Superconductivity: The Meissner Effect, Persistent Currents, and the Josephson Effects
MIT Department of Physics (Dated: March 10, 2005) Several of the phenomena of superconductivity are observed in three experiments carried out in a liquid helium cryostat. The transition to the superconducting state of each of several bulk samples of Type I and II superconductors is observed in measurements of the exclusion of magnetic field (the Meisner effect) from samples as the temperature is gradually reduced by the flow of cold gas from boiling helium. The persistence of a current induced in a superconducting cylinder of lead is demonstrated by measurements of its magnetic field over a period of a day. The tunneling of Cooper pairs through an insulating junction between two superconductors (the DC Josephson effect) is demonstrated, and the magnitude of the fluxoid is measured by observation of the effect of a magnetic field on the Josephson current.
1. PREPARATORY QUESTIONS temperature. The liquid helium (liquefied at MIT in the Cryogenic Engineering Laboratory) is stored in a highly 1. How would you determine whether or not insulated a sample Dewar flask. Certain precautions must be taken of some unknown material is capable of in being its a manipulation. It is imperative that you read superconductor? the following section on Cryogenic Safety before proceeding with the experiment. 2. Calculate the loss rate of liquid helium from the dewar in L −1 . d The density of liquid helium at 4.2 K is 0.123 − g 3 . cm At STP helium gas has a density of 0.178 −1 . g Data L for the measured 2.1. CRYOGENIC ASPECTS AND SAFETY boiloff rates are given later in the labguide. The Dewar flask shown in Figure 5 contains the liq 3. Consider two solenoids, each of length 3 uid cm, helium di in a nearly spherical metal container (34 cm ameter 0.3 cm, and each consisting of 200 in turns diameter) of which is supported from the top by a long copper wire wrapped uniformly and on top access of one or neck tube (length about 5060 cm and diame another on the same cylindrical form. A solid ter cylin about 3 cm) of low conductivity metal. ∼25 It holds der of lead of length 3 cm and diameter liters 0.2 of cm liquid. is The boiling rate of the liquid helium is located inside the common interior volume determined of the by the rate of heat transfer which is slowed solenoids. Suppose there is an alternating current by a surrounding vacuum space which minimizes direct with an amplitude of 40 mA and a frequency thermal of conduction 5 and multiple layers of aluminized my KHz in one of the solenoids. What is the lar induced which minimizes radiative coupling from the room. open circuit voltage across the second solenoid The be internal surfaces are all carefully polished and silver fore and after the lead is cooled below plated its critical for low radiation emissivity. Measurement shows temperature? that helium gas from the boiling liquid in a quiet Dewar 4. What is the Josephson effect? is released with a flow rate of gas at STP (standard tem perature and press ure = 760 torr and 293K) about 5 5. Calculate the critical current for a 1mm diameter cm3s−1 . Niobium wire at liquid Helium temperatures (4.2 The only access to the helium is through the neck of K). Use equation 1 to evaluate the critical the magnetic Dewar. Blockage of this neck by a gastight plug will field at 4.2 K and knowing that Bo = result 0.2 Tesla in a for buildup of pressure in the vessel and a con Niobium. sequent danger of explosion. The most likely cause of a neck blockage is frozen air (remember everything except helium freezes hard at 4 K) in lower sections of the neck 2. INTRODUCTION tube. Thus it is imperative to inhibit the streaming of air down the neck. In normal quiet storage condition, In this experiment you will study several of the the top re of the neck is closed with a metal plug resting markable phenomena of superconductivity, a property loosely on the top flange. When the pressure in the De that certain materials (e.g. lead, tin, mercury) war exhibit rises above 0 = p W/A (where w is the weight of the when cooled to very low temperature. As the plug cooling and A is its crosssectional area) the plug rises and agent you will be using liquid helium which boils some at pressure 4.2 is released. Thus the pressure in the closed K at standard atmospheric pressure. With suitable Dewar op is regulated 0 at which p has been set at approx eration of the equipment you will be able to imately control 0.5 the in. Hg.This permits the vaporized helium temperatures of samples in the range above this gas boiling to escape and prevents a counterflow of air into the
Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 2 neck. When the plug is removed, air flows downstream into the neck where it freezes solid. You will have to re move the plug for measurements of the helium level and for inserting probes for the experiment, it is and impor tant that the duration of this open condition be minimized. Always have the neck plug inserted when the Dewar is not in use. In spite of precautionary measures, some frozen air will often be found on the surface of the neck. This can be scraped from the tube surface with the neck reamer, con sisting of a thinwall halftube of brass. Insertion of the warm tube will liquefy and evaporate the oxygen ni trogen layer or knock it into the liquid helium where it will be innocuous. If you feel any resistance while the probe is being inserted in the Dewar, remove the probe immediately and ream the surface (the whole way around) before reinserting the probe. The penalty for not doing this may be sticking FIG. of 1: deli Critical field plotted against temperature for various cate probe components to the neck surface. Warmed superconductors. and refrozen air is a strong, quickdrying glue! In summary: Zero resistivity is, of course, an essential characteris 1. Always have the neck plug on the Dewar tic when of it a is superconductor. However superconductors ex not in use. hibit other properties that distinguish them from what one might imagine to be simply a perfect conductor, i.e. 2. Minimize the time of openneck condition when an ideal in substance whose only peculiar property is zero serting things into the Dewar. resistivity. The temperature below which a sample is supercon 3. Ream the neck surface of frozen sludge if the probe ducting in the absence of a magnetic field is called the doesn’t go in easily. critical temperature, Tc. At any given temperature, T < Tc, there is a certain minimum Bc(T ), field called the critical field, which will just quench the superconduc 3. THEORETICAL BACKGROUND tivity. It is found (experimentally and theoretically) that Bc is related T to by the equation 3.1. Superconductivity
� �T �2� Superconductivity was discovered in 1911 by H. Bc = B0 1 − (1) Kamerlingh Onnes in Holland while studying the electri Tc cal resistance of a sample of frozen mercury as a function where B is the asymptotic value of the critical field of temperature. On cooling with liquid helium, which he 0 as T → 0 K. Figure 1 shows this dependence for various was the first to liquify in 1908, he found that the resis materials including those you will be studying in this tance vanished abruptly at approximately 4 K. In 1913 experiment. he won the Nobel prize for the liquification of helium Note the extreme range of the critical field values. and the discovery of superconductivity. Since that time, These diagrams can be thought of as phase diagrams: be many other materials have been found to exhibit this low its curve, a material is in the superconducting phase; phenomenon. Today over a thousand materials, includ above its curve the material is in the nonconducting ing some thirty of the pure chemical elements, are known phase. to become superconductors at various temperatures rang ing up to about 20 K. Within the last several years a new family of ceramic compounds has been discovered which are insulators at room temperature and superconductors 3.2. Meissner Effect and the Distinction Between a at temperatures of liquid nitrogen. Thus, far from Perfect be Conductor and a Super Conductor ing a rare physical phenomenon, superconductivity is a fairly common property of materials. Exploitation of An this electric field E� in a normal conductor causes a cur resistancefree property is of great technical importance rent density J� which, in a steady state, is related to the in a wide range of applications such as magnetic electric reso field by the equation J� = σE� where σ is called the nance imaging and the bending magnets in particle electrical ac conductivity. In a metal the charge carriers are celerators such as the Tevatron at Fermi Lab. electrons, and at a constant temperature σ is a constant Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 3 characteristic of the metal. In these common medium circum attained its perfect conductivity, after which it stances the relation between E �and J � is called “Ohm’s cannot be changed. It came as quite a surprise when law”. A material in whichσ is constant is called an ohmic Meissner and Ochsenfeld in 1933 showed by experiment conductor. that this was not true for the case of superconductors. Electrical resistance in an ohmic conductor is They caused found instead that the magnetic field inside a su by scattering of the individual conduction electrons perconductor by is always zero, B � = i.e. 0 rather than the ˙ lattice defects such as impurities, dislocations, and less the stringent requirement B � = 0. This phenomenon is displacements of atoms from their equilibrium positions now referred to as the Meissner Effect. in the lattice due to thermal motion. In principle, Shortly if there after the Meissner effect was discovered it was were no such defects including, in particular, no given thermal a phenomenological explanation by F. and H. Lon displacements, the conductivity of a metal would don be infi[1]. They suggested that in the case of a super nite. Although no such substance exists, it is conductor interesting equation 2 above should be replaced by the to work out the theoretical consequences of perfect equation con ductivity according to the classical laws of electromag netism and mechanics. Consider a perfect conductor in the presence of a changing magnetic field. According to 4πλ � × J � = −B � (3) Newton’s second law, an electron inside the conductor c must obey the equation eE � = m�v˙, which is called the London equation. Continuing as where �v˙ represents the time derivative of the velocity before, one obtains vector. By definition J� = ne�v where n is the conduction electron density (number per unit volume). It follows ˙ − z � m � B �= B � (o)e λL (4) that E = ne2 J or more conveniently for later purposes ˙ 2 E � = 4π λ2J� where λ2 = mc . (Note how this relation c2 4πne2 which implies that B � ≈ 0 for depths appreciably be differs from Ohm’s law). From Maxwell’s equations we yond λL, in agreement with the Meissner Effect. � 1 �˙ have the relation (CGS � units), × E = − c B. London’s idea was based originally on thermodynamic Thus arguments. However, it is also useful to think of a su perconductor as being a perfect diamagnetic material. 