Prof. Harvinder Kaur Govt College for Girls

1. CHAPTER 7: SUPERCONDUCTIVITY Prof. Harvinder Kaur Govt College for Girls

2. Outline • Introduction • Mechanism of Superconductors • Meissner Effect • Type I and Type II superconductors • Characteristic properties of superconductors • BCS theory of Superconductivity • Applications of Superconductivity

3. INTRODUCTION For some materials, the resistivity vanishes at some low temperature: they become superconducting. Superconductivity is the ability of certain materials to conduct electrical current with no resistance. Thus, superconductors can carry large amounts of current with little or no loss of energy In July 1909, Heike Kamerlingh Onnes found that the resistance of mercury dropped suddenly to an immeasurable small value when it is cooled below 4.2K. Onnes termed the new electrical state that the mercury had entered the superconducting state.

4. PROPERTIES VIS-A-VIS SUPERCONDUCTIVITY • Properties not affected : • Elastic properties • Thermal expansion behaviour • Photoelectric properties • Internal arrangement of crystal lattice as confirmed by X-ray diffraction pattern before and after such a transition • Properties affected : • Magnetic properties change • Electrical properties : as the electrical resistivity tendo to zero at T=Tc • All thermo electric effects disappear for T  Tc • Specific heat shows a discontinuous change • Some latent heat of transition may also be involved • The transition in zero magnetic field from the superconducting state to the nornal state is not exactly involving latent heat , though there is discontinuity in the heat capacity – temp2 graph • Entropy shows a decrease for T  Tc

5. NON SUPERCONDUCTOR SUPERCONDUCTOR Bint = 0 Bint = Bext

6. MESSINER EFFECT MEISSNER EFFECT : Meissner and Ochsenfeld discovered that when a superconductor is cooled in a magnetic field to below the value of transition temperature corresponding to that field, then the lines of magnetic induction B are pushed out of the bulk superconductor.

7. TYPE I SUPERCONDUCTORS Type I superconductors : These are superconductors which exhibit Complete Meissner effect. • There are 30 pure metals which exhibit zero resistivity at • low temperature. • They are called Type I superconductors (Soft • Superconductors). • The superconductivity exists only below their critical temperature and below a critical magnetic field strength.

8. Mat. Mat. Tc (K) Tc (K) Be Gd* 0 1.1 Rh Al 0 1.2 W Pa 1.4 0.015 Th Ir 0.1 1.4 Lu Re 0.1 1.4 Hf Tl 2.39 0.1 Ru In 3.408 0.5 Sn Os 3.722 0.7 Hg Mo 4.153 0.92 Zr Ta 4.47 0.546 V V Cd 5.38 0.56 U La 6.00 0.2 Pb Ti 0.39 7.193 Tc Zn 0.85 7.77 Ga Nb 1.083 9.46 Type I Superconductors

9. TYPE II SUPERCONDUCTORS Type II superconductors : These are superconductors which do not exhibit Meissner effect strictly • Starting in 1930 with lead-bismuth alloys, were found which exhibited superconductivity; they are called Type II superconductors (Hard Superconductors). • They were found to have much higher critical fields and therefore could carry much higher current densities while remaining in the superconducting state.

10. Type II Superconductors

11. CHARACTERISTICS PROPERTIES OF A SUPERCONDUCTOR : FACTOR AFFECTING Temperature : If a ring made of superconducting material is cooled in a magnetic field from ordinary temeprature to a value below its critical temperature and then the magnetic field is removed, an induced current is set up in the ring. The resistance in the superconducting state being practically zero, the decay of thie induced current will take infinitely long time. Magnetic field : Application of magnetic field to a superconducting specimen brings a stage when for H=Hc, the critical field, the superconductor behaves like a normal material i.e., the superconductivity disappears. Current : If the magnetic field around the superconductor is increased beyond the critical field the superconductivity is destroyed and the sample behaves as a normal material. Therefore the supercurrent will flow only up to its critical value .Once the field exceeds Hc(T) the current becomes just the ordinary current. Stress : Application of stress increases the transition temperature. As Hc(T) is temperature dependent, increased stress is found to result in a slight change of Hc(T). Size : Size of specimen exhibiting superconductivity is an important parameter for its behaviour. Impurity : The presence of impurities changes almost all properties of a superconductor especially its magnetic behaviour. Isotopic Constitution of the Specimen : The critical temperature of a specimen depends on the isotopic mass. The presence of various isotopes in a given specimen decided what its average isotope mass will be. The dependence of Tc on such a mass is also called Isotope Effect. MaTc = constant or Tc M-1/2

12. THERMODYNAMICAL PROPERITES OF SUPERCONDUCTING STATE Entropy : Going from Normal state to superconducting state the entropy decreases, so the superconducting state is more ordered than the normal state. Specific Heat :The specific heat of the normal metal obeys the relation ship, Cn(T) =  T + βT3 where as for the superconducting state the specific heat is Ces(T) = A exp (-/kβT) where A is some constant and  is superconducting energy group which is equal to one half of the minimum value of energy for destroying a cooper pair. Energy Gap : The energy gap of superconductors is of entirely different nature than the energy gap in insulators. In superconductor the energy gap is due to electron-electron interaction in fermi gas whereas in insulator or semiconductor the energy gap is caused by electron lattice interaction. In insulators the gap prevents the flow of electrical current. Energy must be added to lift electrons from the valence band to conduction band before the current can flow. In a superconductor, on the other hand, the current flows despite the presence of energy gap . In a superconductor the electrons in the excited state above the gap behave as normal electron. The transition in zero magnetic filed from superconducting state to normal state is observed to be a second–order phase transition.

13. BCS THEORY OF SUPERCONDUCTIVITY The microscopic theory put forward by Bradeen , Cooper and Schruffier (BCS) forms the basis of quantum theory of Superconductivity. The fundamental postulate of BCS theory is that when an attractive interaction between two electrons by means of phonon exchange dominates the repulsive coulomb interaction then the superconducting state is formed. Electron-phonon-electron interaction : During an interaction of an electron with a positive ion of the lattice through electrostatic coulomb force, some electron momentum get transferred. As a result, these ions set up elastic wave in the lattice due to distortion. If another electron happens to pass through this region then the interaction between two occurs which in its effect lowers the energy of the second electron. The two electrons interact via the lattice distortion or the phonon field resulting in the lowering of energy of the electron which implies the force between two electrons is attractive. This interaction is strongest when two electrons have equal and opposite moments and spin and this pair is known as cooper pair.

14. COOPER PAIR • When the temperature of the specimen is lowered, if the attractive force between two electrons via a phonon exceeds coulomb repulsion between them, then a weakly bound cooper pair is formed having the binding energy of the order of 10-3 eV. The energy of Cooper pair is less than the energy of the pair in free state. The binding energy of cooper pair is called energy bang gap, Eg. When h  Eg strong absorption occurs as the cooper pairs break apart. • The electrons in cooper pair have opposite spins so the total spin of the pair is zero. As a result cooper pairs are bosons whereas electrons are fermions.

15. APPLICATIONS OF SUPERCONDUCTIVITY • Superconductors are used to make the powerful electromagnets, including those used in MRI machines, beam steering magnets used in particle accelerators. • Superconductors have also been used to make digital circuits and microwave filter for mobile phone base stations. • Promising future applications include high performance transformers, power storage devices, electric power transmission, electric motors and magnetic levitation devices.