Superconductivity. The Discovery of Superconductivity. Basic Properties

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Kamerlingh Onnes found that the resistivity of mercury

1 Superconductivity Basic Properties The Discovery of Superconductivity Using liquid helium, (b.p. 4.2 K), H. Kamerlingh Onnes found that the resistivity of mercury suddenly dropped to zero at 4.2 K. H. K. Onnes, Commun. Phys. Lab.12,120, (1911) 1

The Hampson-Linde Cycle Other Superconducting Materials M. K.

2 Making Liquid He Isothermal compression: compress He while cooling it with LN 2 (77 K). Expansion: Allow He to expand and cool. The Hampson-Linde Cycle Other Superconducting Materials M. K. Wu, et al., Phys. Rev. 58, 908 (1987) B. T. Matthias, et al., Phys. Rev. 95, 1435, (1954) 2

3 Elemental Superconductors Types of Superconductor Type I: Very Sharp transition to superconducting state at the critical temperature T C. 3

4 Types of Superconductors Type II: More gradual transition to superconducting state. Mostly alloys or compounds. Generally higher T C than Type I. Is it really zero resistance? If a current is generated in a superconducting ring, it will persist because of the zero resistivity. In a normal metal the current would dissipate due to resistive effects. Experiments have demonstrated that currents in superconducting coils can persist for years without any measurable degradation. Experimental evidence points to a current lifetime of at least 100,000 years. 4

Circulating currents will be induced to oppose the buildup of magnetic field in the conductor.

5 Superconductivity Magnetic Properties Perfect Diamagnetism According to Faraday s Law a conductor will oppose any change in externally applied magnetic field. Circulating currents will be induced to oppose the buildup of magnetic field in the conductor. A perfect conductor would be a perfect diamagnet. Induced currents in it would meet no resistance, so they would persist in whatever magnitude necessary to perfectly cancel the external field change. 5

6 Meisner Effect What happens if the material becomes superconducting in an external field? For a perfect diamagnet you would expect the field to be unchanged. Meisner Effect When a material becomes superconducting it actively expels the magnetic field. This is the Meisner Effect. 6

7 Type II In Type II superconductors the magnetic field is not excluded completely, but is constrained in filaments within the material. Type II These filaments are in the normal state, surrounded by supercurrents in what is called a vortex state. 7

Critical Magnetic Fields The critical field depends on temperature: The existence of a critical magnetic

8 Critical Magnetic Fields Magnetic fields can destroy the superconducting state. Above the critical magnetic field B C, the material will not remain superconducting even at absolute zero. Critical Magnetic Fields The critical field depends on temperature: The existence of a critical magnetic field implies the existence of a maximum current in a wire of the superconducting material because the current itself generates a magnetic field. 8

9 Examples of Type I and II B C Rohlf, James William, Modern Physics from a to Z0, Wiley 1994 Superconductivity BCS Theory 9

10 The Isotope Effect The critical temperatures of different isotopes of the same element depend on the mass of the isotope. As mass increases the critical temperature decreases. The Isotope Effect The dependence is given by This implies that the lattice vibrations play a role in superconductivity. As M the T C 0. 10

BCS Theory A theory for the mechanism of Type I

attractive interaction between electrons.

11 BCS Theory A theory for the mechanism of Type I superconductivity was developed by John Bardeen, Leon Cooper, and Robert Schrieffer. They received the Nobel Prize in 1972 for the BCS theory. BCS Theory In the model the lattice mediates an attractive interaction between electrons. An electron passing through the lattice causes the ions to move slightly together. The positive charge density propagates through the lattice. Another electron passing by the increased positive charge density region experiences an attractive Coulomb interaction. 11

12 BCS Theory The net effect of this is that the two electrons have exchanged momentum via the lattice. The interaction between the electrons is attractive as each participates in an attractive Coulomb interaction (with the lattice.) The BCS theory shows that in some instances the energy of this attractive interaction can exceed that of the (shielded) repulsive interaction that the electrons exert on each other. In this case the electrons form a bound pair called a Cooper Pair. BCS Theory This pairing can be modeled in terms of electron-phonon interactions. The 1st electron emits a phonon and it is absorbed by the 2nd electron. (Remember that a phonon is a quanta of lattice vibration.) 12

Forming Cooper Pairs The requirements for the formation of large numbers of Cooper pairs are Low temperature so that random thermal phonons do not interfere with the mediating phonons.

