초전도의 짝짖기 대칭성과 불순물 효과

1. 초전도의 짝짖기 대칭성과 불순물 효과 숭실대학교 물리학과 김 희 상

2. Outline • Introduction service • basics on SC • What is a superconductor? / G-L theory, type I, type II / Cooper pair, BCS theory / What kinds of SC? • order parameter symmetry • Unconventional SC • Exotic s-wave SC • impurity scattering • summary

3. 초전도가 할 수 있는 것

5. From “The hunt for Red October”

7. <= 가속기 초고속 컴퓨터 =>

8. <= MRI 의료기기

9. 대표적인 광고 Diagram for politicians 하지만…… 지구를 영하 200도 까지 냉각 시켜야 된다는 거….

13. Outline • Introduction service • basics on SC • What is a superconductor? / Perfect conductor vs. Superconductor / G-L theory, type I, type II / Cooper pair, BCS theory / What kinds of SC? • order parameter symmetry • Unconventional SC / Exotic s-wave SC / impurity scattering • summary

14. 1. Perfect conductivity • 1908 – H. Kermerlingh Onnes (네덜란드) – Helium의 액화 성공 • 1911 – 4.2 K, 수은(Hg)의 초전도 발견 H. Kermerlingh Onnes H. K. Onnes, Commun. Phys. Lab.12,120, (1911) 초전도체의 정의

15. 2. Perfect diamagnetism • 1933 – Meissner & Oschenfeld –not only perfect conductor • but also perfect diamagnetism Perfect conductor와 superconductor의 차이는?

16. 1st cooling Apply B field Becomes p.c. Lenz 의 법칙-mag flux 유지 Remove B field Lenz 의 법칙-mag flux 유지 Perfect conductor below Tc • cooling 1st & field next

17. Apply B field Current dissipation Field penetrates Lenz 의 법칙-mag flux 유지 Now cooling Becomes p.c. Remove B field Lenz 의 법칙-mag flux 유지 Perfect conductor below Tc • Field 1st & cooling next BUT SCs always expel the B field below Tc, no matter what.

18. B field Superconductor London penetration depth • 1935 – London brothers – two fluid model => penetration depth Magnetic length scale

19. 1950 – Ginzburg-Landau theory => free energy expansion

20. Where is a complex order parameter, and is to represent local density of sc electrons, . Take the variation w.r.t. and . There exists sc coherence length. There exists flux quantum. Flux quantization. • 1950 – Ginzburg-Landau theory => free energy expansion

21. Vortex state Flux quantum • 1957 –Abrikosov-predict type II SC

22. How to understand type I, II ? Introduce a vortex in SC 이득 : 자기장을 상쇄시키지 않아도 됨 손실 : 응축에너지의 이득을 못 봄

24. Physics Letters, 24A, 526(1967) PRL, 62, 214 (1989)

25. 1957 – BCS theory –초전도 현상을 설명 John Robert Schrieffer John Bardeen Leon Neil Cooper

26. e e Fermi Sea and for otherwise zero! Cooper pair problem • fully filled F.S. + two interacting electrons • two electrons interact with F.S. • only through Pauli exclusion principle.

27. Conclusion • F.S. becomes unstable for arbitrarily small attractive interaction. • electrons are bounded, i.e., get paired. • Bound energy is not analytic in v. => pertubation is not possible Cooper’s results Let and, then, Size of the bound state

28. => Ion plays a role => lattice vibration, i.e., phonon Where could the attractive interaction come from? Isotope effect

29. The pairs are heavily entangled!! Indirect interaction through phonon

31. BCS theory Hamiltonian Order parameter BCS ground state wave function <= trial wave function Quasiparticle’s Excitation energy Variational Method

32. BCS explains exp. data

33. 초전도의 분류 • type I, type II - magnetic property • BCS type SC • He3 • heavy fermion SC • high Tc cuprates • Fullerine C60 • organic SC • MgB2 금속화합물 • and many more …… • conventional, unconventional– OP symmetry

34. CeCu2Si2 - heavy effective mass ~ 200me UBe13– rich phase diagram UPt3– possible spin triplet • 1972 – Osheroff, Richardson, Lee –superfluidity in He3 ; Leggett –theory based on BCS • 1979 – Steglich Heavy fermion superconductor • 1986 – Bednorz, Muller - High Tc superconductor

35. High Tc SC; copper oxides; Cuprates

37. We are interested in the order parameter symmetry!!!

38. antisymmetric Spin part Spatial part Singlet pairing antisymm. Spherical symm.있는 경우 Triplet pairing symm. • Spherical harmonics s, d, g, … symm. Singlet pairing p, f, … antisymm. Triplet pairing Order parameter in SC Two particle func.

39. using the generalized BCS Therefore, OP symm. has info. of the interaction, i.e. the mechanism. The solution has the following form.

40. Tetragonal symm. group; D4 YBCO Irreducible rep. dimension Base func Etc. A1 1 s-wave A2 1 B1 1 d-wave B2 1 xy E 2 (xz,yz) Unconventional SC(USC) Definition – order parameter(spatial part) has less rotational symmetry than the host lattice

41. Cubic symm. group; Oh Irreducible rep. dimension Base func Etc. A1 1 s-wave A2 1 E 2 T1 3 (x,y,z) T2 3 (xz,yz,zx) Heavy fermion SC

42. Structure of SC OP could be very complicated !!! • Conventional SC • s-wave • extended s-wave (sign change) Non-zero ave. on F.S. No node Gap-yes Exponential behavior Ignore imp. scattering • Unconventional SC • d-wave(spin singlet) • p-wave(spin triplet) • and more …… 1.Zero average of OP on F.S. 2.Nodes exist. gapless, power law behavior Sensitive to imp. scattering

43. 1.Zero average of OP on F.S. • 2.Nodes exist. • => structure of nodes (point node, line node, etc.) determines SC property • gapless, power law behavior • sensitive to impurity scattering • Line node : d-wave • Extended s-wave, d+s wave, ellipsoid • Point node • Nodeless UOP

44. Eqs. to solve self-consistently

45. parameters describing impurity Scattering cross section (normalized by strong limit) Scattering rate

46. Line node (d-wave) Striking difference

47. Sensitive to imp scattering Finite DOS at FS

48. Exotic s-wave SCs Extended s-wave, d+s wave

49. Two-gap like feature • critical value of imp. exists • Impurity-induced gap

50. Ellipsoid ~ D(1 + a cos(theta)) Single peak Exotic s-wave SCs Two gap like feature Maki (2002)