2 Turning on a magnetic field in the neighborhood of a 4πλ ˙ ˙ � × J� = −B � (2) perfect diamagnetic material would generate internal cur c rents which flow without resistance and annul the field Another of Maxwell’s equations is inside. � ˙ � � × B � = 1 4πJ� + E � The constant λL, called the London penetration depth, c is the depth at which the internal field has fallen to 1/e ˙ ˙ from which it follows λ2� that × (� × B� ) = −B � where of its surface value. Experiments have demonstrated the we assume the low frequency of the action permits universal us validity to of equation 4 and have measured its drop the displacement term E� . The latter equation can value for many superconducting materials. The magni then be expressed as tude of λL may well differ from λ that since of the density of superconducting electrons is not necessarily the same 2 �˙ �˙ � B = B as that of conduction electrons in a normal metal. It The solution of this equation is varies from material to material and is a function of tem ˙ ˙ −z B�(z) = B � (0)e λ perature. where z is the distance below the surface. Thus the rate of change B � of decreases exponentially with depth leaving B � essentially constant below a characteristic pen3.3. IMPLICATIONS OF THE MEISSNER etration depth λ. If a field is present when the medium EFFECT attains perfect conductivity, that field is retained (frozen in) irrespective of what happens at the surface. The If Meissner we Effect has remarkable implications. Con attempted to change the magnetic field inside a sider perfect a cylinder of material which is superconducting be conductor by changing an externallyapplied field, low curTc. If the temperature is initially Tc, above appli rents would be generated in such a way as cation to keep of the a steady magnetic B � will field result in full internal field constant at depths λ beyond . This may penetration of the field into the material. If the temper be thought of as an extreme case of Lenz’s ature law. is If now a reduced T below c, the internal field must perfect conductor had a density of conduction electrons disappear. This implies the presence of a surface current like that of copper (approximately one conduction around elec the cylinder such that the resulting solenoidal tron per atom), the penetration depth would be field of exactly order cancels the applied field throughout the vol 100 ˚A. A magnetic field can exist in a medium ume of of per the rod. Elementary considerations show that a fect conductivity providing it was already there when current the in a long solenoid produces inside the solenoid a Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 4 uniform field parallel to the axis with a magnitude ever, partially de ionized gas of interstellar ≈ 1 space hy ( termined by the surface current density (current drogen per unit atom − cm3) is virtually collisionless with the re length along the solenoid axis), and no field outside sult that the it can be accurately described by the theory solenoid. In the case of the superconducting cylinder of collisionless in plasma under the assumption of infinite a magnetic field, the surface current is in a surface conductivity. layer with a thickness of the λ order L. Any of change of the externally applied field will cause a change of the surface current that maintains zero field inside the cylinder. 4. SUPERCONDUCTIVITY The THEORY TODAY difference between this behavior and that of a perfectly conducting cylinder is striking. As mentioned previously, 4.1. BCS Theory if such a cylinder underwent a transition to a state of perfect conductivity in the presence of a magnetic We field, note that the London equation, equation 3, is not the internal field would remain unchanged and no a surface fundamental theory of superconductivity. It is an ad current would appear. If the field were then hoc reduced, restriction a on classical electrodynamics introduced surface current would be induced according to Faraday’s to account for the Meissner Effect. However, the London law with the result that the flux of the internal equation field would has been shown to be a logical consequence of remain constant. the fundamental theory of Bardeen, Cooper, and Schrief Next we consider the case of a hollow cylinder fer of the ma BCS theory of superconductivity for which they terial which is superconducting T below c. Just as in received the the Nobel Prize in 1972 [2]. A complete discus solid rod case, application of a field Tc will above result sion of the BCS theory is beyond the scope of these notes, in full penetration both within the material of but the you tube will find an interesting and accessible discussion and in the open volume within the inner surface. of it Reduc in [3] (vol. III, chapter 21) and in references [2, 4, 5] ing the temperature below Tc with the field still on gives According to the BCS theory , interaction between rise to a surface current on the outside of electrons the cylinder and phonons (the vibrational modes of the pos which results in zero field in the cylinder material. itive ions By in the crystal lattice) causes a reduction in the itself, this outsidesurface current would also annul Coulomb the repulsion between electrons which is sufficient field in the open space inside the cylinder: but at Faraday’s low temperatures to provide a net positive and long law requires that the flux of the field inside range the cylinder attraction. This attractive interaction causes the remain unchanged. Thus a second current must formation appear of bound pairs of remote electrons of opposite on the inside surface of the cylinder in the momentum opposite di and spin, the socalled Cooper pairs. Being rection so that the flux in the open area is bosons, just that many of Cooper pairs can occupy the same quan the original applied field. These two surface currents tum state. re At low temperatures they “condense” into a sult in zero field inside the superconducting medium single and quantum state (Bose condensation) which can con an unchanged field in the central open region. stitute Just an as electric current that flows without resistance. before, the presence of these two surface currents is what The quenching of superconductivity T above c is caused would be expected if a magnetic field were imposed by on the a thermal breakup of the Cooper pairs. The crit hollow cylinder of perfectly diamagnetic material. ical temperature Tc is therefore a measure of the pair If now the applied field is turned off while binding the cylin energy. The BCS theory, based on the principles der is in the superconducting state, the field in of the quantum open theory and statistical mechanics, is a funda space within the tube will remain unchanged as mental before. theory that explains all the observed properties This implies that the insidesurface current continues, of lowtemperature superconductors. and the outsidesurface current disappears. The inside surface current (called persistent current) will continue indefinitely as long as the medium is superconducting. 4.2. RECENT DEVELOPMENTS IN HIGHTc The magnetic field inside the open area of the cylinder SUPERCONDUCTING MATERIALS will also persist. The magnetic flux in this region is called the frozeninflux. In effect, the system with its persistent The BCS theory of superconductivity led to the conclu currents resembles a permanent magnet. Reactivation of sion that Tc should be limited by the uppermost value of the applied field will again induce an outsidesurface phonon cur frequencies that can exist in materials, and from rent but will not change the field within the open this one space could of conclude that superconductivity was not to the hollow cylinder. One should also be aware of be the expected obvi at temperatures above about 25 K. Workers ous fact that magnetic field lines cannot migrate in through this field were amazed when Bednorz uller and [6], M¨ a SC. working in an IBM laboratory in Switzerland, reported Various parts of the experiment will demonstrate that the they had found superconductivity at temperatures striking features of the superconducting state, which of the dif order 40 K in samples of LaBaCu0 with various fer so markedly from the hypothetical perfectconducting concentrations. This is all the more surprising because state. these are ceramic materials which are insulators at nor Incidentally, no perfect conductors are known. mal How temperatures Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 5
The discovery of hightemperature superconductors set Lock off a flurry of experimental investigations in search Solenoid of Collar Solenoid other highTc materials and theoretical efforts to identify Test Coil the mechanism behind their novel properties. It has since DT-470 Diode Test Sample DT-470 Diode been reported that samples of YBaCu0 Tc exhibit at Coil Solenoid Test Coil Valve 90 K with symptoms of unusual behavior at even 2200 Turns higher 810 Turns I.D. 14.0mm, O.D. 16.9mm I.D. 7.1mm, O.D. 10.5mm temperature in some samples. Many experiments Length have 31.0mm Length 12.0mm Effluent Gas been directed at identifying the new type of interaction Probe (I) that triggers the T highc transitions. Various theories have been advanced, but none has so far found FIG. complete 2: Diagram of probes I. The distance from the top of acceptance. the lock collar to the bottom of the probe is 30.5”.
