The Discovery of Superconductivity - Department of Physicsnapolj/PHYS2796/SuperconductivitySlides.pdfSlides on Superconductivity Modern Physics 27 March 2015 The Discovery of Superconductivity

Slides on Superconductivity Modern Physics 27 March 2015

The Discovery of Superconductivity

1

Physics Today September 2010

Clay studied resistance R versus temperature T in very thingold and platinum wires.4 Before July 1908 the lowest avail-able temperature was 14 K, at which solid hydrogen subli-mates under reduced pressure. That was low enough to ob-serve that the almost linear decrease of R with T at highertemperatures starts to level off to an almost constant value.In one of his KNAW reports, Kamerlingh Onnes even men-tioned a trace of a minimum in the R(T) plot, which indicatesthat he originally believed in Kelvin’s model.

The almost linear R(T) behavior of platinum above 14 Kmade that metal suitable as a secondary thermometer. It wasmuch more convenient than the helium gas thermometerKamerlingh Onnes had been using. But a disadvantage wasthe platinum thermometer’s rather large size: 10 cm long andabout 1 cm wide.

The resistance of the metal wires depended on the chem-ical and physical purity of the materials. For instance, Kamer-lingh Onnes showed that the resistance increase due toadding small admixtures of silver to the purest available goldwas temperature independent and proportional to the con-centration of added silver. So, improving purity would yieldmetal wires of very low resistance that could serve as second-ary thermometers at temperatures far below 14 K.

Those very low temperatures came within reach after thesuccessful liquefaction of helium in July 1908. The next im-portant requirement was transferring helium from the lique-fier, which lacked adequate space for experiments, to a sep-arate cryostat. In those days, accomplishing that transfer wasa real challenge. Thanks to the notebooks, we can follow quiteclosely the strategy followed by Kamerlingh Onnes; his tech-nical manager of the cryogenic laboratory, Gerrit Flim; andhis master glassblower, Oskar Kesselring.

Experimenting in liquid heliumThe first entry about the liquid-helium experiments in note-book 56 is dated 12 March 1910. It describes the first attempt

to transfer helium to a cryostat with a double-walled con-tainer and a smaller container connected to an impressivebattery of vacuum pumps. “The plan is to transfer, then de-crease pressure, then condense in inner glass, then pumpwith Burckhardt [pump down to a pressure of] 1/4 mm [Hg],then with Siemens pump [to] 0.1 mm.”

Because there was nothing but glass inside the cryostat,the experiment worked well and a new low-temperaturerecord was registered: roughly 1.1 K. The goal of the next ex-periment, four months later, was to continue measuring R(T)for the platinum resistor that had previously been calibrateddown to 14 K. But the experiment failed because the extraheat capacity of the resistor caused violent boiling and fastevaporation of the freshly transferred liquid helium. So it wasdecided to drastically change the transfer system. And thatwould take another nine months.

Meanwhile, interest in the low-temperature behavior ofsolids was growing rapidly. Specific-heat experiments car-ried out in Berlin and Leiden exhibited unexpected decreaseswith descending temperatures. For the first time, quantumphenomena were showing up at low temperature. Kamer-lingh Onnes, playing with theoretical models himself, didn’twant to wait until the new liquid-transfer system was ready.He decided to expand the original liquefier so that it couldhouse a platinum resistor. Thus, on 2 December 1910, hemade the first measurement of R(T) for a metal at liquid-he-lium temperatures.5 Cornelis Dorsman assisted with the tem-perature measurements and student Gilles Holst operatedthe Wheatstone bridge with the galvanometer. That ultrasen-sitive setup for measuring the current was placed in a sepa-rate room, far from the thumping pumps.

The experiment’s outcome was striking. The resistance ofa platinum wire became constant below 4.25 K. There was nolonger any doubt that Kelvin’s theory was wrong. The resis-tivity had fallen to a residual value that presumably dependedon the purity of the sample. Kamerlingh Onnes concluded that

2 September 2010 Physics Today © 2010 American Institute of Physics, S-0031-9228-1009-XXX-X

Figure 1. Heike Kamerlingh Onnes (right) and Gerrit Flim, his chief technician, at the helium liquefier in KamerlinghOnnes’s Leiden laboratory, circa 1911.

