Oda Migaku

STM/STS studies onthe inhomogeneous PG, electronic charge order and

effective SC gap of high-Tc cuprate Bi2Sr2CaCu2O8+

NDSN2009 Nagoya Univ., Sep. 5 & 6, 2009

Collaborators:

・ Hokkaido University Y.H. Liu, K. Takeyama, T. Kurosawa & M. Ido

Prof. W. S. Clark1st Vice Presidentof Hokkaido Univ.

・ Muroran Institute of Technology N. Momono

Tc

T*

Tmax

3D

AF

ord

er

Superconductivity

T

0 p

Electronic phase diagram

2D AFcorrelation

po

optimalunderdoping overdoping

SC gap

node

anti-node

0

EF

00

energy spectrum

pairinginteraction

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 EF and sharp peaks at the gap edges.

Tc

T*

Tmax

3D

AF

ord

er

Superconductivity

T

0 p

Energy gap in the normal state: pseudogap

2D AFcorrelation

po

optimalunderdoping overdoping

Pseudogap

gap-like structurein energy spectrum

In conventional superconductors, the SC gap shrinks as temperature increases and disappears above Tc. In earlier stage of pseudogap studies, pseudogap : something related to superconductivity a kind of precursor of superconductivity

smooth evolution into superconducting gap across Tc

EF

00

In high-Tc cuprates, a gap-like structure, called pseudogap, still exists in the normal state.

PseudogapTc<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 Tc.

Tc

The energy gap that develops on the Fermi arc below Tc will function as an effective SC gap in determining Tc.

・ 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

PG

Fermi Arc

Anti-nodal FSEF

Fermi arc superconductivity

Effective SC gap

EF

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 Tc 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

ECO

coexists with Fermi-arc SC

Tc

T*

Tmax

3D

AF

ord

er

SC

T

0 p

2D AFcorrelation

PGECO

STM image on UD Bi2212 cleaved surface （ p ~ 0.11, T=5 K<<Tc ）

26

0 Å

V0 = 800 mV Bi-O

1-d superstructurewith missing atom rows

Momono et al., J. Phys. Soc. Jpn., 74 (2005) 2400.

・ Bi-O ： semiconducting Eg>0.1 eV

・ Sr-O ： insulating

・ Cu-O ： metallic or superconducting>Eg

V0>Eg/e → Bi-O plane

Oda et al. Phys. Rev. B53 2253 (1996).

STM image on Bi2212 cleaved surface （ p ~ 0.11, T=5 K<<Tc ）

Momono et al., J. Phys. Soc. Jpn., 74 (2005) 2400.

・ Bi-O ： semiconducting Eg>0.1 eV

・ Sr-O ： insulating

・ Cu-O ： metallic or superconducting

Oda et al. Phys. Rev. B53 2253 (1996).

2-d superstructureElectronic charge order

<Eg

V0<Eg/e → Cu-O plane

VS = 30 mV Cu-O

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

A. Sugimoto, Kashiwaya, Eisaki, Uchida et al., PRB 74 094503 (2006).

Gap inhomogeneity in Bi2201 : AIST group

Gap map

STM image

V (mV)

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

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

STM image in the PG state ： sample N （ UD, Tc=76 K ）

STM image ： Cu-O plane

4a×4a charge order

Cu-

O b

ond

dire

ctio

n

4a4a

Fourier map

Line cutsThe period of CO is 4 times lattice constant, 4a, 　　　　　　　　　　　　　　　　　　　　　　　　　　　　　 along the two Cu-O bond directions.

Cu-

O b

ond

dire

ctio

n

4a4a

P1

P2

STS spectra

P1P2

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.

Energy (bias voltage) dependence of charge order in the PG state

Vs (mV) Bragg

CO

Line cut

period: ~4a×4aThe position of ¼ peak is independent of bias voltage or energy.

‘nondispersive’

The modulation amplitude decreases with increasing energy.

Fourier mapVs = 30 mV

Sample L

4a×4a charge order developsat low energies within the PG

Energy (bias voltage) dependence of charge order in the PG state

Spatial average of STS spectra

The characteristic energy of 4a×4a charge order is the PG.

Background level

Am

plit

ude o

f ch

arg

e o

rder

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 > Tc

PG

Fermi surface & energy gap in the PG state

P1

P2

4a 4acharge order

Sample L

How is the SC state in samples showing strong ECOin inhomogeneous PG state?

P1

P2

inhomogeneous gap

P1

P2

homogeneous

inhomogeneous

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

PGinhomo-geneous

SC

homogeneous

Coexistence of electronic charge order and Fermi-arc superconductivity

electronic charge order Fermi-arc SC

homogeneous

SC gap

inhomogeneous PG

Tc

T*

Tmax

3D

AF

ord

er

SC & ECO (PG)

T

0 p

2D AFcorrelation

ECO (PG)

electronic charge order

Fermi-arc SC

PG & ECO seem to compete with SC,leading to the reduction of Tc

0

BCS relation for d-wave 2s~4kBTc

2s

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 Tc

is reduced.

We have examined the effective SC gap eff in determining Tc from the p dependences of Tc and low-T gap amplitude 0.

The effective SC gap eff, p0, develops on the Fermi arc, while the PG develops around the antinodal parts of the Fermi surface.

• Periodicity: nondispersive, ~ 4a4a• 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 Tc, remains below Tc, 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.