5. EXPERIMENTAL APPARATUS bottom of the Dewar and repeat the distance measure ment. Once the dipstick has been lowered to the bottom, 5.1. Checking the level of liquid Helium in it the may get clogged with frozen sludge which has collected dewar in the bottom of the Dewar, and you may have trouble in exciting further throbbing. If this occurs and you want to A “thumper” or “dipstick” consisting of a 1/8” continue tube measurements, raise the stick until the tip just about 1 meter long with a brass cap at the comes end is out used of for the Dewar and start again. Both partners measuring the level of liquid helium in the Dewar. should The assess the level independently. A depthvolume cap is closed with a thin sheet of rubber so calibration that pres curve for the Dewar is taped to the wall next sure oscillations in the tube can be more easily to the sensed experiment. (thumpers are often used without this membrane). Straighten The the dipstick before and after insertion it tube material, being a disordered alloy of CuNi, is has easily very bent, so take care. Be sure to record the depth low thermal conductivity (over three orders of magnitude reading on the Usage Log Sheet on the clipboard above less than that of copper!) particularly at low the tempera experimental station before and after Dewar use. ture and will conduct very little heat into the You helium. will be using three different insert probes which The measurement consists in sensing the change contain of fre different active components. Each probe is essen quency of pressure oscillations in the tube gas tially acting a on long, thinwalled stainless steel tube which can the rubber sheet between when the lower end be is inserted below and positioned in the neck tube of the De and above the liquid level. war. A rubber flange is provided on the probe for sealing After removing the neck plug, hold the dipstick between verti the probe and Dewar neck so that the helium cally above the Dewar and lower it slowly into gas the can neck escape only through the probe tube. Various at a rate which avoids excessive blasts of helium labeled gas electrical be leads from the thermometer, coils and ing released from the Dewar. During the insertion, fieldsensor keep emerge from the top of the probe tube. He your thumb on the rubber sheet and jiggle the lium tube gas up flows up the probe tube, cooling it, and escapes and down slightly as you lower it so as to through avoid station a side valve at the top, either directly to the at ary contact with the neck surface and possible mosphere freezing or through a gas flow gauge – needle valve – of the tube to the neck. When the bottom end vacuum has pump got system which permits accurate control of ten cold with no noticeable release of gas from the the sample Dewar temperature. neck, you will notice a throbbing of the gas column Probe which I has provision for changing the samples (Pb, V changes in frequency and magnitude when the and end Nb), goes each in the form of a small cylinder of common through the liquid helium surface. Vertical jiggling diameter of the 0.60 cm. The samples are inserted in a thinwall dipstick may help to initiate the excitation. This hollow pulsing brass cylinder around which is wound a test coil of is a thermal oscillation set up in the gas column dimensions of the given in Figures 2 3 and 4. Around the test dipstick by the extreme thermal gradient, and it coil changes is wound a solenoid coil which is longer than the test upon opening or closing the lower end of the coil tube. and sample, and which can produce a magnetic field When the probe is in the liquid, the throbbing penetrating is of low both test coil and sample cylinder. Imme frequency and constant amplitude. When pulled diately above above the centered sample is a small commercial the surface of the liquid, the frequency increases silicon and diode the (Lakeshore Model DT470). All electrical amplitude dimishes with distance away from the lines liquid run up the probe tube to the connections at the surface. Identify this change by passing the thumper top. tip up and down through the surface a number of times, The rubber and flange connection on each probe seals the have your partner measure the distance from the Dewar stick neck tube to the probe tube, thereby forcing the top to the Dewar neck top. With a little experience helium gas you to escape through the probe tube. The rubber should be able to establish this to within a millimeter flange should or be stretched over the lip of the Dewar neck so. Following this measurement, lower the dipstick and to tightened. the A knurled, threaded ring at the top of the Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 6
Solenoid 2210 Turns I.D. 14.3, Length 44.5mm
Hall Hall Carbon Resistor Sensor Solenoid Carbon Resistor Lead Tube I.D. 11.0mm, O.D. 14.0mm Length 90mm
85.0cm Probe (II)
FIG. 3: Diagram of probe II. The distance from the top of the lock collar to the bottom of the probe is 30.5”.
