The origin of the anomalously strong influence of out-of-plane
disorder on high-T
superconductivity
Y. Okada,1 T. Takeuchi,2 T. Baba,3 S. Shin,3 and H. Ikuta1
1Department of Crystalline Materials Science,
Nagoya University, Nagoya 464-8603, Japan
2EcoTopia Science Institute, Nagoya University, Nagoya 464-8603, Japan
3Institute for Solid State Physics (ISSP),
University of Tokyo, Kashiwa 277-8581, Japan
(Dated: )
Abstract
The electronic structure of Bi2Sr2−xRxCuOy (R=La, Eu) near the (π,0) point of the first Bril-
louin zone was studied by means of angle-resolved photoemission spectroscopy (ARPES). The
temperature T ∗ above which the pseudogap structure in the ARPES spectrum disappears was
found to have an R dependence that is opposite to that of the superconducting transition tempera-
ture Tc. This indicates that the pseudogap state is competing with high-Tc superconductivity, and
the large Tc suppression caused by out-of-plane disorder is due to the stabilization of the pseudogap
state.
http://arxiv.org/abs/0704.1698v2
High temperature superconductivity occurs with doping carriers to a Mott insulator.
Carriers are usually doped either by varying the oxygen content or by an element substitu-
tion. Unavoidably, these procedures introduce disorder that influences the superconducting
transition temperature Tc even though only sites outside the CuO2 plane are chemically
modified. For instance, Tc of the La2CuO4 family depends on the size of the cation that
substitutes for La,1 and Tc of Bi2Sr1.6R0.4CuOy depends on the R element.
2,3 Recently, some
of the present authors have studied extensively the Bi2Sr2−xRxCuOy system using single
crystals and varied the R content x over a wide range for R=La, Sm, and Eu.4 The results
clearly show that Tc at the optimal doping T
c depends strongly on the R element and
decreases with the decrease in the ionic radius of R, in other words, with increasing disorder.
By plotting Tc as a function of the thermopower at 290 K S(290), it was found that the range
of S(290) values for samples with a non-zero Tc becomes narrower with increasing disorder
(see Fig. 1). Because S(290) correlates well with hole doping in many high-Tc cuprates,
this suggests that the doping range where superconductivity occurs decreases with increas-
ing out-of-plane disorder, in contrast to the naive expectation that the plot of Tc/T
c vs.
doping would merge into a universal curve for all high-Tc cuprates.
Despite the strong influence on Tc and on the doping range where superconductivity
can be observed, out-of-plane disorder affects only weakly the conduction along the CuO2
plane. According to Fujita et al.,6 out-of-plane disorder suppresses Tc more than Zn when
samples with a similar residual resistivity are compared. This means that out-of-plane
disorder influences Tc without being a strong scatterer, and that this type of disorder has
an unexplained effect on Tc. To elucidate the reason of this puzzling behavior and why the
carrier range of high-Tc superconductivity is affected by out-of-plane disorder, we studied
the electronic structure of R=La and Eu crystals by means of angle-resolved photoemission
spectroscopy (ARPES) measurements. We particularly focused on the so-called antinodal
position, the point where the Fermi surface crosses the (π,0)-(π,π) zone boundary (M̄-Y cut),
due to the following reasons. It is generally accepted that in-plane resistivity is sensitive to
the electronic structure near the nodal point of the Fermi surface.7,8,9 The small influence
of out-of-plane disorder on residual resistivity hence suggests that the electronic structure
of this region is not much affected, as Fujita et al. mentioned.6 Therefore, if out-of-plane
disorder causes any influence on the electronic structure, it would be more likely to occur at
the antinodal point of the Fermi surface.
The single crystals used in this study were grown by the floating zone method as re-
ported previously.4 As mentioned in that work and commonly observed for Bi-based high-Tc
cuprates, the composition of the grown crystal is not the same as the starting one and
depends on the position within the boule. Accordingly, the hole doping level can not be
determined from the starting composition of the crystal. On the other hand, it has been
shown for many cuprates that S(290) correlates well with hole doping. Although S(290)
is not directly related to the amount of carriers and should depend on the detail of the
electronic structure, this empirical connection provides a reasonable indicator for the hole
doping level. We note that we have confirmed in a separate experiment that the Fermi
surface of a R=La and a R=Eu crystal with similar S(290) values coincided quite well,10
implying that their hole doping was similar. Therefore, we use S(290) as a measure of doping
in the following.11
All crystals were annealed at 750◦C for 72 hours in air. The ARPES spectra were accu-
mulated using a Scienta SES2002 hemispherical analyzer with the Gammadata VUV5010
photon source (He Iα) at the Institute of Solid State Physics (ISSP), the University of Tokyo,
and at beam-line BL5U of UVSOR at the Institute for Molecular Science, Okazaki with an
incident photon energy of 18.3 eV. The energy resolution was 10-20 meV for all measure-
ments, which was determined by the intensity reduction from 90% to 10% at the Fermi edge
of a reference gold spectrum. Thermopower was measured by a four-point method using a
home-built equipment. S(290) was determined using crystals that were cleaved from those
used for ARPES measurements except the R=La sample that had the largest doping in Fig.
