1. KITPC 23/07/07 Gaps and pseudogaps in n and p-type cuprates from infrared spectroscopy. Ricardo LOBO, Andrés SANTANDER-SYRO, Alexandre ZIMMERS, Nicole BONTEMPS Laboratoire Photons et Matière – CNRS / Physique du Solide - ESPCI - Paris

2. KITPC 23/07/07 Paul Langevin Irène et Frédéric Joliot-Curie Pierre-Gilles de Gennes

3. KITPC 23/07/07 Collaborators Chris HOMES (BNL, USA) Jin HWANG, Tom TIMUSK Mc Master University, Hamilton, Canada Andrew MILLIS Columbia University, NY, USA

4. KITPC 23/07/07 Z. Konstantinovic, Z.Z. Li, H. Raffy Laboratoire de Physique des Solides, Université Paris-Sud hole doped Bi  Sr  CaCu  O  (Bi-2212, Bi-2201) thin films c-axis oriented, epitaxially grown thin films / SrTiO 3 C.P. Hill, M.C. Barr, Y. Dagan, R.L. Greene Center for Superconductivity Research, University of Maryland Electron doped Pr 2-x Ce x Cu O  (PCCO) thin films c-axis oriented, epitaxially grown thin films / SrTiO3 A. Forget, D. Colson Service de Physique de l’Etat Condensé, CEA Saclay, Gif-sur-Yvette Hole doped HgBa  CuO  (Hg-1201) single crystal

5. KITPC 23/07/07 1: the normal state Introduction: reflectivity and optical functions (optical conductivity) 1. Phase diagram of high Tc cuprates 2. Spectral weight, transfer of spectral weight 3. Experiment and analysis 4. Normal state gaps (T>T c ) in hole- and electron-doped cuprates 5. Conclusion

6. KITPC 23/07/07 at ~ normal incidence EiEi E r = r E i Reflectivity TKK* *or fit

7. KITPC 23/07/07 stands for high energy contributions  j   i    dielectric function   =    i    optical conductivity Free electrons (Drude) + excitations at  j dissipationdispersion

8. KITPC 23/07/07 CuO Plane p-doped La 2-x Sr x CuO 4 (HgBa  CuO  ) n-doped (Nd,Pr,Sm) 2-x Ce x CuO 4 apical oxygen High-temperature Superconductors Bi Sr Ca Cu O p-doped Bi 2 Sr 2 CaCu 2 O 8

9. KITPC 23/07/07 Cu 2+ 3d 9  1 hole per site CuO 2 plane t

10. KITPC 23/07/07 Temperature(K ) 0 100 200 0.0 0.1 0.2 0.1 0.2 300 Bi 2 Sr 2 CaCu 2 O 8  Pr  x Ce x CuO 4+y Doping /Cu electrons holes PG T* QCP? gap? HgBa  CuO  Tunnel Alf, Dagan ARPES, IR(Onose, Wang) SC AF NMR, tunnel, ARPES, C p,  Raman  IR(?) Phase diagram QCP?

11. KITPC 23/07/07 History…. C axis optical conductivity (  . cm  ) C. Homes, Physica C 254, 265 (1995)    drops below T* Underdoped YBCO Optimally doped YBCO    drops below Tc 700 800

12. KITPC 23/07/07 1000 2000 3000 4000 (cm -1 ) J. Hwang et al, cd0607653 In plane conductivity Bi  Sr  CaCu  O  underdoped T c =82K    decreases    increases T<T c Just a narrowing of the QP zero frequency peak

13. KITPC 23/07/07 In plane scattering rate 1000 2000 J. Hwang et al, cd/0607653 (2006) Bi2212 J. Hwang et al, cd/0607653 (2006) Depletion at T*>T>T c  cm     cm  

14. KITPC 23/07/07 What’s special with the optical conductivity ? Generalized Drude Just another set of 2 optical functions. Does the pseudogap show up only through the depletion of , or is there a spectral weight loss (as seen along the c axis) ?