FIG. 4: Placement of the sample in probe I. The test coil has 810 turns of wire with a 7.1mm ID and a 10.5mm OD. It’s length is 12.3mm
flange connector permits one to slide the probe tube up or down relative to the rubber flange connector (which of course is in fixed position on the Dewar). This controls the position of the sample in the Dewar neck. A a small back and forth twisting motion during the process eases the motion. Never apply excessive force in sliding the probe tube along the flange. The lock collar on the tube and the side valve tube may be used with FIG. reason 5: Illustration of typical storage Dewar. able restraint as pressure points for providing sliding or twisting. On the top part of the rubber flange assembly, a small gas exit line contains a check valve which judiciously serves positioning the tip of the probe in the De as a safety release if the pressure in the Dewar war exceeds neck tube a and varying the gas flow, we can control set point. Do not disturb it. the temperature of the sample. This can be done by The insert probes are delicate and must pumping be han the gas through a needle valve (for control) and dled with care. This means that they a should flow gauge (for measurement). In this procedure the not be bumped against other objects nor strained normal liquid helium boiling rate is accelerated so that when maneuvering them into or out of the more Dewar. cold gas passes by the sample, thereby reducing its A storage rack is provided for holding them when temperature. not in use. When insterting or withdrawing the probes, Experience with our probes has shown that a good op keep them strictly vertical, no bending please!!! erating position of the bottom of the probe is found to be about x=10 cm (for probe I) andx=4 about cm for probe II above the bottom of the Dewar neck. At these insert 5.2. TEMPERATURE CONTROL OF SAMPLES positions, variation of the flow over the gauge range will provide temperature control over the range of interest (4 Temperature control of the various samples is 20 achieved K). Gas flow is controlled with a smallangle needle by control of the flow rate of cold helium gas valve passing connected the in series with the flow gauge. Use the samples and thermometers in the probe tips. OPENCLOSE valve to isolate the vacuumpump from The probes are designed so that all exiting helium the system gas and stop the pumping. Never close the must pass by the sample and its nearby thermometer gas flow by tightening the metal needle valve to once the probe is sealed on the Dewar. A its large fully tem closed position. This can damage the fine perature gradient exists along the Dewar neck tube. needlesurface. By Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 7
Measure the length of the probes using the lock center collar valve on the tank (turning counterclockwise (Fig 5 ) as a reference so that you know how to looking position down opens it) releases highpressure gas the probes to their desired xpositions. Make a sketch in (as read on the gauge) to a pressureregulating your lab notebook, it is important! valve on the side. Turning the pressureregulating handle, clockwise, controls the pressure of exiting gas. After turning this handle counterclockwise so 5.3. TEMPERATURE MEASUREMENT that no gas is released, connect the exit tubing to the local flow gauge and then to the top exit valve In Probe I, a Silicon diode, located 1 cm above the (set sam OPEN) of the probe tube. ple is used to measure the temperature. A curThe 10µ rent from the source box through the diode in the Carefully forward turn the handle clockwise to start the gas direction causes a voltage drop ∼ 0.5V of at 300K, which flow through the tube until you can just hear it flowing changes little until ∼ 20K, but there changes rapidly from to the bottom of the probe. You should feel a modest flow of gas emanating from the bottom tube holding the ∼1.6V. Using Table I you can determine the tempera ture of the sample material. sample. Continue this flushing operation for 5 10 secs then close the valve on the probe. Important: Keep the open end of the probe pointed down so that the trapped helium gas will not escape! 6. EXPERIMENTAL PROCEDURE:
6.1. Preparing the probe 6.2. Precooling the probe
1. Place the probe on the table near the helium 1. Start gas with the probe in the extended position using tank. The probe assembly should be at room the tem knurled knob assembly After clearing the inside perature and dry. If it is damp from condensation, surface of Dewar neck tube with the neck reamer, use the warm (not hot) air blower and Kleenex hold for the probe tube assembly vertically above the blotting. neck and lower it into the Dewar. Get your instruc tor or TA to help you with this and the following 2. If you are using probe I, slide the selected sam operation the first time it is done. Seat the rubber ple cylinder into the small brass tube. Notice that flange over the Dewar neck lip and push (with some the sample fits loosely in the brass tube: this per twisting) the rubber flange down as far as it goes. mits cold helium gas to pass by the sample and The bottom of the rubber will touch the nitrogen thermometer (see Figure 4) and up the probe tube. vent tubes. Tighten the lower hose clamp around Secure the sample in the brass tube by threading the Dewar neck but do not tighten (or release) the a small loop of copper wire through holes in brass top clamp ring. The probe tube is now sealed to the tube and handtwisting the wire ends. Dewar and all exiting gas must escape through the Take special care that the sample and spacer cannot top exit valve which should now be in the OPEN fall out into the Dewar when the probe is position. in the Dewar. When the probe is properly sealed onto the Dewar, all exiting gas must pass up the 2. Connect brass the probe cable to the 9 pin Dconnector tube and out from the probe at the top. at the top. We will want to follow the temper ature during the precooling operation, so connect 3. The rubber flange assembly (for sealing the probe the thermometer leads to the 10 microamp source tube to the Dewar neck) can be slid on the and probe adjust according to the instructions given pre tube by releasing the 0ring pressure with the viously. The voltage across the silicon diode in knurled ring. We try to keep a very light probe film of I should be about ) 0.5 V since we are still grease on the probe tube to facilitate easy sliding. close to room temperature (– in probe II the resis A combination of twisting while sliding will ease the tance should be about 300 Ω). sliding operation. Slide the rubber flange assembly towards bottom of probe tube so that it contacts 3. Slowly lower the probe tube in the rubber flange the upper bumper guard. Tighten the knurled ring. assembly by releasing the Oring pressure with the knurled ring. CAUTION: if the pressure is released 4. Flush the probe tube with low pressure helium too gas much, the weight of the probe may cause it to from the helium gas bottle to displace the air fall in the abruptly. Avoid this by holding the probe tube probe tube and expel or evaporate any condensed when releasing the pressure. A slight twisting of the water droplets that may have collected in conprobe tube in the Oring may be helpful in achiev stricted sections of the probe tube during the ing pre a smooth sliding movement. Continue lowering vious use. Use a gentle flow of dry helium gas the from probe tube until signs of increased exit gas flow a highpressure storage tank to do this. The appear. top Stop at this position, tighten knurled ring, Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 8
and look for signs of thermometer cooling. Watch the bottom. Temperature control at this work the temperature develop using I Table . Depend ing position is performed by pumping on the he ing upon the liquid helium level in the Dewar, lium you vapor at various rates with the mechanical should notice an increased gas flow and this is pump cool beneath the experimental station and the ing the bottom of the probe. The thermometer flowmeter/needle re valve assembly above the pump. sistance will show very little change until its tem perature gets into the 4070 K range. After waiting a couple of minutes at this 2 cm 6.3. po Measuring Tc for Vanadium sition to see what happens, continue the lowering over the remaining distance in small steps (perhaps After loading probe I with the vanadium sample and 0.5 cm) always waiting a minute after making following a the precooling procedures described earlier with change and locking the knurled ring. The the system probe assembly at the optimum operating height, takes a while to respond to a change in you position. are In ready to experiment with controlling the sam a few minutes the voltage across the temeprature ple temperature. Connect the probe gas exit to the flow sensor should be about 1.6 V indicating gaugecontrol that the valve vacuum pump system. With ON sample is close to 4.2 K. OFF valve closed, turn on the vacuum pump. Slowly During this critical precooling operation, there open the ONOFF valve so as to see gas flow on the should be a modest flow of cool exit gas gauge. – if the This gas can be controlled by adjustment of the metal release becomes uncomfortably cold to your control hand valve and with fine adjustment through the teflon held 4 inches from the exit tube, back micrometer up a little valve. Notice the thermometer response af and let the system settle down before continuing ter making an adjustment. Remember that the system the operation. You should be seeing a thermometer takes some time to adjust to a new equilibrium condition response depending upon this gas flow. Continue – be patient and don’t hurry the operations. the lowering to the lock collar limit and allow Determine the Tc by observing the change of mutual in system to equilibrate, at which time the ductance gas flow between the solenoid and the test coil when should have decreased. the electrical conductivity of the enclosed sample changes abruptly. High conductivity implies that surface currents 4. If you do not see cold gas being released will through be induced in a sample if the external field (from the the top exit valve (and an associated increase solenoid) of is changed with correspondingly less field pen