4(a). For that particular sample, the S(290) value was estimated from the c-axis length
deduced from x-ray diffraction based on the data shown in the inset to Fig. 1.
Figures 2(a) and (c) show the ARPES intensity plots along the (π,0)-(π,π) direction at
100 K for R=La and Eu crystals that have a similar hole concentration. The samples were
cleaved in situ at 250 K in a vacuum of better than 5×10−11 Torr. The S(290) values were
4.7 µV/K and 4.8 µV/K for the R=La and Eu samples, respectively, indicating that they are
slightly underdoped (see Fig. 1). Figures 2(b) and (d) show momentum distribution curves
(MDCs) of the R=La and Eu samples, respectively. We fitted the MDC curves to a Lorentz
function to determine the peak position. The thus extracted dispersion is superimposed by
white small circles on Figs. 2(a) and (c). The momentum where the dispersion curve crosses
the Fermi energy EF corresponds to the Fermi wave vector kF on the (π,0)-(π,π) cut, and
-2002040
S(290) (µV/K)
-2002040
S(290) (µV/K)
FIG. 1: (color online) The critical temperature Tc as a function of S(290), the thermopower at
290 K. Tc was determined from the temperature dependence of resistivity, which was measured
simultaneously with thermopower. Data are based on our previous work,4 and some new data
points are included. Inset: Lattice constant c plotted as a function of S(290).
Fig. 2(e) shows the energy distribution curves (EDCs) of the two samples at kF . Obviously,
the R=La sample has a larger spectral weight at EF , although the doping level of the two
samples is very similar.
Figure 3 shows the EDCs of the two samples of Fig. 2 at various temperatures. To
remove the effects of the Fermi function on the spectra, we applied the symmetrization
method Isym(ω) = I(ω) + I(−ω), where ω denotes the energy relative to EF .
12 As shown in
Figs. 3(a) and (b), the symmetrized spectra of both samples show clearly a gap structure at
the lowest measured temperature, 100 K. Because we are probing the antinodal direction at
a temperature that is higher than Tc, we attribute this gap structure to the pseudogap. With
increasing the temperature, the gap structure fills up without an obvious change in the gap
size. At 250 K, only a small suppression of the spectral weight was observed for the R=La
-0.08
-0.06
-0.04
-0.02
Momentum
T=100KR=Eu
-0.08
-0.06
-0.04
-0.02
Momentum
R=La T=100K
(0,0)
(π,π)
Momentum
−40meV
E-EF=−80meV
Momentum
−40meV
E-EF=−80meV
-0.4 -0.3 -0.2 -0.1 0.0 0.1
E-EF (eV)
(a) (c)
(e) (f)
(b) (d)
FIG. 2: (color online) Intensity plots in the energy-momentum plane of the ARPES spectra at
100 K of slightly underdoped Bi2Sr2−xRxCuOy samples that have a similar doping level with (a)
R=La and (c) R=Eu along the momentum line indicated by the arrow in (f). (b), (d) Momentum
distribution curves (MDCs) of the two samples. (e) The energy distribution curves (EDCs) of the
two samples at kF . (f) Schematic drawing of the underlying Fermi surface.
sample. On the other hand, a clear pseudogap structure can be observed for the R=Eu
sample even at 250 K. This means that the temperature T ∗ up to which the pseudogap
structure can be observed is certainly different despite the closeness of the doping level.
