Superconductivity Lecture 1

Alexy Karenowska Department of Physics, University of Oxford • What is ‘super’ about superconductivity? • What is electrical resistivity? • The discovery of superconductivity • Superconductors in magnetic fields • Introducing electron pairing

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Slides adapted with enormous gratitude from those of Prof. Andrew Boothroyd

UNIQ Summer School, 2020 Dr Alexy Karenowska What is resistance?

x 10–9 20

15 m) e– W 10

5 Resistivity ( Resistivity

0 I 0 50 100 150 200 250 300 V Temperature (Kelvin) Ohm’s Law: V = IR Resistivity of copper Resistivity of copper Resistivity: R = rL A Conductivity: s = 1/r

UNIQ Summer School, 2020 Dr Alexy Karenowska +

UNIQ Summer School, 2020 Dr Alexy Karenowska Ohm’s Law: V = IR

R = ρL/A e- ρ = resistivity σ = ρ-1 = conductivity

-9 ρcopper = 17 x 10 Ωm + ρseawater = 0.2 Ωm 22 ρteflon > 10 Ωm

I V

UNIQ Summer School, 2020 Dr Alexy Karenowska Instantaneous velocity ! = ~10& to 10'ms-1

Drift velocity !( ∝ *

∆, = -./!(∆0

r = 1mm I = 0.5A n = 1034m-3

* 5 = 673

UNIQ Summer School, 2020 Dr Alexy Karenowska “Kwik nagenoeg nul” EDNISIUEO PHYSICS OF INSTITUTE LEIDEN

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

Clay studied resistance R versus temperature T in very thin to transfer helium to a cryostat with a double-walled con- gold and platinum wires.4 Before July 1908 the lowest avail- tainer and a smaller container connected to an impressive able temperature was 14 K, at which solid hydrogen subli- battery of vacuum pumps. “The plan is to transfer, then de- mates under reduced pressure. That was low enough to ob- crease pressure, then condense in inner glass, then pump serve that the almost linear decrease of R with T at higher with Burckhardt [pump down to a pressure of] 1/4 mm [Hg], temperatures starts to level off to an almost constant value. then with Siemens pump [to] 0.1 mm.” In one of his KNAW reports, Kamerlingh Onnes even men- Because there was nothing but glass inside the cryostat, UNIQ Summer School,tioned a trace 2020 of a minimum in the R(T) plot, which indicates the experiment worked well and a new low-temperatureDr Alexy Karenowska that he originally believed in Kelvin’s model. record was registered: roughly 1.1 K. The goal of the next ex- The almost linear R(T) behavior of platinum above 14 K periment, four months later, was to continue measuring R(T) made that metal suitable as a secondary thermometer. It was for the platinum resistor that had previously been calibrated much more convenient than the helium gas thermometer down to 14 K. But the experiment failed because the extra Kamerlingh Onnes had been using. But a disadvantage was heat capacity of the resistor caused violent boiling and fast the platinum thermometer’s rather large size: 10 cm long and evaporation of the freshly transferred liquid helium. So it was about 1 cm wide. decided to drastically change the transfer system. And that The resistance of the metal wires depended on the chem- would take another nine months. ical and physical purity of the materials. For instance, Kamer- Meanwhile, interest in the low-temperature behavior of lingh Onnes showed that the resistance increase due to solids was growing rapidly. Specific-heat experiments car- adding small admixtures of silver to the purest available gold ried out in Berlin and Leiden exhibited unexpected decreases was temperature independent and proportional to the con- with descending temperatures. For the first time, quantum centration of added silver. So, improving purity would yield phenomena were showing up at low temperature. Kamer- metal wires of very low resistance that could serve as second- lingh Onnes, playing with theoretical models himself, didn’t ary thermometers at temperatures far below 14 K. want to wait until the new liquid-transfer system was ready. Those very low temperatures came within reach after the He decided to expand the original liquefier so that it could successful liquefaction of helium in July 1908. The next im- house a platinum resistor. Thus, on 2 December 1910, he portant requirement was transferring helium from the lique- made the first measurement of R(T) for a metal at liquid- fier, which lacked adequate space for experiments, to a sep- helium temperatures.5 Cornelis Dorsman assisted with the arate cryostat. In those days, accomplishing that transfer was temperature measurements and student Gilles Holst oper- a real challenge. Thanks to the notebooks, we can follow quite ated the Wheatstone bridge with the galvanometer. That closely the strategy followed by Kamerlingh Onnes; his tech- ultrasensitive setup for measuring the current was placed in nical manager of the cryogenic laboratory, Gerrit Flim; and a separate room, far from the thumping pumps. his master glassblower, Oskar Kesselring. The experiment’s outcome was striking. The resistance of a platinum wire became constant below 4.25 K. There was no Experimenting in liquid helium longer any doubt that Kelvin’s theory was wrong. The resis- The first entry about the liquid-helium experiments in note- tivity had fallen to a residual value that presumably depended book 56 is dated 12 March 1910. It describes the first attempt on the purity of the sample. Kamerlingh Onnes concluded that