thermometer resistance) during the lowering operetration into the sample volume. If an AC current is ation over the last few centimeters, the probe passed tube through the solenoid, the flux passage through may be blocked and the precooling operation the must test coil (and hence the inductive signal in the test be stopped. Cold gas escaping from the coil) safety will depend upon the sample conductivity. If con release tube on the side of the rubber flange ditions assem were ideal, the existence of the Meissner Effect bly (with consequent cooling and frosting of would nearby imply no flux passage in the superconductor and metallic components) is another indication that hence the zero test coil signal at temperatures Tc. Our below probe tube is blocked. With a normal precooling conditions are not ideal, but there will still be a recog gas flow, only the top section of the metal nizable compo change at the transition, permitting an accurate nents of the probe tube will get cold and determination frosted. of Tc. This frosting will melt and should be wiped Connect with a a function generator, set for a 200 Hz sine cloth once the small equilibrium gas flow has wave, been at 500 RMS mV amplitude to Channel 1 of the attained. If there is any evidence of blockage oscillosope in and teeit to the solenoid marked “OUTER the probe tube, remove it from the Dewar, COIL”. place Because it of the low impedence of the outer coil on the table, warm the assembly to room (5.8Ω), temper the function generator will be loaded down and ature with the cold air blower, dry, and the flush measured with amplitude on the scope ∼100 will be helium gas. Then reinsert the tube into Dewar mVRMS. as Connect the the “TEST COIL” output to above. IF YOU SEE BEHAVIOR OTHER Channel THAN 2 of the oscilloscope and observe the induced THAT DESCRIBED OR ANYTHING NOT signal AN (it should be about RMS 56 with mV the sample TICIPATED, CONSULT YOUR INSTRUCTOR. in the normal state). Observe the sudden reduction of the test coil signal when the sample is cooled through 5. After you have attained precooling thermal the equi transition, and viceversa, by manipulation of the librium (with a very small exit gas flow), gas the flow ther rate. Watch out for the inductance between mometer resistance should indicate a temperature the signal conductors to the “OUTER COIL” and the below about 30 K. You can then proceed “TEST with the COIL” near the point where they enter the cable experiments. These are best performed with together. the sample located in the neck of the dewar. For To Probe measure Tc, record both the test coil signal and the I, place the sample 10cm above the bottom temperature of the sensor voltage simultaneiously. With expe neck and for Probe II, place the sample rience, 4cm above you can adjust the gas flow rate so that the tem Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 9 perature drifts slowly through the transition value gas during flow rate and again establish the thermometer resis which you and your partner can record both tance signal at and the midrange test signal value which is being temperature sensor values. A slow drift of the held temper constant in time. ature will achieve close agreement between sample You and can calculate the magnetic field at the sample from thermometer temperatures. A graph of these quantities the solenoid parameters given earlier and what you ex can be used to assess the resistance of the thermomepect for , ΔT as indicated by Figure 1. Note that from ter at the transition, and Tc. hence Do this a number Equation (1), we have the useful relation of times, in both directions, upward and downward in temperature, looking out for possible hysteresis action, dB 2B and noting how reproducibly the transition can be es c | = 0 (5) dT @Tc T tablished. Tc values are usually taken at the midpoints. c Make graphs of these drift runs as you take them Both – measurements, seeing DC ON and DC OFF, should be them displayed can help with the next one. made under identical conditions. Experience has shown that the hysteresis difference between cooldown and warmup transition curves is strongly dependent upon the speed of passage 6.4. through TRANSITION TEMPERATURE OF OTHER the transition. This is probably due to different time SAMPLES constants associated with temperature flow in (or out) of the sample rod relative to that of the temperature After sensor. you have finished the measurements on vana dium, withdraw the probe from the Dewar neck in the prescribed manner, close the Dewar neck, and carefully 6.3.1. CHANGE OF Tc IN VANADIUM WITH place the probe tube horizontally on the lab table. Parts MAGNETIC FIELD of the probe tube are very cold and will frostup. There is an air blower available to speed its warmup. (CAU According to the phase diagrams of Figure 1 TION: and equa the air blower blows either roomtemperature air tion (1), the presence of a constant DC magnetic or very field hot on air according to the switch setting – DO NOT the sample will shift the superconducting transition direct to hot a air on the probe or you will damage insulation lower temperature. We can see and measure this components shift if on the probe). It is prudent to keep one hand we apply DC current to the solenoid in addition hand to in the the air stream to guard against this. After the AC current needed in the measurement process. probe Since has warmed to room temperature and the frosting there is a limitation on the magnitude of the has DC disappeared, mag water droplets will remain. They should netic field that can be 2R used losses (I in the solenoid be gently blotted (not rubbed) dry with a Kleenex tissue. fine wire would perturb the temperature distribution), Be careful never to insert anything with moisture on its the magnitude of the transition temperature shift surface will be into the Dewar neck. very small and careful measurements must be made The to vanadium rod will slide out from the probe into observe the effect. your hand (NOT dropped on the floor) after removing This is best done by finetuning the flow rate the so twisted that clamp wire. The small sample cylinders the test coil inductive voltage is being held fixed are in delicate time (and expensive), so do not mishandle at the midpoint between the SC and NC signal them levels – keep them in the storage box when not in which you have established from the transition use graphs so that they don’t get lost. of the previous section. If this is accomplished then the drift rate effects are eliminated and the thermometer re sistance at the midrange set point can be used as 6.4.1. a TRANSITION tem TEMPERATURE OF LEAD perature marker. Repeating the same type of measure ment with the magnetic field on can then observe Replace the the vanadium sample with the lead sample and shift in critical temperature. We note that this its procedure brass spacer and follow the same procedure described for measuring Tc Δalso eliminates the effect of a possible ealier for obtaining its transition temperature. You will temperature difference between sample and thermometer find for the lead sample that the inductive signal in the caused by their different positions in the gas stream. test coil decreases slowly with lowering temperature as After getting the midrange set point data for you zero approach DC Tc followed by an abrupt, discontinuous magnetic field, connect the output of the solenoid change DC when the sample becomes superconducting. This Current Supply Box in parallel with the AC current small change, sup occurring when the sample is still a normal ply and adjust to a DC current of 150 mA. conductor, In connecting reflects the temperature dependence of the the DC and AC sources in parallel, the output AClead voltage normal conductivity above Tc but is NOT part of the from the audio oscillator will drop (there is extra superconducting load on transition. Lead is a good conductor at it). You should readjust this to a standard 70 these mv temperatures. RMS. Now redetermine the SC and NC test coil signal You levels may also notice that the magnitude of the frac (they may differ from the earlier levels) by varying tional change the in inductive signal in going Tc for through Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 10 lead is smaller than it was for vanadium. This again re6.5. TRANSITION IN NB flects the higher conductivity of lead Tc. above If you are careful in adjusting the RMS value of the voltage Determine being the transition temperatures for Nb in the applied to the solenoid so that it is the same same for way the as lead you have done for vanadium and lead above. case as it was for the vanadium case, you Lead should is find a Type I superconductor which means that the the same value for the SC inductive signal. The transition sample is very sharp, unlike Type II superconductors. geometry is the same and infinite conductivity Tc below Type II superconductors have “vortices” in them which characterizes both samples. On the other hand, the allow mag for small regions with magnetic fields – as long as nitude of the inductive signal Tc above depends upon the the “width” of these vortices are smaller than the pene normal state conductivity and this varies from sample tration to depth, this behaviour is allowed. These vortices sample, and in fact is a measure of it. act to slow the transition from “normal” to “supercon ductor.” This is why the Niobium and Vanadium (two of the only three elemental Type II superconductors) show rather wide transitions compared with that of lead. 6.4.2. MEISSNER EFFECT IN LEAD