The thin solid lines Ifit(ω) of Figs. 3(a) and (b) are the results of fitting a Lorentz function
to the symmetrized spectrum in the energy range of EF ± 150 meV. The dashed lines are,
on the other hand, the background spectra Ibkg(ω), which were determined by making a
similar fit in the energy range of 150 meV≤ |ω| ≤400 meV. It can be seen that the difference
between the two fitted curves at EF increases with decreasing the temperature, reflecting
the growth of the pseudogap. To quantify how much the spectral weight at EF is depressed,
we define IPG as the difference between unity and the spectral weight of the fitted spectrum
at EF divided by that of the background curve (1 − Ifit(0)/Ibkg(0)). Figure 3(c) shows the
temperature dependence of IPG of the two samples. Obviously, the depression of the spectral
weight is larger for the R=Eu sample at all measured temperatures, and T ∗ is higher. IPG is
roughly linear temperature dependent for both samples with a very similar slope. Therefore,
we extrapolated the data with the same slope as shown by the dashed lines, and estimated
T ∗ to be 282 K and 341 K for the R=La and Eu samples, respectively.
We also measured ARPES spectra of four other samples at 150 K. Assuming that the
temperature dependence of IPG is the same as that of Fig. 3(c), we can estimate T
∗ from
the IPG value at 150 K. The thus estimated T
∗ values are included in Fig. 4(a), which shows
T ∗ of all samples studied in this work as a function of S(290). It can be seen that T ∗ is
higher for R=Eu than R=La when compared at the same S(290) value. Because Tc at the
same hole doping decreases with changing the R element to one with a smaller ionic radius
(Fig. 1), it is clear that Tc and T
∗ have an opposite R dependence. This important finding
is summarized on the schematic phase diagram shown in Fig. 4(b). As shown, both Tmaxc
and the carrier range where superconductivity takes place on the phase diagram decrease
with decreasing the ionic radius of R, while T ∗ at the same hole concentration increases.11
One of the most important issues of pseudogap has been whether such state is a compet-
itive one or a precursor state of high-Tc superconductivity.
14 Figure 4(b) clearly shows that
whatever the microscopic origin of the pseudogap is, it is competing with high-Tc supercon-
ductivity. In contrast, some other studies have concluded that pseudogap is closely related
to the superconducting state because the momentum dependence of the gap is the same
above and below Tc and the evolution of the gap structure through Tc is smooth.
12,15,16 We
point out, however, that several recent experiments revealed the existing of two energy gaps
at a temperature well below Tc for underdoped cuprate superconductors
17,18 as well as for
optimally doped and overdoped (Bi,Pb)2(Sr,La)2CuO6+δ.
19,20 The energy gap observed in
the antinodal region was attributed to the pseudogap while the one near the nodal direction
0 100 200 300
T (K)
-0.2 0 0.2
E-EF (eV)
-0.2 0 0.2
E-EF (eV)
R=La(a)
FIG. 3: (color online) Temperature dependence of the symmetrized ARPES spectrum at the antin-
odal point for the (a) R=La and (b) R=Eu crystals of Fig. 2. (c) Temperature dependence of the
amount of spectral weight suppression IPG.
to the superconducting gap. We think that the conflict encountered in the pseudogap issue
arose because distinguishing these two gaps would be not easy when their magnitudes are
similar.
We next discuss why Tc decreases when T
∗ increases. We think that the ungapped
Carrier Concentration
(a) (b)
S(290) (µV/K)
carrier doping
FIG. 4: (color online) (a) Pseudogap temperature T ∗ plotted as a function of S(290). (b) A
schematic phase diagram of Bi2Sr2−xRxCuOy based on the results of Figs. 1 and 4(a).
portion of the Fermi surface above Tc is smaller for R=Eu when compared at the same
doping and at the same temperature because pseudogap opens at a temperature that is
higher than R=La. Indeed, the results of our ARPES experiment on optimally doped
Bi2Sr2−xRxCuOy confirmed this assumption by demonstrating that the momentum region
where a quasiparticle or a coherence peak was observed was narrower for the R=Eu sample
than the R=La sample.10 In other words, the Fermi arc shrinks with changing the R element
from La to Eu, which mimics the behavior observed when doping is decreased.8,13 Because
the superfluid density ns decreases with underdoping,
21 it is reasonable to assume that
only the states on the Fermi arc can participate to superconductivity. If we can think in
analogy to the carrier underdoping case therefore, ns would be smaller forR=Eu than R=La,
and the decrease of Tc is quite naturally explained from the Uemura relation.
21 The faster
disappearance of superconductivity with carrier underdoping for R=Eu (see Fig. 1) is also
a straightforward consequence of this model. Furthermore, the opening of the pseudogap at
the antinodal direction would not increase much the residual in-plane resistivity because the
in-plane conduction is mainly governed by the nodal carriers.7,8,9 Hence, the observation that
out-of-plane disorder largely suppresses Tc with only a slight increase in residual resistivity
can also be immediately understood.
