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 LaboratoryArgonne National Laboratory

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

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

6. + e- Everything you wanted to know about pair formation … in low-temperature superconductors ++ + e- + ++ + → Interaction is local in space, but delayed in time → T c << Debye frequency + ++ + e- e- 1.First electron deforms lattice of metal ions (ions shift their position due to Coulomb interaction) 2.First electron moves away 3.Second electron is attracted by lattice deformation and moves for former position of first electron

7. Low-temperature (conventional) superconductivity is a solved problem ▻ We know that ion vibrations cause the electrons to pair High-temperature superconductivity is an unsolved problem ▻ We know that ion vibrations play no role in superconductivity ▻ We don’t know (agree) what causes the electrons to pair BardeenCooperSchrieffer 140 100 60 20 Liquid He Temperature [K] 192019601980 1940 2000 Nb 3 Ge MgB 2 2001 Nb 3 Su NbN Nb Hg Pb NbC V 3 Si Low temperature BCS BCS Theory Bednorz and Müller TIBaCaCuO 1988 HgBaCaCuO 1993 HgTlBaCuO 1995 BiSrCaCuO 1988 La 2-x Ba x CuO 4 1986 YBa 2 Cu 3 O 7 1987 High temperature non-BCS Liquid N 2 ?

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

11. Example of a failed theory Phil W. Anderson (1997), Interlayer tunneling mechanism A.A. Tsvetkov et al., Nature 395, 360 (1998) “In the high-temperature superconductor Tl 2 Ba 2 CuO 6 [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-T c Resonating valence bonds Spin fluctuations Stripes Small q phonons Anisotropic phonons Bipolarons Excitons Kinetic energy d-density wave Orbital currents Flux phases Charge fluctuations Spin bags Gossamer superconductivity SO(5) BCS/BEC crossover Plasmons Spin liquids Interlayer Coulomb Interlayer tunneling van Hove singularities Marginal Fermi liquid Anyon superconductivity Phil Anderson Alexei Abrikosov Bob Schrieffer Tony Leggett Bob Laughlin Karl Müller

13. Electrons in the CuO 2 layer CuO 2 layer

14. Antiferromagnetic CuO 2 layer

15. Antiferromagnetic CuO 2 layer with doped holes

19. Hole motion creates “wake” in spin density

20. Antiferromagnetic CuO 2 layer with doped holes Second hole is attracted by wake in spin density

21. Antiferromagnetic CuO 2 layer with doped holes Second hole is attracted by wake in spin density

22. Antiferromagnetic CuO 2 layer with doped holes Second hole restores antiferromagnetic structure when paired with first hole

23. 140 100 60 20 Liquid He Temperature [K] 192019601980 1940 2000 Nb 3 Ge MgB 2 2001 Nb 3 Su NbN Nb Hg Pb NbC V 3 Si Low temperature BCS BCS Theory Bednorz and Müller TIBaCaCuO 1988 HgBaCaCuO 1993 HgTlBaCuO 1995 BiSrCaCuO 1988 La 2-x Ba x CuO 4 1986 YBa 2 Cu 3 O 7 1987 High temperature non-BCS Liquid N 2 A successful theory should explain the large differences in transition temperatures … or even provide a recipe for a ROOM- TEMPERATURE SUPERCONDUCTOR!