High Temperature Superconductivity - After 25 years, where are we at?

1. High Temperature Superconductivity - After 25 years, where are we at? Michael Norman Materials Science Division Argonne National Laboratory Norman, Science 332, 196 (2011) Fermilab- June 22, 2011

2. It All Started Back in 1986

3. Tc Shot Up Like a Rock (many cuprates superconduct above 77K)

4. Woodstock of Physics - March 1987

6. Superconductors: They are perfect conductors They expel magnetic flux Zero resistance Meissner effect (1933) H. K. Onnes (1911)

7. The Path to a Microscopic Theory was Littered with Many Famous Physicists Einstein Heisenberg Landau Feynman

8. Eventually, Three Guys in Illinois Got It Right (Bardeen, Cooper, Schrieffer - 1956,1957)

9. A (Very) Short History of Superconductivity London theory - rigidity to macroscopic perturbations implies a “condensate” (1935,1950) Ginzburg-Landau (Y) theory - order parameter for condensate (1950) Isotope effect (Maxwell, Serin & Reynolds, Frohlich, 1950) Cooper pairs (1956) Bardeen-Cooper-Schrieffer (BCS) microscopic theory (1957) Type-II superconductors (Abrikosov vortices, 1957) Connection of BCS to Ginzburg-Landau (Gorkov, 1958) Strong coupling superconductivity (Eliashberg, Nambu, Anderson, Schrieffer, Wilkins, Scalapino …, 1960-1963) p-wave superfluidity in 3He (Osheroff, Richardson, Lee, 1972; Leggett, 1972) Heavy Fermion Superconductivity (Steglich, 1979) High Temperature Superconductivity (Bednorz & Muller, 1986) Iron Arsenides (Hosono, 2008)

10. From Steve Girvin’s lecture (Boulder Summer School 2000) courtesy of Matthew Fisher

11. Everything You Wanted to Know About Pair Formation (But Were Afraid to Ask) (the electron-phonon case) 1st e- attracts + ions Ions shift position from red to blue 1st e- moves away 2nd e- sees + ion hole and moves to former position of 1st e- Interaction is local in space (s-wave pairs, L=0, S=0) but retarded in time (Tc << Debye frequency)

12. But cuprates have d-wave pairs! (L=2, S=0) van Harlingen; Tsuei & Kirtley - Buckley Prize -1998 Artwork by Gerald Zeldin (2000)

13. Phil Anderson (RVB; interlayer tunneling; RVB) Alex Abrikosov (small q phonons) Bob Laughlin (competing phases) Bob Schrieffer (spin bags) Karl Mueller (bipolarons) Tony Leggett (interlayer Coulomb)

15. Theories Connected with High Tc Superconductivity Resonating valence bonds Spin fluctuations Stripes Anisotropic phonons Bipolarons Excitons Kinetic Energy lowering d-density wave Charge fluctuations Flux phases Gossamer superconductivity Spin bags SO(5) BCS/BEC crossover Plasmons Spin liquids Not to Mention Interlayer tunneling Marginal Fermi liquid van Hove singularities Quantum critical points Anyon superconductivity Slave bosons Dynamical mean field theory

16. Famous Quotes Famous Books Abrikosov - Nobel Lecture - Dec. 2003 “On this basis I was able to explain most of the experimental data about layered cuprates . . . As a result I can state that the so called “mystery” of high-Tc superconductivity does not exist.”

17. Ten Weeks of High Tc (to the tune of Twelve Days of Christmas) On the first week of the program Friend Philip said to me All simply RVB (All sim-pl-ee R-r V B) On the second week of the program Friend Douglas said to me Pair in a d-wave All simply RVB On the third week of the program Friend David said to me It's magnons Pair in a d-wave All simply RVB On the fourth week of the program Friend Chandra said to me Four current rings (fo-or current rings) It's magnons Pair in a d-wave All simply RVB KITP Web Site High Tc Program - Fall 2000 At the end of the program Friend Philip said to me Big Tent is stretching Visons escaping Visons are gapping Slave spinons pairing T sym-try breaking Stripes fluctuating S - O - 5 Four current rings It's magnons Pair in a d-wave All simply RVB --Ilya Gruzberg Smitha Vishveshwara Ilya Vekhter Aditi Mitra Senthil Matthew Fisher - -