www.physicstoday.org September 2010 Physics Today 39 the historic entry, “practically zero.” The notebook further records that the helium level stood quite still. The experiment continued into the late afternoon. At the end of the day, Kamerlingh Onnes finished with an intriguing notebook 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 to control. “Just before the lowest temperature [about 1.8 K] was Thereached, Nobel the boiling Prize suddenly in Physics stopped 1913 and was replaced by wasevaporation awarded in which to Heikethe liquid visibly shrank. So, a remark- ably strong evaporation at the surface.” Without realizing it, Kamerlinghthe Leiden team Onnes had also "forobserved his the superfluid transition of liquid helium at 2.2 K. Two different quantum transitions investigationshad been seen for onthe firstthe time, properties in one lab on one and the ofsame matter day! at low temperatures Three weeks later, Kamerlingh Onnes reported his re- whichsults at led,the April inter meeting alia, of to the the KNAW. 7 For the resistance productionof ultrapure mercury, of liquid he told helium." the audience, his model had yielded three predictions: (1) at 4.3 K the resistance should be much smaller than at 14 K, but still measurable with his equipment; (2) it should not yet be independent of tempera- ture; and (3) at very low temperatures it should become zero within 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 about −7 30 nV. The ratio R(T)/R0 at 3 K turned out to be less than 10 . (The normalizing parameter R0 was the calculated resistance FigureSuperconducting 4. Historic plot of transition resistance (ohms) in mercury versus temper-(2.2K) of crystalline mercury extrapolated to 0 °C.) And that aston- atureis (kelvin) measured for mercury for the from first the time. 26 October April 1911,1911 experi- data ishingly small upper sensitivity limit held when T was low- mentabove shows taken the superconducting October of same transition year. at 4.20 K. ered to 1.5 K. The team, having explored temperatures from Within 0.01 K, the resistance jumps from unmeasurably 4.3 K down to 3.0 K, then went back up to higher tempera- small (less than 10–6 Ω) to 0.1 Ω. (From ref. 9.) tures. The notebook entry in midafternoon reads: “At 4.00 [K] not yet anything to notice of rising resistance. At 4.05 [K] not the cryostat—just in case the helium transfer worked. yet either. At 4.12 [K] resistance begins to appear.” UNIQ Summer School, 2020The mercury resistor was constructed by connecting That entry contradicts theDr oft-told Alexy anecdoteKarenowska about the key seven U-shaped glass capillaries in series, each containing a role of a “blue boy”—an apprentice from the instrument- small mercury reservoir to prevent the wire from breaking maker’s school Kamerlingh Onnes had founded. (The appel- during cooldown. The electrical connections were made by lation refers to the blue uniforms the boys wore.) As the story four platinum feedthroughs with thin copper wires leading to goes, the blue boy’s sleepy inattention that afternoon had the measuring equipment outside the cryostat. Kamerlingh let the helium boil, thus raising the mercury above its 4.2-K Onnes followed young Holst’s suggestion to solidify the mer- transition temperature and signaling the new state—by its cury in the capillaries by cooling them with liquid nitrogen. reversion to normal conductivity—with a dramatic swing of the galvanometer. The first mercury experiment The experiment was done with increasing rather than To learn what happened on 8 April 1911, we just have to fol- decreasing temperatures because that way the temperature low the notes in notebook 56. The experiment was started at changed slowly and the measurements could be done under 7am, and Kamerlingh Onnes arrived when helium circula- more controlled conditions. Kamerlingh Onnes reported to tion began at 11:20am. The resistance of the mercury fell with the KNAW that slightly above 4.2 K the resistance was still −5 the falling temperature. After a half hour, the gold resistor found to be only 10 R0, but within the next 0.1 K it increased was at 140 K, and soon after noon the gas thermometer de- by a factor of almost 400. noted 5 K. The valve worked “very sensitively.” Half an hour later, enough liquid helium had been transferred to test the Something new, puzzling, and useful functioning of the stirrer and to measure the very small evap- So abrupt an increase was very much faster than Kamerlingh oration heat of helium. Onnes’s model could account for.8 He used the remainder of The team established that the liquid helium did not con- his report to explain how useful that abrupt vanishing of the duct electricity, and they measured its dielectric constant. electrical resistance could be. It is interesting that the day be- Holst made precise measurements of the resistances of mer- fore Kamerlingh Onnes submitted that report, he wrote in cury and gold at 4.3 K. Then the team started to reduce the his notebook that the team had checked whether “evacuat- vapor pressure of the helium, and it began to evaporate rap- ing the apparatus influenced the connections of the wires by idly. They measured its specific heat and stopped at a vapor deforming the top [of the cryostat]. It is not the case.” Thus pressure of 197 mmHg (0.26 atmospheres), corresponding to they ruled out inadvertent short circuits as the cause of the about 3 K. vanishing resistance. Exactly at 4pm, says the notebook, the resistances of the That entry reveals how puzzled he was with the experi- gold and mercury were determined again. The latter was, in mental results. Notebook 57 starts on 26 October 1911, “In

