1. High Temperature Superconductivity
Huan Yang

2. Overview Conventional Superconductivity
Basic phenomena in high temperature superconductivity
Current Studies on high temperature superconductivity
High Temperature Superconductivity in the future

3. Zero Resistivity 1908- liquefied helium
First discovered in mercury by Kamerlingh-Onnes in 1911.
Critical temperature 4.21K.
Nobel Prize in
E=0 inside the superconductor!

4. Meissner Effect B=0 inside the superconductor
Superconductor is not just perfect conductor!
Supercurrent flowing around the surface to shield the B field.
Supercurrent is a superfluid.

5. BCS Theory
BCS=John Bardeen, Leon Cooper and Robert Schrieffer
Paring of electron- Cooper Pairs
1972 Nobel Prize in Physics

6. Copper Pair is stable Pairing State SchrÖdinger equation
If |Ek-EF| and |Ek'-EF|<ħω
Copper assumes
otherwise

7. Copper Pair is Stable
So we have Or
E<0 !!!

8. Field point of view In ground state, all electrons are in pairs.

9. Gap in the density of States
Diagonalize the hamiltonian:
S-wave gap function

10. Type I and Type II superconductor

11. Vortex, supercurrent and superfluidity
No scattering with lattice
No viscous force
B=0 in the superconducting regiom
Vorticity vanishes on the supercurrent
Vortex line carries B field
Vortex line carries vorticity

12. High temperature Superconductivity
Discovered by Johannes Georg Bednorz and Karl Alexander MÜller in LaBaCuO in Tc=35K.
Nobel Prize in 1987.
YBCO (YBa2Cu3O7-x) with Tc =95K was discovered in 1987.
Highest Tc we have today is 135K, in Hg1223 (HgBa2Ca2Cu3Ox ).

13. High Temperature Superconductor

14. Crystal Structure of High temperature superconductorsHc
Hab

15. What interactions/orders exist in High-Tc Superconductor?
Electron-phonon interaction
Spin exchange interaction-antiferromagnetic order
Charge density waves, spin density waves and other competing orders.

16. Phase Diagram and Competing Orders
PG: Pseudogap, SC: Superconductivity, CO: Competing order, AFM: Antiferromagnetic

17. Competing order in high-Tc superconductivity
Competing Orders & Superconductivity
Macroscopic Properties
Microscopic Properties
K.McElroy et al. PRL 94, (2005)
Effect of competing orders on
thermodynamic properties.
Local (~5nm) variation in the
Superconducting gap, Δ.

18. H-T Phase Diagram
Coherent phase
CO=Competing Orders
a = doping level

19. H-T Phase Diagram
CO=Competing Orders

20. Magnetic Irreversibility
Hg-1223

21. Magnetic Irreversibility (SQUID DATA)
T(Hirr)
H=2T
H=2T
Hg-1223

22. Magnetic Susceptibility Technique

23. Compare 1st harmonic result with literature
1st Harmonic Signal
YBa2Cu3O7−x
Hg1223 (HgBa2Ca2Cu3Ox )
M. Nikolo, Amer. J. of Phys., Vol. 63, Issue 1, 55-65

24. Coil Data
T(Hirr)

25. Bulk Measurement for Magnetic Irreversible Field
Hc2
Bulk Measurement for Magnetic Irreversible Field
H/HC2
Hc2~355T

26. Scanning Tunneling Microscopy
Piezo-tube scanner and STM tip
V=Bias voltage V
Sample

27. Scanning Tunneling Microscopy
Topography
Vbias=0.5V,Iset=0.63nA Au

28. Scanning Tunneling Microscopy
Spectroscopy
dI/dV ∝ Density of States

29. BCS Theory does not work
Quasiparticle Density of States and Competing Orders
Theory with SC & CO
BCS Theory does not work
normalized
spectra
Best BCS
fitting
Mean-field
(SC & CDW)
D = 10.5 meV
V = 3.8 meV
Exp. data
weaker fluctuations
stronger fluctuations
Nai-Chang Yeh et al.

30. Spatial variation of SC Gap
K.McElroy et al. PRL 94, (2005)

31. High Tc in the future Room temperature superconductor
A satisfactory theory on High temperature superconductivity
Development of superconductor devices

32. Reference
[1] Michael Tinkham, Introduction to superconductivity, chapter 1
[2] H. Kamerling Onnes, Leiden Comm.120b,122b,124c (1911)
[3] J. G. Bednorz and K. A. Müller, Z. Physik, B 64, 189 (1986)
[4] N.-C. Yeh, Bulletin of the Association of Asia Pacific Physical Societies v.12 no.2, pp (2002), also cond-mat/
[5] A. D. Beyer, V. S. Zapf, H. Yang, M. S. Park,K. H. Kim, S.-I. Lee, and N.-C. Yeh. Submitted to Phys. Rev. Lett.; cond-mat/
[6] N.-C. Yeh, C.-T. Chen, V. S. Zapf, A. D. Beyer, C. R. Hughes, M.-S. Park, K.-H. Kim, and S.-I. Lee. Chinese Journal of Physics 43, 505 Suppl. (2005), also cond-mat/
[7] J. Orenstein and A. J. Millis, Science 288, 468 (2000)
[8] S. Sachdev, Science 288, 475 (2000)
[9] E. Demler et.al. Phys. Rev. Lett. 87,