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IEEE/CSC & ESAS EUROPEAN SUPERCONDUCTIVITY NEWS FORUM (ESNF), No. 15, January 2011 Reprinted with permission from Physics Today 63, No. 9, 38-42 (2010). Copyright 2010, American Institute of Physics.

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Kamerlingh-Onnes >100 Years ago


The Discovery Measurement

2

the cryostat—just in case the helium transfer worked.The mercury resistor was constructed by connecting

seven U-shaped glass capillaries in series, each containing asmall mercury reservoir to prevent the wire from breakingduring cooldown. The electrical connections were made byfour platinum feedthroughs with thin copper wires leading tothe measuring equipment outside the cryostat. KamerlinghOnnes followed young Holst’s suggestion to solidify the mer-cury in the capillaries by cooling them with liquid nitrogen.

The first mercury experimentTo learn what happened on 8 April 1911, we just have to fol-low the notes in notebook 56. The experiment was started at7am and Kamerlingh Onnes arrived when helium circulationbegan at 11:20am. The resistance of the mercury fell with thefalling temperature. After a half hour, the gold resistor wasat 140 K, and soon after noon the gas thermometer denoted5 K. The valve worked “very sensitively.” Half an hour later,enough liquid helium had been transferred to test the func-tioning of the stirrer and to measure the very small evapora-tion heat of helium.

The team established that the liquid helium did not con-duct electricity, and they measured its dielectric constant.Holst made precise measurements of the resistances of mer-cury and gold at 4.3 K. Then the team started to reduce thevapor pressure of the helium, and it began to evaporate rap-idly. They measured its specific heat and stopped at a vaporpressure of 197 mmHg (0.26 atmospheres), corresponding toabout 3 K.

Exactly at 4pm, says the notebook, the resistances of thegold and mercury were determined again. The latter was, in

the historic entry, “practically zero.” The notebook furtherrecords that the helium level stood quite still. That entry con-tradicts the oft-told anecdote about the key role of a “blueboy”—an apprentice from the instrument-maker’s schoolKamerlingh Onnes had founded. (The appellation refers to theblue uniforms the boys wore.) As the story goes, the blue boy’ssleepy inattention that afternoon had let the helium boil, thusraising the mercury above its 4.2-K transition temperature andsignaling the new state—by its reversion to normal conductiv-ity—with a dramatic swing of the galvanometer.

The experiment continued into the late afternoon. At theend of the day, Kamerlingh Onnes finished with an intriguingnotebook entry: “Dorsman [who had controlled and meas-ured the temperatures] really had to hurry to make the ob-servations.” The temperature had been surprisingly hard tocontrol. “Just before the lowest temperature [about 1.8 K] wasreached, the boiling suddenly stopped and was replaced byevaporation in which the liquid visibly shrank. So, a remark-ably strong evaporation at the surface.” Without realizing it,the Leiden team had also observed the superfluid transitionof liquid helium at 2.2 K. Two different quantum transitionshad been seen for the first time, in one lab on one and thesame day!

Three weeks later, Kamerlingh Onnes reported his re-sults at the April meeting of the KNAW.7 For the resistanceof ultrapure mercury, he told the audience, his model hadyielded three predictions: (1) at 4.3 K the resistance shouldbe much smaller than at 14 K, but still measurable with hisequipment; (2) it should not yet be independent of tempera-ture; and (3) at very low temperatures it should become zerowithin the limits of experimental accuracy. Those predictions,Kamerlingh Onnes concluded, had been completely con-firmed by the experiment.

For the next experiment, on 23 May, the voltage resolu-tion of the measurement system had been improved to about30 nV. The ratio R(T)/R0 at 3 K turned out to be less than 10−7.(The theory’s normalizing parameter R0 was the calculatedresistance of crystalline mercury extrapolated to 0 °C.) Andthat astonishingly small upper limit held when T was low-ered to 1.5 K. The team having explored temperatures from3.0 to 4.3 K, the notebook entry in midafternoon reads: “At4.00 [K] not yet anything to notice of rising resistance. At 4.05[K] not yet either. At 4.12 [K] resistance begins to appear.”