www.physicstoday.org September 2010 Physics Today 41 VOLUME 10' NUMBER 3 PHYSICAL REVIEW LETTERS 1 PEsRUwmv 1963

a point-by-point measurement would be. In conclusion, a caution should be inserted. The method proposed here can also be used to The derivation given here has assumed an inde- determine the shape of the Fermi surface in semi- pendent-particle model for the electrons in the metals and semiconductors. In fact, measure- metal. If many-body effects are important they ments of this effect in bismuth have already been may invalidate the results given here. made. ' In these materials it is not always true The author is happy to acknowledge very in- that w «&~, and the equations given here have to formative correspondence with Professor T. Kjel be modified accordingly. In particular, 0& in daas, Professor A. B. Pippard, and Professor Eqs. (1'), (5'), and (7) has to be replaced by R. Chambers. k~(I - &u/~c) '. In these materials, because w =~&, the same equipment that measures the R. Bowers, C. Legendy, and F. Rose, Phys. Rev. properties of the helicons (&u and k&) can also Letters 7, 339 (1961). 2F. measure w and thus determine the same geo- Rose, N. Taylor, and R. Bowers, Phys. Rev. metric properties as for metals. 127, 1122 (1962). Jones and R. Chambers (to be published). The It has been pointed out to the author after this author is indebted to Dr. Chambers for a copy of their paper was written that the analysis presented paper before publication. here for helicons has already been done for the ~P. Cotti, P. %yden, A. Quattropani, Phys. Letters case of circularly polarized transverse sound 1, 50 (1962). waves. "~" The general ideas in the analysis 5P. Aigrain, Proceedings of the International Con- for both helicons and circularly polarized sound ference on Semiconductor Physics, Prague, 1960 waves propagating along a magnetic field are the (Czechoslovakian Academy of Sciences, Prague, 1961), 225. same, but the details are somewhat different. p. 6R. G. Chambers, Phil. Nag. 1, 459 (1956). However, helicons to be a much more appear P. B. Miller and K. K. Haering, Phys. Rev. 128, useful means than circularly polarized sound 126 (1962). waves to study this onset of the Doppler-shifted J. E. Drummond, Phys. Rev. 112, 1460 (1958). absorption. It is not possible to produce circu- ~A. B. Pippard, Reports on Progress in Physics larly polarized transverse sound waves except (The Physical Society, London, 1960), Vol. 23, p. 176. along a few high-symmetry directions. "~' Hel- The techniques used in deriving the equations of this icons do not have this limitation and can propa- paper follow very closely the methods described in this reference. gate in all directions. It also appears that the OJ. Kirsch and A. G. Redfield, Bull. Am. Phys. Soc. distinction between the onset of absorption at a 7, 477 (1962). point or at a finite-sized orbit is more striking "T. Kjeldaas, Phys. Rev. 113, 1473 (1959). for helicons. '2Reference 9, pp. 252-255. VOLUME 10, NUMBER 3 PHYSICAL RE VIE%' LETTERS 1 FEBRUARY 1963