When you have the lead sample in probe I for deter7. PERSISTENT CURRENT IN A mining its Tc value, you can do another experiment that SUPERCONDUCTOR (PROBE II) unequivocally demonstrates the Meissner Effect, namely, the flux exclusion from a superconductor. By applying We can demonstrate the existence of a persistent cur a DC magnetic field to the sample in the NC rent state in a and superconductor using the hollow lead cylinder then simply cooling it T below c, the flux should be sample sud in Probe II. According to an earlier discussion, if denly expelled in a transient manner. This would we induce apply an axial magnetic field to the T sample , above a transient voltage (and current) in the test coil of our c cooling the sample below Tc will generate two oppositely assembly. We can see this transient signal by flowing connect persistent currents on the inside and outside sur ing the test coil to a current integrating circuit faces (for of total the cylinder. Thereafter, removing the external charge measurement) as available in a circuit box. field will remove the outsidesurface current but leave the The transient current integrator is simple opamp insidesurface cir current producing the frozeninflux inside cuit, with the induced voltage delivered from the the test cylinder. coil We can measure this flux, or magnetic field, being amplified and driving a speaker. with the Hall magnetic field sensor, which is positioned Apply a DC field with the solenoid current along supply the tube axis of Probe II as indicated 3 . in Fig. (≈200 mA) in the normal state and connect the Probe test coil II contains a hollow cylindrical sample of pure output into the current integrator box with the lead box (I.D. out 1.11 cm, O.D. 1.43 cm, length about 9 cm) put to the oscilloscope. Set the oscilloscope for around a slow which is wound a solenoidal coil of fine Cu wire ‘rolling display mode’ ≈ 2 ( sec/division) and for AC(2210 turns, length 4.45 cm). Current in the solenoidal couple the input, so that you can see the transient coil will change produce a reasonably uniform magnetic field in potential. Upon cooling the sample Tc through with throughout its volume. The field strength can be cal gas flow regulation, a kick in the oscilloscope beam culated should from the dimensions of the coil and the current. be observed (up or down) indicating flux passage outward Inside the lead cylinder and along its axis is a tiny mag through the test coil. Warming the sample Tc through netic field sensor (a Hall field probe described later) and should give an oppositely directed kick when also the field a small thermometer (a carbon resistor). The elec goes back in. You can check the absolute sense trical of the lines di run inside the probe tube to the connections rection by merely turning off the solenoid current at the when top of the probe. All of the components of probe II the sample is in the normal state. With our are charge in a fixed assembly and will remain unchanged during measuring circuit, the inductive kick is on the the scale experiment. of 100 mV, so set the oscilloscope sensitivity appropriately. Probe II uses a small carbon resistor to determine the It is to be emphasized that this test for the sample presence temperature. It’s resistance varies ∼ 300Ω from of the Meissner Effect is a most unequivocal at one room for temperature a ∼ 2000Ω to below 20K. Simply us superconductor. It does not occur in a PC. There ing an have ohmeter to measure the resistance would produce been reports in the literature of experiments in too which much the heating 2R (= I 10−4W). We therefore limit sample’s electrical conductivity ) ( was σ found to change the current I to 10A µ using the current source box and drastically with Tc (so one would observe an AC test measure coil the voltage drop in which case the power dissi signal change), yet the Meissner action failed to pated appear. is ∼10−6W. The calibration is not given, you will An abrupt change in normal conductivity could have accom to establish it T using c for lead. pany, for example, a crystallographic transition occurring In a Hall probe a longitudinal DC current is passed at low temperatures, and this could mimic a through supercon a semiconductor (InSb in our probe) in the pres ducting transition in producing an AC mutual inductance ence of the magnetic field to be measured. A transverse change. potential appears across the material which varies lin Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 11 early with the magnetic field and with the DC the current. carbon resistance thermometer Tc. at With the DC Our Hall probe has a sensitivity of about −1 20 , mV field gauss on, arrange the gas flow so that the temperature as you will determine, when operated with a drifts standard down slowly through the transition region. Record DC current of 35 mA at low temperature. A your Hallprobe thermometer resistance and Hall voltage readings circuit box is located at the experiment station. as Before the change occurs. Graphing these data as you go using it for field measurement, it must be balanced along with will help you to determine the resistance of the a bias voltage in zero magnetic field. thermometer at the transition. Probe II should be flushed first with helium gas Now as in de this SC state, turn off the solenoid current scribed earlier. The lock collar on probe II supply is in (and fixed this is the “punchline”), and observe that position 85.0 cm above the sample and thus the this field probe remains. This shows that there is a persistent can be lowered farther into the Dewar than probe current I. on It the inside surface of the lead cylinder with is imperative that you use Figure 5 to help no determine outside field. Flowing without resistance, the current the position of the probe bottom after it is inserted should continue into indefinitely as long as the lead sample the Dewar. After insertion, follow the same precooling is in the superconducting state. You have thus made a sequence as with probe I and approach low temperature “Persistent Current Superconducting Magnet” like those thermal equilibrium at the position where the probe which bot are now commercially available and which have tom is 2 cm above the Dewar neck bottom. almost The resis entirely replaced electromagnets in technical ap tance of the carbon thermometer will be about plications 2800Ω where steady, uniform highintensity fields are at Tc ≈ 7 K for lead (and 300Ω at room temperature). required. If the sample is now warmed slowly by reducing The thermometer response and gas release pattern the offer cooling gas flow, the internal frozenin field will sud guidance in this precooling. After stability is attained, denly disappear (quench) at the transition. Record the raise the probe ≈ to 4 X cm where the experiment is resistance best and Hall voltage readings during this change performed and connect the gas pumping system and for tem compare with the earlier cooldown graph. (What perature control. Practice controlling the temperature. happens to the magnetic field energy when a quench oc Connect the DC solenoid current supply box curs?) to the solenoid and the Hallsensor current and potential Another leads series of observations will show that one can to the Hall probe box, taking care to match generate the color a “frozenin zeroflux” state. With zero field, codes. After bringing the probe temperature to cool low tem the sample below Tc and then turn on the field by passing a DC current through the solenoid. What is the perature but above Tc so that the lead sample is in the normal state, turn on the Hall current (35 mA Hall by probe ad response during these steps, and how do you justment of rheostat control). With zero solenoid explain cur it? You can now understand why superconduct rent (hence zero magnetic field), adjust the bias ing control assemblies are sometimes used to provide nearly per so that zero Hall voltage (less than 2 mV) fect is read shields on against electromagnetic disturbances, as in the most sensitive voltage scale of the Agilent the 34401A experiment now under development at Stanford Uni multimeter. This bias adjustment must be done versity at low to detect the LenseThirring effect on a gyroscope temperature, namely when the thermometer resistance in orbit is about the earth. about 14001500Ω. Now apply 100 mA of DC QUESTIONS: solenoid current from its supply box and measure the Hall 1. voltage Is there an upper limit to the magnitude of this (it should be around one millivolt) corresponding to persistent the current and frozen field that we can gen magnetic field at the Hallsensor that is produced by erate the in our sample? Why? solenoid current. This serves to calibrate the Hallsensor since you can calculate the field produced by the 2. solenoid What current can we pass along a long SC wire of current. The Hall voltage should be proportional to radius the 1 mm and still expect the wire to remain field and you can get a calibration curve for the superconducting Hall (use lead wire at 4 K)? probe by measuring the Hall voltage for several values of the solenoid current. 3. What is the areal current density −2 (amp ) in cm After activating the Hallsensor when the lead samthe persistent current that you measured (assume −6 ple is NC and measuring the field, reduce the sample λL = 10 cm), and how does it compare with temperature so that it is SC (by increasing the gas that flow) flowing in a wire (1 mm diameter) supplying thereby inducing the two persistent surface discussed eara household 100watt light bulb? lier. For ideal conditions (long solenoid, long tube, com plete Meissner effect), we expect no change in the field at the Hallsensor. With our geometry, you will probably 8. THE JOSEPHSON EFFECTS notice a small drop in the magnetic field at the transi tion Tc, but the important observation is that the The field passage of electrons through a A) ˚ thin in (<50 inside the open area of the tube is maintained. sulating This small barrier is a wellknown example of quantum change in Hall voltage Tc can at be used to identify mechanical the tunneling. The currentvoltage (IV) char onset of the transition and in essence it serves to acteristic calibrate of such a barrier is ohmic (linear) at low bias. Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 12
In accordance with the exclusion principle, the [3]. current He derives the following relations: is proportional to the number of electron states per unit energy in the conductors on either side of the barrier. J(t) = J0 sin δ(t) (6) Giaever [7] discovered that if the electrodes are su perconducting the curve becomes highly nonlinear and with the current remaining nearly zero for voltages up to 2e � δ(t) = δ + V (t)dt (7) V = 2Δ/e, where Δ is the superconducting energy gap, 0 h as illustrated in Figure 6. where J is the Josephson current density, δ(t) is the phase difference across the junction, V is and the voltage across the junction. These simple equations are the basis of the theory of both the dc and ac Josephson effects.