The experiment was done with increasing rather thandecreasing temperatures because that way the temperaturechanged slowly and the measurements could be done undermore controlled conditions. Kamerlingh Onnes reported tothe KNAW that slightly above 4.2 K the resistance was stillfound to be only 10−5R0, but within the next 0.1 K it increasedby a factor of almost 400.

Something new, puzzling, and usefulSo abrupt an increase was very much faster than KamerlinghOnnes’s model could account for.8 He used the remainder ofhis report to explain how useful that abrupt vanishing of theelectrical resistance could be. It is interesting that the day be-fore Kamerlingh Onnes submitted that report, he wrote inhis notebook that the team had checked whether “evacuat-ing the apparatus influenced the connections of the wires bydeforming the top [of the cryostat]. It is not the case.” Thusthey ruled out inadvertent short circuits as the cause of thevanishing resistance.

That entry reveals how puzzled he was with the experi-mental results. Notebook 57 starts on 26 October 1911, “In he-lium apparatus, mercury resistor . . . with mercury contactleads.” That is, the team had spent the whole summer replac-

4 September 2010 Physics Today www.physicstoday.org

Figure 4. Historic plot of resistance (ohms) versus temper-ature (kelvin) for mercury from the 26 October 1911 experi-ment shows the superconducting transition at 4.20 K.Within 0.01 K, the resistance jumps from unmeasurablysmall (less than 10–6 Ω) to 0.1Ω. (From ref. 9.)

IEEE/CSC & ESAS EUROPEAN SUPERCONDUCTIVITY NEWS FORUM (ESNF), No. 15, January 2011 Reprinted with permission from Physics Today 63, No. 9, 38-42 (2010). Copyright 2010, American Institute of Physics.

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Electrical Resistance of Metals

3

The Correct (Quantum Mechanical) Explanation

k

kElectrons travel

in Bloch Waves, so expect no resistance.

But electron-lattice interactions deform the lattice (vibration)

k′

These interactions scatter the electrons, i.e. electrical resistance


Some Data

4

Temperature (K)

Resi

stiv

ity

Sodium

Different samples

Lead

Super- conductor!


“Normal” or Superconducting

5

Superconductors have higher resistivity at low temperatures than do “normal” metals.

Does superconductivity have something to do with strong e-lattice interaction?


Bardeen Cooper Schrieffer (BCS)

6

An electron moves through the lattice, distorting it and creating a phonon

Another electron moving in the opposite direction, is attracted to the distortion

Creation of “Cooper Pairs” of opposite spin electrons

Electrons attract each other through positive ion distortion


Bardeen Cooper Schrieffer (BCS)

7

The attraction gets stronger as temperature lowers. (Less random oscillator excitation at low temps?)

At a “critical temperature” the Cooper Pair binds, and a boson is created from the two fermion electrons, removing electrons from the Fermi sea.

More bound pairs form, and a “superconducting phase transition” occurs.

Lower the temperature further, and the attraction gets stronger, so the Cooper Pairs are bound even more tightly.


The BCS Band Gap

8

Krane “Modern Physics” 3e, Figure 11.34


Measuring the Band Gap

9

Electron tunneling and superconductivity*IVBF GI88V8l'General Electric Research and Development Center, Schenectady, Ne~ York

In my laboratory notebook dated May 2, 1960 is theentry: "Friday, April 22, I performed the followingexperiment aimed at measuring the forbidden gap in asuperconductor. " This was obviously an extraordinaryevent not only because I rarely write in my notebook, butbecause the success of that experiment is the reason Ihave the great honor and pleasure of addressing youtoday. I shall try in this lecture, as best I can, to recollectsome of the events and thoughts that led to this notebookentry, though it is dificult to describe what now appearsto me as fortuitous. I hope that this personal andsubjective recollection will be more interesting to youthan a strictly technical lecture, particularly since thereare now so many good review articles dealing withsuperconductive tunneling. '

