. Rev. Lett. 9, 306  (  1962)and 13, 794 (1964); P. W. Anderson,Phys.   Rev. Lett. 9, 309 (1962); P. L.Richards, P. W. Anderson, Phys. Rev.Lett. 14, 540 (1965).

10. W. H. Parker, B. N. Taylor, D. N.Langenberg, Phys. Rev. Lett.   18, 287(1967).

11. J. Clarke, Phil. Mag. 13, 115 (1966).

12. C. C. Grimes, P. L. Richards, S. Sha- piro, Phys. Rev. Lett. 17,  431 (1966);A. H. Dayem,   C. C. Grimes, Appl.Phys.  Lett.   9, 47 (1966).

13. I. Giaever, Phys. Rev. Lett. 20, 1286(1968).   0

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