1. Oda Migaku STM/STS studies on the inhomogeneous PG, electronic charge order and effective SC gap of high-T c cuprate Bi 2 Sr 2 CaCu 2 O 8+  NDSN2009 Nagoya Univ., Sep. 5 & 6, 2009 Collaborators: ・ Hokkaido University Y.H. Liu, K. Takeyama, T. Kurosawa & M. Ido Prof. W. S. Clark 1 st Vice President of Hokkaido Univ. ・ Muroran Institute of Technology N. Momono

2. TcTc T* T max 3D AF order Superconductivity T 0 p Electronic phase diagram 2D AF correlation p o optimal underdopingoverdoping SC gap node anti- node 00 EFEF 00  0 energy spectrum pairing interaction Energy gap in the SC state Electronic phase diagram of Bi2212, showing how the electronic property changes as a function of temperature and hole doping level of the Cu-O plane, which is responsible for the superconductivity. Tc is reduced in the underdoped region, although the pairing interaction is expected to be stronger towards the AF phase. This is very old, but still studying extensively as one of the most interesting problems in high-Tc research field. Fermi surface SC gap opening on the FS : d-wave, whose magnitude is zero at node and maximum at anitinode. d-wave gap in the electronic energy spectrum : strong suppression around E F and sharp peaks at the gap edges.

3. TcTc T* T max 3D AF order Superconductivity T 0 p Energy gap in the normal state: pseudogap 2D AF correlation p o optimal underdopingoverdoping Pseudogap gap-like structure in energy spectrum In conventional superconductors, the SC gap shrinks as temperature increases and disappears above T c. In earlier stage of pseudogap studies, pseudogap : something related to superconductivity a kind of precursor of superconductivity smooth evolution into superconducting gap across T c EFEF 00  0 In high-T c cuprates, a gap-like structure, called pseudogap, still exists in the normal state. Pseudogap T c < T < T* Fermi arc effective SC gap ARPES experiments : the pseudogap opens on the antinodal parts of the FS, and the FS becomes of an arc shape in the normal state, that is called Fermi arc, and an energy gap seems to open on the Fermi arc below T c. TcTc

4. The energy gap that develops on the Fermi arc below T c will function as an effective SC gap in determining T c. ・ M. Ido et al., J. Low Temp. Phys. 117 (1999) 329. ・ M. Oda et al., J. Phys. Soc. Jpn. 69 (2000) 983. ・ N. Momono et al., J. Phys. Soc. Jpn. 71 (2002) 2832. Fermi surface, PG & Effective SC Gap ・ STM/STS: Uchida, Devis （ MacElroy et al., PRL 94 197005 (2005). ） ・ ARPES ： Yoshida, Fujimori, Shen ( Tanaka et al., Science 314 (2006) 1910, Hashimoto et al., PRB 75 (2007) 140503. ） Fermi arc is mainly responsible for the superconductivity. node Effective SC gap PG Fermi Arc Anti-nodal FS EFEF Fermi arc superconductivity

5. Effective SC gap EFEF PG Effective SC gap, PG & ECO ECO is associated with antinodal parts and accompanied by an inhomogeneous PG. ECO and PG coexist and compete with the homogeneous superconductivity on the Fermi arc, leading to the reduction of T c in the underdoped region. Very recently, an electronic charge order was found in the PG state, and it is paid attention as a candidate for the hidden order in the PG state. ・ Our STM/STS experiments : the charge order develops in an inhomogeneous PG state ・ M. Vershinin et al. Science 303 1995 (2004). ・ T. Hanaguri et al. Nature 430 1001 (2004). ECO coexists with Fermi-arc SC TcTc T* T max 3D AF order SC T 0 p 2D AF correlation PG ECO

6. STM image on UD Bi2212 cleaved surface （ p ~ 0.11, T=5 K<<T c ） 260 Å V 0 = 800 mV Bi-O 1-d superstructure with missing atom rows Momono et al., J. Phys. Soc. Jpn., 74 (2005) 2400. ・ Bi-O ： semiconducting E g >0.1 eV ・ Sr-O ： insulating ・ Cu-O ： metallic or superconducting >Eg>Eg V 0 >E g /e → Bi-O plane Oda et al. Phys. Rev. B53 2253 (1996).