A recent headline in an Oslo paper read approximatelyas follows: "Master in billiards and bridge, almostflunked physics —gets Nobel Prize. The paper refers tomy student days in Trondheim. I have to admit that thereporting is reasonably accurate. Therefore I shall notattempt a "cover up, " but confess that I almost flunkedin mathematics as well. In those days I was not veryinterested in mechanical engineering and school in gen-eral, but I did manage to graduate with an average degreein 1952. Mainly because of the housing shortage whichexisted in Norway, my wife and I finally decided toemigrate to Canada where I soon found employmentwith Canadian General Electric. A three year Companycourse in engineering and applied mathematics known as"the A, B and C course" was ofI'ered to me. I realized thistime that school was for real, and since it probably wouldbe my last chance, I really studied hard for a few years.%'hen I was 28 years old I found myself in Schenecta-

dy, New York, where I discovered that it was possible forsome people to make a good living as physicists. I had.worked on various Company assignments in appliedmathematics, and had developed the feeling that themathematics was much more advanced than the actualknowledge of the physical systems that we applied it to.Thus, I thought perhaps I should learn some physics and,even though I was still an engineer, I was given theopportunity to try it at the General Electric ResearchLaboratory.The assignment I was given was to work with thin

films, and to me films meant photography. However Iwas fortunate to be associated with John Fisher whoobviously had other things in mind. Fisher had startedout as a mechanical engineer as well, but had latelyturned his attention towards theoretical physics. He hadthe notion that useful electronic devices could be madeusing thin film technology, and before long I was workingwith metal films separated by thin insulating layers,

' This lecture was delivered by Ivar Giaever on the occasion of hisreceiving the l973 Nobel Prize in Physics. The Nobel Foundation1974.' See, for example, Tunneling Phenomena in Solids, 1969, edited by E.Burstein and S. Lundquist (Plenum Press, New York); Supercortductivity, 1969, edited by R. D. Parks (Marcel Dekker, New York).

trying to do tunneling experiments. I have no doubt thatFisher knew about Leo Esaki's tunneling experiments atthat time, but I certainly did not. The concept that aparticle can go through a barrier seemed sort of strangeto me, just struggling with quantum mechanics at Rens-selaer Polytechnic Institute in Troy, where I took forrnalcourses in Physics. For an engineer it sounds ratherstrange that if you throw a tennis ball against a wallenough times it will eventually go through without dam-aging either the wall or. itself. That must be the hard wayto a Nobel Prize! The trick, of course, is to use very tinyballs, and lots of them. Thus if we could place two metalsvery close together without making a short, the electronsin the metals can be considered as the balls and the wallis represented by the spacing between the metals. Theseconcepts are shown in Fig. 1. While classical mechanicscorrectly predicts the behavior of large objects such astennis balls, to predict the behavior of small objects suchas electrons we must use quantum mechanics. Physicalinsight relates to everyday experiences with large objects,thus we should not be too surprised that electronssometimes behave in strange and unexpected ways.Neither Fisher nor I had much background in experi-

mental physics, none to be exact, and we made severalfalse starts. To be able to measure a tunneling current thetwo metals must be spaced no more than about 100Aapart, and we decided early in the game not to attemptto use air or vacuum between the two metals because ofproblems with vibration. After all, we both had trainingin mechanical engineering! We tried instead to keep thetwo metals apart by using a variety of thin insulatorsmade from Langmuir films and from Formvar. Invaria-bly, these films had pinholes and the mercury counterelectrode which we used would short the films. Thus wespent some time measuring very interesting but alwaysnonreproducible current-voltage characteristics which wereferred to as miracles since each occurred only once.After a few months we hit on the correct idea: to useevaporated metal films and to separate them by a natu-rally grown oxide layer.To carry out our ideas we needed an evaporator, thus

I purchased my first piece of experimental equipment.While waiting for the evaporator to arrive I worried alot—I was afraid I would get stuck in experimentalphysics tied down to this expensive machine. My plans atthe time were to switch into theory as soon as I hadacquired enough knowledge. The premonition was cor-rect; I did get stuck with the evaporator, not because itwas expensive, but because it fascinated me. Figure 2shows a schematic diagram of an evaporator. To preparea tunnel junction we first evaporated a strip of aluminumonto a glass slide. This film was removed from thevacuum system and heated to oxidize the surface rapidly.Several cross strips of aluminum were then depositedover the first film making several junctions at the sametime. The steps in the sample preparation are illustratedin Fig. 3. This procedure solved two problems: First,there were no pinholes in the oxide because it is self-healing, and second, we got rid of mechanical problems