8.1. THE DC JOSEPHSON EFFECT
If the coupled superconductors are linked to a current source by an external circuit, the tunneling current that flows without a voltage is given by the first equation. The maximum critical current, j0, which corresponds to a phase difference π/ of 2, is proportional to the strength of the coupling across the barrier, and is determined by the dimensions of the barrier region, the materials and the temperature. It is inversely proportional to the normal ohmic resistance of the junction at roomtemperature. With a dc voltage across the junction, the current will FIG. 6: Single particle tunneling at T = 0 oscillate K at a frequency given by
2e −1 According to the BCS theory of superconductivity, all ν = V0 = 484 MHz µV (8) h of the electrons near the Fermi level (at 0 K) are con densed into pairs of opposite spin and momentum. In Single the V �= 0 region the current oscillates too fast to electrons are not available for the tunneling process be seen nor on the low frequency IV plot, averaging to zero. are there any available electron states to receive them. As Feynman As points out, one obtains the curious situation the voltage is raised to the energy gap, pairs that, are broken with no voltage across the junction, one can have up into normal single electrons (quasiparticles) a which large current but if any voltage is applied, the current exhibit ohmic tunneling. oscillates and its average goes to zero. The current will The remarkable discovery of Josephson [8] was remain his the zero as the dc voltage is raised until, as mentioned oretical prediction that not only can the quasiparticles above, the (Giaever type) quasiparticle tunneling region tunnel through the insulating barrier; the Cooper is pairs reached at the gap V voltage, = 2Δ/e. This type can also do so, provided that the barrier is of small curve, com illustrated in Figure 7, is sometimes obtained pared to the decay length of the wave function but, of more the commonly, with the circuitry that we will be Cooper pairs in the barrier < 10A˚). ( This is a conseusing, the results look like Figure 8. In this experiment quence of the inapplicability of the exclusion principle the current to will be swept by a symmetrical sine wave pairs which are, in effect, bosons. so that the currentvoltage characteristics will appear in When the two superconductors are separated bytwo a large quadrants of the plane. Note the hysteresis which insulating barrier, the condensed state of the Cooperpair is usually too fast for the oscilloscope to record. It can, bosons in each can be described by a wave function however, with a be observed by reducing the bandwidth of the single value of phase. But as the barrier becomes Y amplifier smaller, on the oscilloscope. phase correlations extend across the intervening space and the two superconductors act like coupled oscillators. The isolated pieces of superconductor begin to act like 8.2. a THE AC JOSEPHSON EFFECT single superconductor although the superconductivity in the insulating region is weak (i.e. the order parameter, There are two categories of high frequency effects which is a measure of the ratio of pairs to single which can electrons be observed in these systems, though not with is small) and electromagnetic potentials can be sustained the equipment of this experiment. We have seen that the within the barrier. application of a dc voltage across the junction causes the Perhaps the most accessible description of the current theory to oscillate at the frequency shown in Equation 8. of the Josephson effect has been provided by An Feynman applied voltage of approximately µV produces 50 24 Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 13 the exposed surface. Next another stripe, running per pendicular to the first stripe and consisting of the same or different superconducting metal, is deposited on top of the oxide layer. Tunneling occurs between the two stripes in the rectangle of oxide in the crossing area. The niobiumlead junctions used in this experiment and shown in Figure 9.
FIG. 7: Tunneling IV curve showing both Josephson tunnel ing and singleelectron (quasiparticle) tunneling
FIG. 9: Photograph of the Junior Lab Josepshson Junction chip provided by Dr. Will Oliver of MIT’s Lincoln Laboratory and Professor Terry Orlando of MIT.
The dimensions of the junction µm are x 5 µm 5 and the critical current is A µ 10mµ−2 . The aluminum ox ide barrier thickness is 1.5 2.0nm. There is an addi tional very thin layer of aluminum between the oxide layer and the Nb but this should have a negligible effect on the penetration depth. This The London penetration depth for Nb T at = 0K is 39nm. This value changes FIG. 8: Typical oscilloscope trace of Josephson junction slightly IV at T = 4K, through a correction factor that is −1/2 curve. � 4 = 1 − (T/Tc) which is about 1.02 T = at 4K. Thus GHz oscillations, corresponding to Kband microwaves. Such oscillations have been detected with extremely sen λL ≈ 39nm × 1.02 (9) sitive apparatus. Feynman explains that if we apply a highfrequency voltage in addition to a dc voltage to the junction, and if the frequency is related to the The dc junction volt is mounted on the bottom of the third age by the above relation, we will get a dc probe, component and of 6 electrical lines (4 for the junction IV mea the Josephson current. This can be seen as steps surements in the and 2 for the solenoid) run up the inside of IV curve at voltages corresponding to harmonics the of probe the tube to the blue junction box on the top of the applied frequency. probe. The Josephson Junction chip used in this lab actually has two junctions in the circuit (Figure 10), but only one 8.3. JOSEPHSON JUNCTIONS of them is active in the experiment. The active junction is 5m µ × 5µm in area, and is probed by sourcing current Thinfilm tunnel junctions are commonly made from by de I+ to I, while measuring the voltage drop from V+ positing a narrow stripe of the superconducting to metal V. on an insulating substrate, usually glass, and then causing A photograph of the probe assembly is shown in Fig an oxide layer of the desired thickness to build ure 11. up on Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 14
FIG. 10: Schematic circuit for Josephson Junction chip. The junctions are denoted × by symbols, and represent regions where two niobium layers overlap with a thin layer of insulat ing oxide between them.
the long side; do not use that. Frequencies faster than 100 Hz can work.
