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systems. But at the other extremesuperconductors are used in SQUIDmagnetometers, which can measure the tinymagnetic fields associated with electrical activity

in the brain, and there is great interest in theirpotential as extremely fast switches for a newgeneration of very powerful computers.

PROPERTIES OF SUPERCONDUCTORS

1.ZERO ELECTRICAL RESISTANCE

The most obvious characteristic of asuperconductor is the complete disappearance ofits electrical resistance below a temperature that

is known as its critical temperature. Experimentshave been carried out to attempt to detectwhether there is any small residual resistance inthe superconducting state. A sensitive test is tostart a current flowing round a superconductingring and observe whether the current decays. The

current flowing in the superconducting loopclearly cannot be measured by inserting anammeter into the loop, since this wouldintroduce a resistance and the current wouldrapidly decay.

The magnitude of the magnetic field is directly proportional to the current circulating in theloop, and the field can be measured without

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drawing energy from the circuit. Experiments ofthis type have been carried out over periods ofyears, and the magnetic field and hence thesuperconducting current has always remained

constant within the precision of the measuringequipment. Such a persistent current ischaracteristic of the superconducting state. Fromthe lack of any decay of the current it has beendeduced that the resistivity of a

superconductor is less than 1026 m. This isabout 18 orders of magnitude smaller than theresistivity of copper at room temperature (108 m).

Resistivity is the reciprocal of conductivity, that

is, = 1. We prefer to describe a

superconductor by = 0, rather than by = .

2. CRITICAL MAGNETIC FIELD

An important characteristic of a superconductor

is that its normal resistance is restored if asufficiently large magnetic field is applied. Thenature of this transition to the normal statedepends on the shape of the superconductor andthe orientation of the magnetic field, and it isalso different for pure elements and for alloys. If

an increasing magnetic field is applied parallel toa long thin cylinder of tin at a constant

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temperature below the critical temperature,then the cylinder will make a transition from thesuperconducting state to the normal state whenthe field reaches a well-defined strength. This

field at which the superconductivity is destroyedis known as the critical magnetic field strength,Bc. If the field is reduced, with the temperatureheld constant, the tin cylinder returns to thesuperconducting state at the same critical fieldstrength Bc.

Experiments indicate that the critical magneticfield strength depends on temperature, and theform of this temperature dependence is shown inFigure 11 for several elements. At very lowtemperatures, the critical field strength is

essentially independent of temperature, but asthe temperature increases, the critical fieldstrength drops, and becomes zero at the criticaltemperature. At temperatures just below thecritical temperature it requires only a very smallmagnetic field to destroy the superconductivity.

The temperature dependence of the critical fieldstrength is approximately parabolic:

where Bc(0) is the extrapolated value of thecritical field strength at absolute zero and Tc is

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the critical temperature. The curves in Figure 11indicate that a superconductor with a highcritical temperature Tc has a high critical fieldstrength Bc at T = 0 K, confirms this correlation

for a larger number of superconducting elements.

Figure 11 The temperature dependences of the

critical magnetic field strengths of mercury,tin, indium and thallium.

3. THE MEISSNER EFFECTThe second defining characteristic of a

superconducting material is much less obviousthan its zero electrical resistance. It was over 20years after the discovery of superconductivitythat Meissner and Ochsenfeld published a paperdescribing this second characteristic. Theydiscovered that when a magnetic field is applied

to a sample of tin, say, in the superconductingstate, the applied field is excluded, so that B = 0

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throughout its interior. This property of thesuperconducting state is known as the Meissnereffect.

The exclusion of the magnetic field from asuperconductor takes place regardless of whetherthe sample becomes superconducting before orafter the external magnetic field is applied. Inthe steady state, the external magnetic field iscancelled in the interior of the superconductor byopposing magnetic fields produced by a steadyscreening current that flows on the surface of thesuperconductor.

It is important to recognise that the exclusion ofthe magnetic field from inside a superconductorcannot be predicted by applying Maxwell's

equations to a material that has zero electricalresistance. We shall refer to a material that haszero resistance but does not exhibit the Meissnereffect as aperfect conductor, and we shall showthat a superconductor has additional propertiesbesides those that can be predicted from its zero

resistance.

Consider first the behaviour of a perfectconductor. We showed in the previous subsectionthat the flux enclosed by a continuous path

through zero resistance material a perfectconductor remains constant, and this must be

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true for any path within the material, whateverits size or orientation. This means that themagnetic field throughout the material mustremain constant, that is, B/t = 0. The

consequences of this are shown in Figure 10 parts(a) and (b).