Reviews of Modern Physics, Vol. 46, No. 2, April 1974





















Ivan Giaever: Eiectron tunneling and superconductivity

FERMIENERGY

~B VAPPLIED

ratory and they properly questioned my experiment. Howdid I know I did not have metallic shorts? Ionic current~Semiconduction rather than tunneling'? Of course, I didnot know, and even though theory and experimentsagreed well, doubts about the validity were always in mymind. I spent a lot of time inventing impossible schemessuch as a tunnel triode or a cold cathode, both to try toprove conclusively that I dealt with tunneling and to.perhaps make my work useful. It was rather strange forme at that time to get paid for doing what I consideredhaving fun, and my conscience bothered me. But just likequantum mechanics, you get used to it, and now I oftenargue the opposite point; we should pay more people todo pure research.I continued to try out my ideas on John Fisher who

was now looking into the problems of fundamentalparticles with his characteristic optimism and enthu-siasm; in addition, I received more and more advice andguidance from Charles Bean and Walter Harrison, bothphysicists with the uncanny ability of making things clearas long as a piece of chalk and a blackboard wereavailable. I continued to take formal courses at Rensse-laer Polytechnic Institute, and one day in a solid statephysics course taught by Professor Huntington we got tosuperconductivity. Well, I didn t believe that the resist-ance drops to exactly zero—but what really caught myattention was the mention of the energy gap in a super-conductor, central to the new Bardeen —Cooper —.Schrief-fer theory. If the theory was any good and if my

tunneling experiments were any good, it was obvious tome that by combining the two, some pretty interestingthings should happen, as illustrated in Fig. 5. When I gotback to the GE Laboratory I tried this simple idea out onmy friends, and as I remember, it did not look as good tothem. The energy gap was really a many-body efI'ect andcould not be interpreted literally the way I had done. Buteven though there was considerable skepticism, everyoneurged me to go ahead and make a try. Then I realizedthat I did not know what the size of the gap was in unitsI understood —electron volts. This was easily solved bymy usual method: first asking Bean and then Harrison,and, when they agreed on a few millielectron volts, I washappy because that is in an easily measured voltagerange.I had never done an experiment requiring low temper-

atures and liquid helium —that seemed like a complicatedbusiness. However one great advantage of being associat-ed with a large laboratory like General Electric is thatthere are always people around who are knowledgeablein almost any field, and better still they are willing to lendyou a hand. In may case, all I had to do was go to theend of the hall where Warren DeSorbo was already doingexperiments with superconductors. I no longer rememberhow long it took me to set up the helium Dewars Iborrowed, but probably no longer than a day or two.People unfamiliar with low temperature work believe thatthe whole field of low temperature is pretty esoteric, butall it really rquires is access to liquid helium which wasreadily available at the Laboratory. The experimentalsetup is shown in Fig. 6. Then I made my samples usingthe familiar aluminum —aluminum oxide, but I put lead

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Fta. 5. (a) An energy diagram of two metals separated by a barrier.The Fermi energies in the two metals arc at differen levels because ofthe voltage difference applied between the metals. Only the left metalelectrons in the energy range e . V», can make a transition to the metalon the right, because only these electrons face empty energy states. ThePauli Principle allows only one electron in each quantum state. (b) Theright-hand metal is now superconducting, and an energy gap 2h hasopened up in the electron spectrum. No single electron in a supercon-ductor can have an energy such that it will appear inside the gap. Theelectrons from the metal on the left can still tunnel through the barrier,but they cannot enter into the metal on the right as long as the appliedvoltage is less than 5/e, because the electrons either face a filled stateor a forbidden energy range. When the applied voltage exceeds 5/eecurrent will begin to flow. (c) A schematic current-voltage characteris-tic. When both metals are in the normal state the current is simplyproportional to the voltage. When one metal is superconducting thecurrent-voltage characteristic is drastically altered. The exact shape ofthe curve depends on the electronic energy spectrum in the supercon-ductor.

