The essence of superconductivity and superconductors.

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Electrons in crystal lattice of conductorIn metals such as copper and aluminium, electricityis conducted as outer energy level valence electronsmigrate as individuals from one atom to another,forming electrical current. These atoms form avibrating lattice, the warmer the metal the more itvibrates. As the electrons begin moving through thelattice structure, they collide with tiny impurities orimperfections in the lattice. When the electronsbump into these obstacles they fly off in alldirections and lose energy in the form of heat.Fig 3. Atoms arranged in a crystalline lattice andmoving electrons bouncing off the atoms that are intheir way.The ability of electrons to pass throughsuperconducting material unobstructed has puzzledscientists for many years. The warmer a substance isthe more it vibrates. Conversely, the colder asubstance is the less it vibrates. Early researcherssuggested that fewer atomic vibrations would permitelectrons to pass more easily. However this predictsa slow decrease of resistivity with temperature. Itsoon became apparent that these simple ideas couldnot explain superconductivity. It is much morecomplicated than that.Cooper Pairs and electron-phononinteractionMathematically complex BCS theory relies on anearlier discovery by Cooper (1956), who showed thatin extreme temperatures the electrons are formingthe pairs of two - these pairs are known as Cooperpairs.Cooper managed to found as answer to the questionwhy electrons, which normally repel one another,must feel an overwhelming attraction insuperconductors. The answer to this problem wasfound to be in phonons, packets of sound wavespresent in the lattice as it vibrates. Although thislattice vibration cannot be heard, its role as amoderator is indispensable.Fig. 4. Phonon interaction between electrons of theCooper pair.Figure 4 shows that electron pairs are coupling overa range of hundreds of nanometers, three orders ofmagnitude larger than the lattice spacing. Thesecoupled electrons can take the character of a bosonand condense into the ground state.Normally the electrons are fermions which areparticles with half-integer spin. The fact thatelectrons are fermions is foundational to the buildupof the periodic table.The fermions obey the “Pauliexclusion principle” which states that two fermionscannot have the same quantum state and the samespin.The bosons, however, are particles which haveinteger spin and therefore are not constrained by thePauli exclusion principle. The energy distribution ofbosons is described by Bose-Einstein statistics. Atlow temperatures, bosons can behave verydifferently than fermions because an unlimitednumber of them can collect into the same energystate. The collection into a single state is calledcondensation, or Bose-Einstein condensation. Theboson-like behavior of such electron pairs wasfurther investigated by Cooper and they are called"Cooper pairs". The condensation of Cooper pairs isthe foundation of the BCS Theory ofsuperconductivity.BCS TheoryThe BCS theory explains superconductivity attemperatures close to absolute zero. According to thetheory, as one negatively charged electron passes bypositively charged ions (cations) in the lattice of thesuperconductor, the lattice distorts inwards. This inturn causes phonons to be emitted, which forms adensity of positive charges around the electron.Figure 5 illustrates a wave of lattice distortion due toattraction to a moving electron.Fig. 5. Electron moving in superconducting metalcausing the atoms to distort towards negativecharge.As negatively charged electron passes betweenmetal’s positively charged atoms in the lattice, theatoms are attracted inwards. The distortion of thelattice creates a region of enhanced positive chargeand another electron at some distance in the lattice isthen attracted to this charge distortion - the electronphononinteraction. The electrons are thus indirectlyattracted to each other and form a Cooper pair - anattraction between two electrons mediated by thelattice which creates a 'bound'state of the twoelectrons.The forces exerted by the phonons overcome theelectrons natural repulsion. The electron pairs are134
coherent with one another as they pass through theconductor in unison. The electrons are screened bythe phonons and are separated by some distance.When one of the electrons that make up a Cooperpair and passes close to an ion in the crystal lattice,the attraction between the negative electron and thepositive ion cause a vibration to pass from ion to ionuntil the other electron of the pair absorbs thevibration. The net effect is that the electron hasemitted a phonon and the other electron has absorbedthe phonon. It is this exchange that keeps the Cooperpairs together. It is important to understand,however, that the pairs are constantly breaking andreforming. Because electrons are indistinguishableparticles, it is easier to think of them as permanentlypaired.The identifying characteristics of Type 1superconductors are very sharp transition tosuperconducting state and perfect diamagnetism. Theapplied magnetic field induces eddy-currents on thesurface of the superconductor which then generatethe opposite magnetic field and repels the appliedmagnetic field as described in figure 7.Fig. 7. Induced magnetic field repels completely theapplied field.Figure 7 shows that when an external magnetic field(horizontal abscissa) is applied to a Type Isuperconductor the induced magnetic field (verticalordinate) exactly cancels that applied field until thereis an abrupt change from the superconducting stateto the normal state.Fig. 6. The electron is attracted to the positivecharge density (red glow) created by the firstelectron distorting the lattice around itself, formingthe Cooper pair.The Cooper pairs within the superconductor are whatcarry the supercurrent, but why do they experiencesuch perfect conductivity? Mathematically, becausethe Cooper pair is more stable than a single electronwithin the lattice, it experiences less resistance.Physically, the Cooper pair is more resistant tovibrations within the lattice as the attraction to itspartner will keep it 'on course'- therefore, Cooperpairs move through the lattice relatively unaffectedby thermal vibrations (electron-phonon interactions)below the critical temperature.Type 1 superconductorsThe Type 1 category superconductors are mainlymetals and metalloids that show some conductivityat room temperature. The thirty pure metals are type1 superconductors. They require incredible cold toslow down molecular vibrations sufficiently tofacilitate unimpeded electron flow in accordancewith what is known as BCS theory. Remarkably, thebest conductors at room temperature (gold, silver,and copper) do not become superconducting at all.They have the smallest lattice vibrations, so theirbehavior correlates well with the BCS Theory.While instructive for understanding superconductivity,the Type I superconductors have beenof limited practical usefulness because the criticalmagnetic fields are so small and the superconductingstate will appear at extreme temperature of liquidHelium. Type I superconductors are sometimescalled "soft" superconductors.Fig. 8. Superconductor compared with ordibaryconductor in magnetic field.This phenomenon is called Meissner effect (Fig. 8.)and can be easily demonstrated in a form ofmagnetic levitation. If a small magnet is broughtnear a superconductor, it will be repelled becausedinduced supercurrents will produce mirror images ofeach pole. If a small permanent magnet is placedabove a superconductor, it can be levitated by thisrepulsive force, see figure 9.Fig. 9. Permanent magnet is levitating over thesuperconductor.135
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