Finally, we discuss our results in conjunction with the reported data of scanning tunneling
microscopy/spectroscopy (STM/STS) experiments, which unveiled a strong inhomogeneity
in the local electronic structure for Bi2Sr2CaCu2Oy.
22,23,24 It was demonstrated that the
volume fraction of the pseudogapped region increases with underdoping. The ARPES ex-
periments, on the other hand, show that the spectral weight at the chemical potential of the
antinodal region decreases with carrier underdoping.14 Hence, the antinodal spectral weight
at EF is likely to correlate with the volume fraction of the pseudogap region. In the present
work, we increased the degree of out-of-plane disorder while the hole doping was unaltered,
and observed that the spectral weight at the chemical potential is lower for the R=Eu sample
when compared at the same temperature, as shown in Fig. 3(c). We thus expect that the
fraction of superconducting region in real space is smaller for R=Eu. Indeed, quite recent
STM/STS experiments on optimally doped Bi2Sr2−xRxCuOy report that the averaged gap
size is larger when the ionic radius of R is smaller,25 which is attributable to an increase of
the pseudogapped region. Moreover, our results complement the STM/STS data and indi-
cate that not only the area where a pseudogap is observed at low temperature but also T ∗
increases with disorder which means that the pseudogap state is stabilized and persists up to
higher temperatures. Further, while the STM/STS studies on Bi2Sr2−xRxCuOy investigated
only optimally doped samples,25,26 we have varied hole doping, which further corroborates
the conclusion that the pseudogap state competes with high-Tc superconductivity.
In summary, we have studied the mechanism why Tmaxc and the carrier range where
high-Tc superconductivity occurs strongly depend on the R element in the Bi2Sr2−xRxCuOy
system by investigating the electronic structure at the antinodal direction of the Fermi sur-
face of R=La and Eu samples. We observed a pseudogap structure in the ARPES spectrum
up to a higher temperature for R=Eu samples when samples with a similar hole doping are
compared, which clearly indicates that the pseudogap state is competing with high-Tc su-
perconductivity. This result suggests that out-of-plane disorder increases the pseudogapped
region and reduces the superconducting fluid density, which explains its strong influence
on high-Tc superconductivity. We stress that the present results are relevant to all high-Tc
superconductors because they are more or less suffered from out-of-plane disorders.
We would like to thank T. Ito of UVSOR and T. Kitao and H. Kaga of Nagoya University
for experimental assistance.
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	References

  The electronic structure of Bi2Sr2-xRxCuOy(R=La, Eu) near the (pi,0) point of
the first Brillouin zone was studied by means of angle-resolved photoemission
spectroscopy (ARPES). The temperature T* above which the pseudogap structure in
the ARPES spectrum disappears was found to have an R dependence that is
opposite to that ofthe superconducting transition temperature Tc. This
indicates that the pseudogap state is competing with high-Tc superconductivity,
and the large Tc suppression observed with increasing the out-of-plane disorder
is due to the stabilization of the pseudogap state.

The origin of the anomalously strong influence of out-of-plane
disorder on high-T
superconductivity
Y. Okada,1 T. Takeuchi,2 T. Baba,3 S. Shin,3 and H. Ikuta1
1Department of Crystalline Materials Science,
Nagoya University, Nagoya 464-8603, Japan
2EcoTopia Science Institute, Nagoya University, Nagoya 464-8603, Japan
3Institute for Solid State Physics (ISSP),
University of Tokyo, Kashiwa 277-8581, Japan
(Dated: )
Abstract
The electronic structure of Bi2Sr2−xRxCuOy (R=La, Eu) near the (π,0) point of the first Bril-
louin zone was studied by means of angle-resolved photoemission spectroscopy (ARPES). The
temperature T ∗ above which the pseudogap structure in the ARPES spectrum disappears was
found to have an R dependence that is opposite to that of the superconducting transition tempera-
ture Tc. This indicates that the pseudogap state is competing with high-Tc superconductivity, and
the large Tc suppression caused by out-of-plane disorder is due to the stabilization of the pseudogap
state.
http://arxiv.org/abs/0704.1698v2
High temperature superconductivity occurs with doping carriers to a Mott insulator.