A current spike at V=0 represents the Josephson cur rent. Record this current; you can deterimine its mag nitude by finding the vertical distance between the two points where the IV curve becomes nonlinear. The curve obtained should resemble Figure 8 although the horizon tal parts switch so fast they may not show up on the scope. It should be possible to estimate the supercon ducting energy gap from this curve. The magnitude of the zerovoltage Josephson current is strongly dependent upon magnetic field, and it is just this dependence which provides the basis for Josephson devices such as SQUIDs (superconducting quantum interference devices.) FIG. 11: Photograph of the Junior Lab Josepshson Junction Probe Assembly. Note that the outer solenoid is shown The dis probe includes a solenoid which provides a mag assembled. netic field in the plane of the junction. Using a DC power supply, vary the field in the ±30 range Gauss (you should 8.3.1. JOSEPHSON JUNCTION EXPERIMENTS use the known value of the flux quantum and the dimen sions of the junction to calculate aprori the range of B 1. Hook up V + and V − to the preamp inputs fields us to explore). The coil has been designed to give a ing two BNC cables. Set the preamp to field AB of and 110 Gauss −1 and A the calibration is shown in FLAT. Figure 13. 2. Hook up I+ and I− to the output of the blue inline Plot the maximum value of the zerovoltage Josephson 1K resistor box. The other end of the box current should against be the magnetic field. From this and the connected to a BNC tee, which is then dimensions connected of the junction cited above, you can estimate to the HP function generator. the magnitude of the flux quantum (see Reference [9]). 3. Connect the third output of the BNC tee to scope channel 1 (the X input). 1. Hook up the HP variable supply power to the solenoid BNC input. Put into constant current 4. Connect the preamp output to scope channel 2 mode (the and vary current (and polarity) continuously Y input). to observe the change in the supercurrent. 5. Set the function generator to output a 100 Hz tri angle wave, 2 V peaktopeak. 2. You should be able to see at least Be two zeros. careful not to apply very large currents to the 6. You should see a nonlinear voltage spectrum. solenoid. You may also want to have the scope av Putting the scope in XY mode will give the IV erage trace the preamp output signal to reduce its noise. similar to that shown in Figure 12. Also note that the blue resistor box has a third BNC connector, on Other useful references include Superconductivity: [10–12], for Josephson Effects: [13–15], for Miscella neous Topics: [16, 17].
FIG. 12: Typical results with the Junior Lab Josepshson Junction Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 15
2500 data 2 linear
2000
y = 1.1e+02*x + 19
1500
1000 Magnetic Field (mG)
500
0 0 2 4 6 8 10 12 14 16 18 Current (mA)
FIG. 13: Calibration of the Josephson Junction solenoid mag netic field versus current.
[1] F. London and H. London, Proc. in Roy. Soc. (1935), pp. ical Review 102 (1954). 71–88. [2] L. C. J.R. Schrieffer and J. Bardeen, Physics Today pp. 23–41 (1973), qC.P592 Physics Department Reading APPENDIX A: EQUIPMENT LIST Room. [3] R. Feynman, Lectures on Physics, vol. III (Addison Wesley, New York, 1966), qC23.F435 Physics Depart ment Reading Room. Model Description Source [4] R. L. Liboff, Introductory Quantum Mechanics (Holden Agilent 54621A Oscilliscope agilent.com Day, 1980), qC174.12.L52 Physics Department Reading Room. Agilent 34401A Multimeter agilent.com [5] C. Kittel, Introduction to Solid State Physics, vol. Wavetek III 142 Waveform Generator manualman.com (Wiley, New York, 1976), qC176.K62 Science Library Welch R1402 Pump sargentwelch.com Stacks. MIT Pump Equipment n/a [6] Bednorz and uller, M¨ Z. Phys. B64 (1986), qC.Z483 Sci MIT Probes n/a ence Library Journal Collection. [7] L. Esaki and I. Giaever, Nobel lectures: Experimental disMIT Depth Probe n/a coveries regarding tunneling phenomena in semiconducMIT Reamer n/a tors and superconductors (1973). MIT Samples (Pb,Va,Nb) n/a [8] B. D. Josephson, Nobel lecture: Theoretical predictions MIT of Hall Probe Control n/a the properties of a supercurrent through a tunnel barrier, in articular those phenomena which are generally MIT known Transient Current Int n/a as josephson effects (1973). MIT 10 microA Current Source n/a [9] D. Scalapino, Encyclopedia in of Physics, edited by MIT Josephson Box n/a R. Lerner and G. Trigg (AddisonWesley, 1991), pp. MIT 479– Solenoid Cur. Supply n/a 481, 2nd ed. [10] Tinkham, Introduction to Superconductivity (McGraw Hill, 1996), 2nd ed. [11] D. Ginsberg, American Journal of 32 Physics (1964). [12] Superconductivity: Selected Rerprints (1964). [13] D. J. S. D. N. Langenberg and B. J. Taylor, Scientific American 214, 30 (1966), t.S416 Science Library Journal Collection. [14] J. Clarke, American Journal of 38 Physics , 1071 (1970). [15] S. S. P.L. Richards and C. Grimes, Anerican Journal of Physics 36, 690 (1968). [16] L. D. Landau, Pioneering theories for condensed matter, especial ly liquid helium, Nobel Lectures (1962). [17] C. S. W.S. Corak, B.B. Goodman and A. Wexler, Phys Id: 39.superconductivity.tex,v 1.106 2005/02/22 20:00:56 sewell Exp 16
Voltage Kelvin Voltage Kelvin 1.69812 1.4 1.13598 23 1.69521 1.6 1.12463 24 1.69177 1.8 1.11896 25 1.68786 2 1.11517 26 1.68352 2.2 1.11212 27 1.67880 2.4 1.10945 28 1.67376 2.6 1.10702 29 1.66845 2.8 1.10263 30 1.66292 3 1.09864 32 1.65721 3.2 1.09490 34 1.65134 3.4 1.09131 36 1.64529 3.6 1.08781 38 1.63905 3.8 1.08436 40 1.63263 4 1.08093 42 1.62602 4.2 1.07748 44 1.61920 4.4 1.07402 46 1.61220 4.6 1.07053 48 1.60506 4.8 1.06700 50 1.59782 5 1.06346 52 1.57928 5.5 1.05988 54 1.56027 6 1.05629 56 1.54097 6.5 1.05267 58 1.52166 7 1.04353 60 1.50272 7.5 1.03425 65 1.48443 8 1.02482 70 1.46700 8.5 1.01525 75 1.45048 9 1.00552 80 1.43488 9.5 0.99565 85 1.42013 10 0.98564 90 1.40615 10.5 0.97550 95 1.39287 11 0.95487 100 1.38021 11.5 0.93383 110 1.36809 12 0.91243 120 1.35647 12.5 0.89072 130 1.34530 13 0.86873 140 1.33453 13.5 0.84650 150 1.32412 14 0.82404 160 1.31403 14.5 0.80138 170 1.30422 15 0.77855 180 1.29464 15.5 0.75554 190 1.28527 16 0.73238 200 1.27607 16.5 0.70908 210 1.26702 17 0.68564 220 1.25810 17.5 0.66208 230 1.24928 18 0.63841 240 1.24053 18.5 0.61465 250 1.23184 19 0.59080 260 1.22314 19.5 0.56690 270 1.21440 20 0.54294 280 1.17705 21 0.51892 290 1.15558 22 0.49484 300
TABLE I: Probe I Sidiode (DT470) calibration.