Figure 10 A comparison of the response of a perfect conductor, (a) and (b), and asuperconductor, (c) and (d), to an appliedmagnetic field.

In part (a) of this figure, a perfect conductor is

cooled in zero magnetic field to below thetemperature at which its resistance becomes

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zero. When a magnetic field is applied, screeningcurrents are induced in the surface to maintainthe field at zero within the material, and whenthe field is removed, the field within the

material stays at zero. In contrast, part (b) showsthat cooling a perfect conductor to below itscritical temperature in a uniform magnetic fieldleads to a situation where the uniform field ismaintained within the material. If the applied field is then removed, the field within the

conductor remains uniform, and continuity ofmagnetic field lines means there is a field in theregion around the perfect conductor. Clearly, themagnetisation state of the perfect conductordepends not just on temperature and magneticfield, but also on the previous history of thematerial.

Contrast this with the behaviour of asuperconductor, shown in Figure 10 parts (c) and(d). Whether a material is cooled below itssuperconducting critical temperature in zero

field, (c), or in a finite field, (d), the magneticfield within a superconducting material is alwayszero. The magnetic field is always expelled froma superconductor. This is achieved spontaneouslyby producing currents on the surface of thesuperconductor. The direction of the currents is

such as to create a magnetic field that exactlycancels the applied field in the superconductor. It

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is this active exclusion of magnetic field theMeissner effect that distinguishes asuperconductor from a perfect conductor, amaterial that merely has zero resistance. Thus we

can regard zero resistance and zero magnetic field as the two key characteristics ofsuperconductivity.

Perfect diamagnetism

Diamagnetism is due to currents induced in

atomic orbitals by an applied magnetic field. Theinduced currents produce a magnetisation withinthe diamagnetic material that opposes theapplied field, and the magnetisation disappearswhen the applied field is removed. However, thiseffect is very small: the magnetisation generally

reduces the applied field by less than one part in105 within the material. In diamagnetic material,B = 0H, with the relative permeability slightlyless than unity.

Superconductors take the diamagnetic effect tothe extreme, since in a superconductor the field

B is zero the field is completely screened fromthe interior of the material. Thus the relativepermeability of a superconductor is zero.

4.CRITICAL CURRENT

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The current density for a steady current flowingalong a wire in its normal state is essentiallyuniform over its cross-section. A consequence ofthis is that the magnetic field strength B within a

wire of radius a, carrying current I, increaseslinearly with distance from the centre of thewire, and reaches a maximum value of 0I / 2 a atthe surface of the wire . Within asuperconductor, however, the magnetic fieldB iszero.

The magnetic field strength B just outside thesurface of the wire is 0I / 2 a. It follows that ifthe current flowing in a superconducting wire isincreased, eventually the field strength at thesurface of the wire will exceed Bc and the sample

will revert to its normal state. The maximumcurrent that a wire can carry with zero resistanceis known as its critical current, and for a longstraight wire the critical current Ic is given byIc = 2 aBc / 0. A current greater than Ic will causethe wire to revert to its normal state. This

critical current is proportional to the radius ofthe wire.

We saw that the critical field strength isdependent on temperature, decreasing to zero asthe temperature is increased to the criticaltemperature. This means that the

superconducting current that a wire can carrywill also decrease as the temperature gets closer

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CLASSIFICATION OF SUPERCONDUCTOR

1.TYPE-I SUPERCONDUCTORS: Thesuperconductor in which magnetic field istotally excluded from the interior of thesuperconductor below a certain magnetisingfield Hc and at Hc

the material looses superconductivity and the

magnetic field penetrates fully are termed asType-1 superconductors.

We saw that superconductivity in a tin cylinder isdestroyed when an applied field with strength B0> Bc is applied parallel to the cylinder. However,

when the field is applied perpendicular to thecylinder, as shown in Figure 18, the field strengthat points A and C is substantially greater than thestrength of the applied field at a distance fromthe cylinder, and this is indicated by theincreased concentration of the field lines shown

near these points. In fact, it can be shown thatthe field strength at these points is a factor oftwo greater than the applied field strength. Thismeans that as the applied field B0 is increased,the field at points A and C will reach the criticalfield strength Bc when B0 = Bc/2.

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Figure 18 The magnetic field B in a plane

perpendicular to the axis of asuperconducting cylinder (shown in cross-section) for an applied field with B0 < Bc/2.

.

2.TYPE-II SUPERCONDUCTORS: The

superconductor in which the material loosesmagnetisation gradually rather then suddenlyare termed as Type-2 superconductor.