OBSERVATION OF PERSISTENT CURRENT IN A SUPERCONDUCTING SOLENOID

J. File and R. G. 2I04.Mills8— Plasma Physics Laboratory, Princeton University, Princeton, New Jersey (Received 21 September 1962; revised manuscript received 26 December 1962) VOLUME 10, NUMBER 3 PHYSICAL RE VIE%' LETTERS 1 FEBRUARY 1963 The classical ' in netic resonance experiment of Onnes, which a (NMR)I techniques I to the measure- persistent current is induced in a closed super- ment of the field. A doublePROBE SIZElayered solenoid of conducting circuit and the trapped magnetic field 984 2I04.turns4 of 0.020-in. diameter Nb-25% Zr alloy observed over a 4 ' period' of time, has been repeated approximately in. in diameter and 10 in. long several times ~ From the length of the period as shown2104.2 in Fig. 1 was constructed2I04.8— to provide a — — of observation and the accuracy of the measure- homogeneous0.3 0.2field. -01The measured0 i O. I axial field t0,pro-3 QISTANCE FROM COIL CENTERLINE - INCHES ment, one can set a lower limit to the time con- file of the central 0. 5 in. is shown in Fig. 2. The FIG. 2. Measured axial field profile. stant of the circuit. Apparently the highest value terminals of the coil are permanentlyCurrentconnected persists for to this limit was set in the experiment of Collins' by spot welding. I I 5 PROBE SIZE at a value of approximately 250 years. After inducing a persistent current>10in yearsthe coil, the data but eliminates the possibility2I04.4 of a position- To extend this limit several orders of rnagni- by itsal magneticshift indicatingfield wasa falsemeasureddecrease.by NMR tech- tude, we undertookFIG. 1. Constructionto modernof solenoid.nuclear mag- niques and apply Run two recordedextended over.with time.a periodTheof first37 days,run be-ex- 2104.2 end of— run one.— The data -23 ginning 9 days after the 0.3 0.2 -01 0 i O. I t0, 3 tended over a period of 21 days, and was termi- Resistivity <10 - Ωm are shown in Fig. 3. The solid lines QISTANCEare least-FROM COIL CENTERLINE INCHES nated at that time because of two coincidental ac- (15 orders of magnitude — N squares fits of the data to the leadingFIG. 2.termsMeasuredof anaxial field profile. cidents one a failure in the electronic system, exponential decay, and the other a mechanical shock to the system smaller than Copper) =B,(l- t/~), (i) which probably disturbed the position of some of a the data but eliminates the possibility of a position- = = the turns andS the position of the probe. The super- where B observed field alstrength,shift indicatingBo fielda false decrease. FIG. 1. Construction of solenoid. = current, however, was maintained, and the experi- strength at time zero, andRunr timetwo extendedconstant over.of thea period of 37 days, be- shown in The ment continued. The observed data of run one circuit, giving the resultsginning 9 daysTableafterI.the end of run one. The data tended over a period of 21 days, and was termi- that of run one. seemed to indicate a real field decay. Since the result of run two is consistentare shownwith in Fig. 3. The solid lines are least- probe had been displacednatedfromatthethatfieldtimemaximum,because of twoAncoincidentalattempt hasac-been made to correlate the data — squares fits of the data to the leading terms of an it was not possible to determinecidents theone contributiona failure in the electronicwith the worksystem,of Kim, Hempstead,exponential anddecay,Strnad to apparent decrease in andfieldtheby otherthis mechanicala mechanical shockbasedto onthethesystemflux-creep theory of Anderson. ' In =B,(l- t/~), (i) shift. which probably disturbed the positiontheir work,of somefield ofdecays were observed aof the form = = A slightly inferior set theof electronicsturns and thewaspositionsub- of the probe. The super- where B observed field strength, Bo field = of the stituted and the measuringcurrent,techniquehowever,changedwasto maintained, and the experi-B =8 - cln(t/tstrength), at time zero, and r time constant C C reposition the probe to fieldment maximumcontinued. beforeThe observedeach data of run one circuit, giving the results shown in Table I. The measurement. This introducesseemed tomoreindicatescattera realin fieldwheredecay.B isSincethe observedthe resultfield asof arunfunctiontwo is ofconsistenttime, with that of run one. UNIQ Summer School, 2020 probe had been displaced from the field maximum, An attempt has been madeDr Alexyto correlate Karenowskathe data it was not possible to determine the contribution with the work of Kim, Hempstead, and Strnad Flf LD ' RUN I decrease in field this mechanical based on the flux-creep theory of Anderson. In GAuSSto apparent by 8=2I04.88B2{I-800xl0 t) IIIII7fRRUp7IQQ shift. RUN 2 their work, field decays were observed of the form 264884 A slightly inferior set of electronics 8=2I04.was 88Isub-I 8{I-Q,6lxl0 t) stituted and the measuring technique changed to B =8 - cln(t/t ), C C reposition the probe to field maximum before each 0 0 2I049$measurement. This introduces more scatter a dlin where B is the observed field as a function of time, o + op 0 0 0 O 0 0 e Flf LD RUN I e~ 2I04$% GAuSS 0 8=2I04.88B2{I-800xl0 t) IIIII7fRRUp7IQQ RUN 2 264884 8=2I04.88I I 8{I-Q,6lxl0 t)