18. Why is the High Tc Problem So Hard to Solve? (Laughlin’s Lecture for Teachers - ITP, 2000)

19. Electronic Structure of Cuprates

20. Electronic structure from density functional theory Fermi surface Len Mattheiss PRL (1987) Energy vs Momentum

21. Short (and biased!) tutorial on cuprates Cu2+ Large U charge-transfer gap Dpd ~ 2 eV best evidence for large U metal? Mott insulator antiferromagnet J~1400 K doping Hubbard t = 0.3 eV, U = 2 eV, J = 4t2/U = 0.12 eV (slide from Phil Anderson)

22. Phase Diagram of Cuprates

23. What We DO Know There are 2e- pairs The pairs are d-wave (L=2, S=0) There are “normal” (i.e., 2e-) vortices Quasiparticles exist (but only below Tc) d-wave pairing observed by phase sensitive tunneling - van Harlingen, Kirtley & Tsuei Kirtley et al, Nat. Phys. (2006)

24. Extraction of the Superconducting Energy Gap from Photoemission Campuzano, Shen, Johnson – Buckley Prize (2011) Dk --> cos(kxa) - cos(kya) --> Implies near-neighbor pairs Bi2212, Tc=87K Dirac cone Ding et al., PRB (1996)

25. Photoemission spectrum above and belowTc at momentum k=(p,0) for Bi2212 peak Incoherent normal state Coherent superconductor dip Norman et al, PRL (1997)

26. Neutron Spin Resonance (S=1 excitation) Rossat-Mignod/Bourges, Mook/Dai, Keimer/Fong Dai et al, Nature (1999)

27. Dispersion of magnetic excitations has the form of an hourglass Arai et al, PRL (1999)

28. The “strange metal” phase exhibits linear T resistivity Martin et al PRB (1990)

29. What is the Pseudogap Due to? Spin singlets Pre-formed pairs Spin density wave Charge density wave d density wave 6. Orbital currents 7. Flux phase 8. Stripes/nematic 9. Valence bond solid/glass 10. Combination?

30. Temperature evolution of the Fermi surface T < Tc (node) Tc < T < T* (Fermi arc) T > T* (full FS) Norman et al., Nature (1998)

31. Is the T=0 limit of the pseudogap phase a nodal metal? Kanigelet al, Nat Phys (2006) Chatterjeeet al, Nat Phys (2010)

32. A Nernst signal (due to fluctuating vortices?) appears above Tc Wang et al PRB (2001)

33. Evolution of the Fermi surface with doping Doiron-Leyraud et al Nature (2007)

34. electron pockets due to magnetic stripes? RH < 0 forms a dome around 1/8 The Hall number is negative! LeBoeufet al., Nature (2007) and PRB (2011) Doiron-Leyraud et al. Nature (2007)

35. Antiphase Stripes - Tranquada et al. - Nature (1995) Charge peaks at (±2x,0),Spin peaks at (1/2±x,1/2), x~1/8 spin peaks doped holes local spins charge peaks

37. Circular dichroism above Tc in the pseudogap phase? Kaminski et al Nature (2002)

38. Orbital moments above Tc in the pseudogap phase? Fauque et al PRL (2006)

39. Science, February 1987

40. RVB has many critics Bob Laughlin Annals of Improbable Research, May-June 2004

41. RVB (“resonating valence bond”) is a ‘strong coupling’ theory for cuprates developed by Phil Anderson and his colleagues It postulates a liquid of spin singlets Neel LatticeRVB

42. RVB Model (Phil Anderson - 1987, Gabe Kotliar - 1988, Patrick Lee, Mohit Randeria, Maurice Rice, etc.) The pseudogap phase corresponds to a d-wave pairing of spins (left). At zero doping, this is quantum mechanically equivalent to an orbital current phase (middle). The spin gap, D, is not equivalent to the superconducting order parameter, Dsc, as it would be in BCS theory (right).

43. Two Theories of the Phase Diagram Quantum Critical RVB Relation of T* to Tc

44. Chatterjeeet al., PNAS (2011)

45. “Emery-Kivelson” picture Nature (1995) Pairing occurs below mean field transition temperature Coherence occurs below phase ordering temperature Superconductivity occurs only below both temperatures

46. SO(5)vsSU(2) Demler, Hanke, and Zhang Lee, Nagaosa, and Wen Rev Mod Phys (2004) Rev Mod Phys (2006)

47. Antiferromagnetic spin fluctuations can lead to d-wave pairs (an e- with up spin wants its neighbors to have down spins) Heavy Fermions - Varma (1986), Scalapino (1986) High Tc - Scalapino (1987), Pines (1991) < Repulsive < Attractive

48. d-wave pairing due to a half-breathing phonon mode? Shen, Lanzara, Ishihara, Nagaosa - Phil Mag B (2002)

49. Holographic approach to high temperature superconductors? Hartnoll, Science (2008)