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How does Superconductivity Work?

How does Superconductivity Work?. Thomas A. Maier. Why are we interested in Superconductors?.

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How does Superconductivity Work?

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  1. How does Superconductivity Work? • Thomas A. Maier

  2. Why are we interested in Superconductors? • Power plants must increase their current to high voltages when transmitting it across country: to overcome energy lost due to resistance. Resistance is to electrons moving down a wire as rocks are in a stream. Imagine if we could find a way to remove resistance; • Energy in would equal Energy out • Energy Crisis Solved

  3. This photo shows the Meissner effect, the expulsion of a magnetic field from a superconductor in super conducting state. Image courtesy Argonne National Laboratory

  4. Electrons move independently Resistance is due to scattering Electrons form “Cooper” pairs Cooper pairs are synchronized and are not affected by scattering Superconductivity = Cooper danceCooper Pair Flash Mob Tc Tc

  5. e- e- But negative charges repel! So how can electron pairs form?

  6. Everything you wanted to know about pair formation … in low-temperature superconductors First electron deforms lattice of metal ions (ions shift their position due to Coulomb interaction) First electron moves away Second electron is attracted by lattice deformation and moves for former position of first electron e- + + e- e- + + e- + + + + + → Interaction is local in space, but delayedin time → Tc << Debye frequency + + +

  7. LiquidHe Bardeen High temperaturenon-BCS Low temperature BCS Cooper Schrieffer HgTlBaCuO 1995 HgBaCaCuO 1993 140 ? Bednorzand Müller Temperature [K] TIBaCaCuO 1988 BCS Theory BiSrCaCuO 1988 100 • Low-temperature (conventional) superconductivity is a solved problem • We know that ion vibrations cause the electrons to pair • High-temperature superconductivity is an unsolvedproblem • We know that ion vibrations play no role in superconductivity • We don’t know (agree) what causes the electrons to pair YBa2Cu3O7 1987 Liquid N2 60 La2-xBaxCuO4 1986 MgB2 2001 20 NbC Nb3Ge V3Si Pb Nb3Su NbN Hg Nb 1940 1920 1960 1980 2000

  8. Why do electrons pair up into Cooper pairs in the high-temperature superconductors?

  9. Complexity in high-temperature superconducting cuprates • Low-temperature superconductors behave like normal metals above the transition (to superconductor) temperature • High-temperature superconductors display very strange behavior in their normal state • Stripes • Charge density waves • Spin density waves • Inhomogeneities • Nematic behavior • … • Many theories have been proposed,most of them are refuted by experiments “If one looks hard enough, one can find in the cuprates something that is reminiscent of almost any interesting phenomenon in solid state physics.” (Kivelson & Yao, Nature Mat. ’08)

  10. (Incomplete) list of theories for high-Tc Interlayer tunneling Marginal Fermi liquid Anyon superconductivity van Hove singularities Spin fluctuations Phil Anderson d-density wave SO(5) Alexei Abrikosov Resonating valence bonds Small q phonons Flux phases Excitons Stripes Charge fluctuations Interlayer Coulomb Bipolarons Tony Leggett BCS/BEC crossover Kinetic energy Bob Schrieffer Spin bags Orbital currents Plasmons Gossamer superconductivity Anisotropic phonons Spin liquids Bob Laughlin Karl Müller

  11. A.A. Tsvetkov et al., Nature 395, 360 (1998) Example of a failed theory Phil W. Anderson (1997), Interlayer tunneling mechanism “In the high-temperature superconductor Tl2Ba2CuO6 [measurements provide evidence for] a discrepancy of at least an order of magnitude with deductions based on the ILT model.”

  12. (Incomplete) list of theories for high-Tc Interlayer tunneling Marginal Fermi liquid Anyon superconductivity van Hove singularities Spin fluctuations d-density wave Phil Anderson SO(5) Resonating valence bonds Alexei Abrikosov Small q phonons Flux phases Excitons Stripes Charge fluctuations Interlayer Coulomb Bipolarons BCS/BEC crossover Kinetic energy Tony Leggett Bob Schrieffer Spin bags Orbital currents Plasmons Gossamer superconductivity Anisotropic phonons Spin liquids Bob Laughlin Karl Müller

  13. Electrons in the CuO2 layer CuO2 layer

  14. Antiferromagnetic CuO2 layer

  15. Antiferromagnetic CuO2 layer with doped holes

  16. Antiferromagnetic CuO2 layer with doped holes

  17. Antiferromagnetic CuO2 layer with doped holes

  18. Antiferromagnetic CuO2 layer with doped holes

  19. Antiferromagnetic CuO2 layer with doped holes Hole motion creates “wake” in spin density

  20. Antiferromagnetic CuO2 layer with doped holes Second hole is attracted by wake in spin density

  21. Antiferromagnetic CuO2 layer with doped holes Second hole is attracted by wake in spin density

  22. Antiferromagnetic CuO2 layer with doped holes Second hole restores antiferromagnetic structure when paired with first hole

  23. A successful theory should explain the large differences in transition temperatures LiquidHe High temperaturenon-BCS Low temperature BCS HgTlBaCuO 1995 HgBaCaCuO 1993 140 Bednorzand Müller Temperature [K] TIBaCaCuO 1988 BCS Theory BiSrCaCuO 1988 100 YBa2Cu3O7 1987 Liquid N2 … or even provide a recipe for aROOM-TEMPERATURE SUPERCONDUCTOR! 60 La2-xBaxCuO4 1986 MgB2 2001 20 NbC Nb3Ge V3Si Pb Nb3Su NbN Hg Nb 1940 1920 1960 1980 2000

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