Figure 23 Surface of a superconducting alloythat had a magnetic field applied

perpendicular to the surface. The darkregions were normal and the light regions

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superconducting. In this case, smallferromagnetic particles were applied to thesurface, and collected where the fieldstrength was largest. The particles

remained in position when the specimenwarmed up to room temperature, and thesurface was then imaged with an electronmicroscope.

QUANTUM THEORY OFSUPERCONDUCTIVITY : BCS THEORY

BCS Theory of Superconductivity

In 1957, Bardeen, Cooper and Schrieffer (BCS)proposed a theory that explained the microscopicorigins of superconductivity, and couldquantitatively predict the properties of

superconductors. Prior to this, there wasGinzburg-Landau theory, suggested in 1950,which was a macroscopic theory. This will not bedealt with here, but Ginzburg-Landau theory canbe derived from BCS theory.

Cooper Pair Formation

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Mathematically, BCS theory is complex, but relieson an earlier 'discovery' by Cooper (1956), whoshowed that the ground state of a material isunstable with respect to pairs of 'bound'

electrons. These pairs are known as Cooper pairsand are formed byelectron-phonon interactions -an electron in the cation lattice will distort thelattice around it, creating an area of greater positive charge density around itself. Anotherelectron at some distance in the lattice is then

attracted to this charge distortion (phonon) - theelectron-phonon interaction. The electrons arethus indirectly attracted to each other and forma Cooper pair - an attraction between twoelectrons mediated by the lattice which creates a'bound' state of the two electrons:

The formation of Cooper pairs is supported by thefact that BCS and the Ginzburg-Landau theoriespredict the charge and mass of the supercurrent'particle' to be 2e and 2Me respectively.

Cooper Pairs - BCS Theory SupercurrentCarriers

The Cooper pairs within the superconductor arewhat carry the supercurrent, but why do theyexperience such perfect conductivity?Mathematically, because the Cooper pair is morestable than a single electron within the lattice, itexperiences less resistance (although the

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superconducting state cannot be made up entirelyof Cooper pairs as this would lead to the collapseof the state).Physically, the Cooper pair is more resistant to

vibrations within the lattice as the attraction toits partner will keep it 'on course' - therefore,Cooper pairs move through the lattice relativelyunaffected by thermal vibrations (electron- phonon interactions) below the criticaltemperature.

APPLICATIONS

1.SQUID :The superconducting quantuminterference device (SQUID) consists of twosuperconductors separated by thin insulating

layers to form two parallel Josephson junctions.The device may be configured as a magnetometerto detect incredibly small magnetic fields -- smallenough to measure the magnetic fields in livingorganisms. Squids have been used to measure themagnetic fields in mouse brains to test whether

there might be enough magnetism to attributetheir navigational ability to an internal compass.

2. SUPERCONDUCTING MAGNETS :Type IIsuperconductors such as niobium-tin andniobium-titanium are used to make the coil windings for

superconducting magnets. These two materialscan be fabricated into wires and can withstand

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high magnetic fields. Typical construction of thecoils is to embed a large number of fine filaments( 20 micrometers diameter) in a copper matrix.The solid copper gives mechanical stability and

provides a path for the large currents in case thesuperconducting state is lost. Thesesuperconducting magnets must be cooled withliquid helium. Superconducting magnets can usesolenoid geometries as do ordinary electromagnets.

3. Superconducting Transmission Lines:

Since 10% to 15% of generated electricity isdissipated in resistive losses in transmission lines,the prospect of zero loss superconducting

transmission lines is appealing. In prototypesuperconducting transmission lines at BrookhavenNational Laboratory, 1000 MW of power can betransported within an enclosure of diameter 40cm. This amounts to transporting the entireoutput of a large power plant on one enclosed

transmission line. This could be a fairly lowvoltage DC transmission compared to largetransformer banks and multiple high voltage ACtransmission lines on towers in the conventionalsystems. The superconductor used in these prototype applications is usually niobium-

titanium, and liquid helium cooling is required.

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4. Superconducting Maglev Trains:

While it is not practical to lay downsuperconducting rails, it is possible to construct a

superconducting system onboard a train to repelconventional rails below it. The train would haveto be moving to create the repulsion, but oncemoving would be supported with very littlefriction. There would be resistive loss of energyin the currents in the rails. Ohanian reports an

engineering assessment that such superconductingtrains would be much safer than conventional railsystems at 200 km/h.

A Japanese magnetically levitated train set aspeed record of 321 mi/h in 1979 using

superconducting magnets on board the train. Themagnets induce currents in the rails below them,causing a repulsion which suspends the trainabove the track.

Numerical

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