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FIG. 6. A standard experimental arrangement used for low tempera-ture experiments. It consists of two Dewars, the outer one containingliquid nitrogen, the inner one consisting of liquid helium. Helium boilsat 4.2 K at atmospheric pressure. The temperature can be lowered toabout I' K by reducing the pressure. The sample simply hangs into theliquid helium supported by the measuring leads.

Rev. Mod. Phys. , Vol. 46, No. 2, April 1974

Ivan Giaever: Electron tunneling and superconductivity

strips on top. Both lead and aluminum are superconduc-tors. Lead is superconducting at 7.2 K and thus all youneed to make it superconducting is liquid helium whichboils at 4.2 K. Aluminum becomes superconductingonly below 1.2 K, and to reach this temperature a morecomplicated experimental setup is required.The first two experiments I tried were failures because

I used oxide layers which were too thick. I did not getenough current through the thick oxide to measure itreliably with the instruments I used, which were simply astandard voltmeter and a standard ammeter. It is strangeto think about that now, only 13 years later, when theLaboratory is full of sophisticated x-y recorders. Ofcourse, we had plenty of oscilloscopes at that time but Iwas not very familiar with their use. In the third attemptrather than deliberately oxidizing the first aluminumstrip, I simply exposed it to air for only a few minutes,and put it back in the evaporator to deposit the crossstrips of lead. This way the oxide was no more than about30A thick, and I could readily measure the current-voltage characteristic with the available equipment. Tome the greatest moment in an experiment is always justbefore I learn whether the particular idea is a good or abad one. Thus even a failure is exciting, and most of myideas have of course been wrong. But this time it worked!The current-voltage characteristic changed markedlywhen the lead changed from the normal state to thesuperconducting state as shown in Fig. 7. That wasexciting-! I immediately repeated the experiment using a

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FK". 8. The current —voltage characteristic at 1.6' K as a function ofthe applied magnetic field. A,t 2400 G the films are normal, at 0 G thelead film is superconducting. The reason for the change in the charac-teristics between 800 G and 0 G is that thin films have an energy gapthat is a function of the magnetic field.

diferent sample —same results! Another sample —stillthe same results —everything looked good! But how tomake certain? It was well known that superconductivityis destroyed by a magnetic field, but my simple setup ofDewars made that experiment impossible. This time Ihad to go all the way across the hall where Israel Jacobsstudied magnetism at low temperatures. Again I waslucky enough to go right into an experimental rig whereboth the temperature and the magnetic field could becontrolled and I could quickly do all the proper experi-ments. The basic result is shown in Fig. 8. Everythingheld together and the whole group, as I remember it, wasvery excited. In particular, I can remember Bean enthu-siastically spreading the news up and down the halls inour Laboratory, and also patiently explaining to me the

I 2 3MILLIVOLTS POTENTIAL DIFf ERENCE

Fro. 7. The current-voltage characteristic of an aluminum —aluminumoxide—lead sample. As soon as the lead becomes superconducting thecurrent ceases to be proportional to the voltage. The large changebetween 4.2 K and 1 6 K is due to the change in the energy gap withtemperature. Some current also Aows at voltages less than 6/e becauseof thermally excited electrons in the conductors.

FK. 9. Informal discussion over a cup of coA'ee. From left: IvarGiaever, Walter Harrison, Charles Bean, and John Fisher.

Rev. Mod. Phys. , Vol. 46, No. 2, April 1974


Comparison with BCS

10

Excellent agreement with theory!

BCS Predicts:Eg(0)=3.53 kTC

“Binding energy” of a Cooper Pair

For TC=10K get Eg(0)=3 meV


Applications

11

Accelerator Technology MedicineLHC

JLab


Modern Developments

12

MgB2: Profs Xi and IavaroneSo-called Hi-TC MaterialsNot!BCS

BCS at 40K

39.5 40.0 40.5 41.0 41.50.00

0.05

0.10

ρ (µΩ

cm)

T (K)

Documents

The Discovery of Superconductivity - Department of Physicsnapolj/PHYS2796/SuperconductivitySlides.pdfSlides on Superconductivity Modern Physics 27 March 2015 The Discovery of Superconductivity