7. STM image on Bi2212 cleaved surface （ p ~ 0.11, T=5 K<<T c ） Momono et al., J. Phys. Soc. Jpn., 74 (2005) 2400. ・ Bi-O ： semiconducting E g >0.1 eV ・ Sr-O ： insulating ・ Cu-O ： metallic or superconducting Oda et al. Phys. Rev. B53 2253 (1996). 2-d superstructure Electronic charge order <Eg<Eg V 0 <E g /e → Cu-O plane V S = 30 mV Cu-O

8. P1 P2 P1 P2 Strong charge order & inhomogeneous gap in the SC state strong charge order inhomogeneous gap structure!! another example of low bias STM images in the SC state of UD Bi2212 STS

9. A. Sugimoto, Kashiwaya, Eisaki, Uchida et al., PRB 74 094503 (2006). Gap inhomogeneity in Bi2201 : AIST group Gap map STM image V (mV)

10. P1 P2 P1 P2 Strong charge order & inhomogeneous gap in the SC state In samples showing a strong charge order, the gap structure is inhomogeneous.in nanometer scale. another example of low bias STM images in the SC state of UD Bi2212 STS

11. T = 7 K no electronic charge order  0 mV gap map In samples showing no electronic charge order, the gap structure is homogeneous. Cu-O plane STM image showing no electronic charge order homogeneous

12. STM image in the PG state ： sample N （ UD, T c =76 K ） STM image ： Cu-O plane 4a×4a charge order Cu-O bond direction 4a Fourier map Line cuts The period of CO is 4 times lattice constant, 4a, along the two Cu-O bond directions.

13. Cu-O bond direction 4a P1 P2 STS spectra P1 P2 strong charge order inhomogeneous PG STM image ： Cu-O plane Strong Charge Order & Inhomogeneous Gap in the PG state The spatial dependence of PG is strongly inhomogeneous in samples showing strong charge order.

14. Energy (bias voltage) dependence of charge order in the PG state Sample L V s =30 mV Fourier map V s (mV) Bragg CO Line cut period: ~4a×4a The position of ¼ peak is independent of bias voltage or energy. ‘nondispersive’ The modulation amplitude decreases with increasing energy. Fourier map V s = 30 mV FT Sample L

15. 4a×4a charge order develops at low energies within the PG Energy (bias voltage) dependence of charge order in the PG state Spatial average of STS spectra M. Vershinin et al., Science 303 1995 (2004). The characteristic energy of 4a×4a charge order is the PG. Background level Amplitude of charge order

16. PG PG ： inhomogeneous Fermi arc (coherent) Characteristic energy of ECO ： PG antinodal region (incoherent) electronic charge order (ECO) inhomogeneity PG The antinodal region, in which the PG opens, will also be responsible for ECO !! PG: inhomogeneous in samples showing strong ECO T > T c  PG Fermi surface & energy gap in the PG state

17. P1 P2 4a  4a charge order Sample L How is the SC state in samples showing strong ECO in inhomogeneous PG state? P1 P2 inhomogeneous gap

18. P1 P2 homogeneousinhomogeneous Ref.: McElroy et al. Nature 422 592 (2003). Hashimoto et al. PRB 74 64508 (2006). The inhomogeneous gap in the SC state will come from the inhomogeneous PG. 0 Energy gap in the SC state PG inhomo- geneous SC homogeneous

19. Coexistence of electronic charge order and Fermi-arc superconductivity electronic charge order Fermi-arc SC homogeneous SC gap inhomogeneous PG TcTc T* T max 3D AF order SC & ECO (PG) T 0 p 2D AF correlation ECO (PG) electronic charge order Fermi-arc SC PG & ECO seem to compete with SC, leading to the reduction of T c 0 BCS relation for d-wave 2  s ~ 4k B T c 2s2s ss In UD region: PG & ECO develop markedly. Fermi arc shrinks.  s can be determined from the homogeneous part of the spectra coexist !!  s in determining T c is reduced.

20. We have examined the effective SC gap  eff in determining T c from the p dependences of T c and low-T gap amplitude  0. The effective SC gap  eff, p  0, develops on the Fermi arc, while the PG develops around the antinodal parts of the Fermi surface. Periodicity: nondispersive, ~ 4a  4a Characteristic energy scale: energy gap (  PG in the PG state,  SC or  PG in the SC state) Strong correlation between charge order and gap inhomogeneity Dynamical 4ax4a charge order will be a candidate for the hidden order in the homogeneous PG state. Summary Static charge order, which is associated with incoherent quasiparticle (or pair) states in antinodal region and develops in inhomogeneous PG state above T c, remains below T c, together with the gap inhomogeneity in antinodal region, and coexists with Fermi arc superconductivity. We have also examined the charge order in the PG and SC states.