The two electrons in a pair have equal and opposite momentum (in the absence of an applied field.) Cooper Pairs Because they are weakly bound Cooper pairs constantly breaking up and reforming.

13 Forming Cooper Pairs The requirements for the formation of large numbers of Cooper pairs are Low temperature so that random thermal phonons do not interfere with the mediating phonons. Interaction between lattice and electrons be strong. The number of electrons lying just below the Fermi energy must be large. The two electrons in each pair have opposite spin orientations. The two electrons in a pair have equal and opposite momentum (in the absence of an applied field.) Cooper Pairs Because they are weakly bound Cooper pairs constantly breaking up and reforming. The weak binding also causes them to be large. In the region of the pair there are many electrons that would like to bond into a pair. If the total momentum of each Cooper pair is zero then the number of pairs will be a maximum. 13

14 The BCS Superconductor The state of the system is highly ordered with all of the pairs having the same center of mass motion. When an external field is applied the pairs behave as particles with two electron charges moving through the lattice. The system moves together as a unit with all of the Cooper pairs locked together in motion. This is why there are no scatterings from lattice imperfections. The Band Gap According to BCS the binding energy of a Cooper pair is about (7/2)kT C at 0 K. It is energetically favorable for two electrons near the Fermi level to to promote themselves above the Fermi energy so that they can participate in the Cooper pair interaction. For each electron there is a nearly continuous distribution of single electron states For the system there is the superconducting ground state and then an energy band gap, and above that normal conducting states. 14

15 The Band Gap The incoming phonon (or photon) must have enough energy to promote the electron to an unfilled level AND break the bond. This means that there is a minimum energy to go from a superconducting state to a normal state for a Cooper pair. The band gap between the superconducting ground state and the normal states is related to the Cooper pair binding energy. The system (at 0 K) can only accept energies greater than the binding energy of a pair. Fermi Energy Evidence for the Band Gap A band gap is implied by the fact that the resistance is precisely zero. If charge carriers can move through a lattice without interacting at all, it must be because their energies are quantized such that they do not have any available energy levels within reach of the interaction energy with the lattice. Experiments measuring the absorption of microwave photons by superconducting materials indicate an energy gap. 15

16 Band Gap and T C As predicted by BCS the band gap is dependent on the critical temperature. Superconductivity Applications 16

Superconducting Magnets Type II superconductors such as niobium-tin and niobiumtitanium are used to make the coil windings for superconducting magnets.

Typical construction of the coils is to embed a large number of fine filaments ( 20 micrometers diameter) in a copper matrix.

17 Superconducting Magnets Type II superconductors such as niobium-tin and niobiumtitanium are used to make the coil windings for superconducting magnets. These two materials can be fabricated into wires and can withstand high magnetic fields. Typical construction of the coils 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 the superconducting state is lost. These superconducting magnets must be cooled with liquid helium. Superconducting Magnets Used in MRI with highly uniform and stable fields of about 1-7 Tesla. Used in accelerator applications: bending magnets have been designed to produce up to 20 Tesla. 17

Power transmission Reduction in power loss through cables when transmitting electrical power can be achieved by the use of Type II superconductors.

18 Power transmission Reduction in power loss through cables when transmitting electrical power can be achieved by the use of Type II superconductors. In 2000 Los Alamos researchers were able to produce meter lengths of YBCO superconducting tapes with critical current exceeding 100 amps and current densities of one million amps per square centimeter at liquid nitrogen temperatures. 18

For their 1948 discovery of the transistor, John Bardeen, Walter Brattain, and William Shockley were awarded the 1956 Nobel prize in physics.

For their 1948 discovery of the transistor, John Bardeen, Walter Brattain, and William Shockley were awarded the 1956 Nobel prize in physics. Modern Physics (PHY 3305) Lecture Notes Modern Physics (PHY 3305) Lecture Notes Solid-State Physics: Superconductivity (Ch. 10.9) SteveSekula, 1 April 2010 (created 1 April 2010) Review no tags We applied