240 480 ?20 950 I200 I440 l580 0 0 — a dl 2I049$7l IIII E HOURS o + op 0 0 0 O 0 0 FIG. 3. Experimental data for runs one and two. e e~ 2I04$% 0

240 480 ?20 950 I200 I440 l580 — 7l IIII E HOURS

FIG. 3. Experimental data for runs one and two. MagneticMagnetic flux flux exclusion exclusion – –MeissnerMeissnereffecteffect

B B B B

CoolCool down down below below superconductingsuperconducting Walter Meissner Robert Ochsenfeld WaltherWalther Meissner MeissnerRobertRobert Ochsenfeld Ochsenfeld transitiontransition (1882-1974) (1901-1993) (1882(1882–1974)–1974) (1901(1901–1993)–1993) normalThenormal Meissner metal metal -Ochsenfeldsuperconductorsuperconductoreffect, 1933

B B W.W. Meissner Meissnerandand R. R. Ochsenfeld Ochsenfeld, 1933, 1933

Cool in field B to T below Tc

UNIQ Summer School, 2020 Dr Alexy Karenowska Karl Alexander Müller, b. 1927 Georg Bednorz, b. 1950 Discovery of copper oxide superconductors, 1986 Nobel prize, 1987

Lowest temperature recorded on earth is -89.2 oC, 184 K

© Pia Jensen Ray. University of Copenhagen. Copenhagen, Denmark, DOI:10.6084/m9.figshare.2075680.v2

UNIQ Summer School, 2020 Dr Alexy Karenowska Magnetic levitation

Maglev transportation Maglev trains (EDS — electrodynamic suspension) • 1. Conventional Maglev with Onboard high Tc magnets combined with superconducting magnet on board train; magnets in rails can reach speeds up to 550 km/h • Speeds in excess of 350 mph

2. Meissner effect Maglev, Chengdu, China (2000) Yamanashi Maglev, Japan

UNIQ Summer School, 2020 Dr Alexy Karenowska UNIQ Summer School, 2020 Dr Alexy Karenowska UNIQ Summer School, 2020 Dr Alexy Karenowska Electron pairing and energy gap Next lecture

– e e- Superconducting electrons Superconducting electrons are bound in a are bound in pairs condensate of pairs e– e- What is the pairing mechanism? What is pairing mechanism? + + + e– + Electrons cause instantaneous distortion of the atoms and leave e– a trail of positive charge + + Electrons cause instantaneous distortion of ionic + + lattice and leave “trail” of positive charge.

UNIQ Summer School, 2020 Dr Alexy Karenowska