oda migaku stm/sts studies on the inhomogeneous pg, electronic charge order and effective sc gap of...
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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.