15. KITPC 23/07/07 Semi-classical approximation for  If a gap  opens over the full Fermi surface (FS),  QP → 0 up to ~  M.Norman et al 392, 157 (1998), P. Coleman ibid P.134 Bi-2212 from ARPES If a gap  (k) opens only over a part of the FS, Only part of  QP is lost

16. KITPC 23/07/07 T 2 < T 1 T1T1 W D increases as T decreases f - sum rule

17. KITPC 23/07/07 T 1 >T* T 2 <T* Opening of a partial gap at T* Decrease of the related spectral weight W G integrated up to  C as T < T*, W G (T) could make W(T) decrease Two competing SW transfer processes W(T)=W D (T)+W G (T) CC NB: in order to observe that, integrate from 0: needs proper extrapolation.

18. KITPC 23/07/07 Bi 2 Sr 2 CaCu 2 O 8+  Look at the change vs T / 300K A. F. Santander-Syro et al PRB 70, 134504 (2004)

19. KITPC 23/07/07 A. Santander et al, PRL 88, 097005 (2002) revisited W increases   C W also increasing, but: saturation ~ 150K

20. KITPC 23/07/07 Pictorial sketch Bi-2212 Pseudogap from the in-plane spectral weight?

21. KITPC 23/07/07 ARPES Bi2212 The PG is clearly seen in a (k x,k y ) range around  Why is optics " blind"?

22. KITPC 23/07/07 Belief that optics probes only the nodal (N) directions in the k space J AN N

23. KITPC 23/07/07 STM atomic scale pictures vs T K. Gomes et al, Nature 447, 569 (2007) T>>Tc T=20K What is the optical response of such an inhomogenous state? Vs T? 300 Å

24. KITPC 23/07/07 Preliminary results: small (~5%) systematic decrease below 150K Note: competition with QP peak narrowing underestimates the “gap opening temperature”. Hg-1201 Tc=89K – underdoped (Tcmax=95K)

25. KITPC 23/07/07 Pseudogap in hole doped cuprates No clear signature in Bi-2212 small but significant, loss of spectral weight in slightly underdoped Hg-1201, which we assign to the PG opening

26. KITPC 23/07/07 Electron doped Pr  x Ce x CuO  thin films

27. KITPC 23/07/07 Real part    of the optical conductivity QP contribution at low energy T c =15K T c =21K

28. KITPC 23/07/07 T c =15K T c =21K Optical conductivity The energy scale over which  1 is depleted is ~twice larger

29. KITPC 23/07/07 Gap opening at T>T W 2  < 2000 cm -1 Spectral weight X=0.17 - T c =15K X=0.13 - T c =15K A. Zimmers et al, Europhys. Lett. 70, 225 (2005) No signature of a gap

30. KITPC 23/07/07 Pictorial sketch: QP + gap

31. KITPC 23/07/07 High energy " PG" in electron doped cuprates" 0.00.10.2 0 100 200 300 400 500 Concentration en Ce T(K) T c T W NCCO Onose et al. T W PCCO QCP ? A. Zimmers et al. Europhys. Lett. 70, 225 (2005) Y. Dagan et al, PRL 92, 167001 (2004)

32. KITPC 23/07/07 H. Matsui et al., 2006 APS meeting 2002 x = 0.13x = 0.15 x = 0.16 2006 ARPES x = 0.04 x = 0.10 N.P. Armitage et al, PRL 81, 257001 (2002) x = 0.17 A. Santander-Syro et al, preprint 2007 NCCO SCCO

33. KITPC 23/07/07 Conclusion Signatures for a normal state gap in the infrared optical conductivity are present in both hole doped and electron doped cuprates, however very different -Energy scales are different. -Downturn of SW significantly larger in electron doped than in hole doped cuprates. -Different origin: the high energy PG in electron doped cuprates is magnetic, the nature of the PG is still a question mark in hole doped cuprates.