Carriers are usually doped either by varying the oxygen content or by an element substitu-
tion. Unavoidably, these procedures introduce disorder that influences the superconducting
transition temperature Tc even though only sites outside the CuO2 plane are chemically
modified. For instance, Tc of the La2CuO4 family depends on the size of the cation that
substitutes for La,1 and Tc of Bi2Sr1.6R0.4CuOy depends on the R element.
2,3 Recently, some
of the present authors have studied extensively the Bi2Sr2−xRxCuOy system using single
crystals and varied the R content x over a wide range for R=La, Sm, and Eu.4 The results
clearly show that Tc at the optimal doping T
c depends strongly on the R element and
decreases with the decrease in the ionic radius of R, in other words, with increasing disorder.
By plotting Tc as a function of the thermopower at 290 K S(290), it was found that the range
of S(290) values for samples with a non-zero Tc becomes narrower with increasing disorder
(see Fig. 1). Because S(290) correlates well with hole doping in many high-Tc cuprates,
this suggests that the doping range where superconductivity occurs decreases with increas-
ing out-of-plane disorder, in contrast to the naive expectation that the plot of Tc/T
c vs.
doping would merge into a universal curve for all high-Tc cuprates.
Despite the strong influence on Tc and on the doping range where superconductivity
can be observed, out-of-plane disorder affects only weakly the conduction along the CuO2
plane. According to Fujita et al.,6 out-of-plane disorder suppresses Tc more than Zn when
samples with a similar residual resistivity are compared. This means that out-of-plane
disorder influences Tc without being a strong scatterer, and that this type of disorder has
an unexplained effect on Tc. To elucidate the reason of this puzzling behavior and why the
carrier range of high-Tc superconductivity is affected by out-of-plane disorder, we studied
the electronic structure of R=La and Eu crystals by means of angle-resolved photoemission
spectroscopy (ARPES) measurements. We particularly focused on the so-called antinodal
position, the point where the Fermi surface crosses the (π,0)-(π,π) zone boundary (M̄-Y cut),
due to the following reasons. It is generally accepted that in-plane resistivity is sensitive to
the electronic structure near the nodal point of the Fermi surface.7,8,9 The small influence
of out-of-plane disorder on residual resistivity hence suggests that the electronic structure
of this region is not much affected, as Fujita et al. mentioned.6 Therefore, if out-of-plane
disorder causes any influence on the electronic structure, it would be more likely to occur at
the antinodal point of the Fermi surface.
The single crystals used in this study were grown by the floating zone method as re-
ported previously.4 As mentioned in that work and commonly observed for Bi-based high-Tc
cuprates, the composition of the grown crystal is not the same as the starting one and
depends on the position within the boule. Accordingly, the hole doping level can not be
determined from the starting composition of the crystal. On the other hand, it has been
shown for many cuprates that S(290) correlates well with hole doping. Although S(290)
is not directly related to the amount of carriers and should depend on the detail of the
electronic structure, this empirical connection provides a reasonable indicator for the hole
doping level. We note that we have confirmed in a separate experiment that the Fermi
surface of a R=La and a R=Eu crystal with similar S(290) values coincided quite well,10
implying that their hole doping was similar. Therefore, we use S(290) as a measure of doping
in the following.11
All crystals were annealed at 750◦C for 72 hours in air. The ARPES spectra were accu-
mulated using a Scienta SES2002 hemispherical analyzer with the Gammadata VUV5010
photon source (He Iα) at the Institute of Solid State Physics (ISSP), the University of Tokyo,
and at beam-line BL5U of UVSOR at the Institute for Molecular Science, Okazaki with an
incident photon energy of 18.3 eV. The energy resolution was 10-20 meV for all measure-
ments, which was determined by the intensity reduction from 90% to 10% at the Fermi edge
of a reference gold spectrum. Thermopower was measured by a four-point method using a
home-built equipment. S(290) was determined using crystals that were cleaved from those
used for ARPES measurements except the R=La sample that had the largest doping in Fig.
4(a). For that particular sample, the S(290) value was estimated from the c-axis length
deduced from x-ray diffraction based on the data shown in the inset to Fig. 1.
Figures 2(a) and (c) show the ARPES intensity plots along the (π,0)-(π,π) direction at
100 K for R=La and Eu crystals that have a similar hole concentration. The samples were
cleaved in situ at 250 K in a vacuum of better than 5×10−11 Torr. The S(290) values were
4.7 µV/K and 4.8 µV/K for the R=La and Eu samples, respectively, indicating that they are
slightly underdoped (see Fig. 1). Figures 2(b) and (d) show momentum distribution curves
(MDCs) of the R=La and Eu samples, respectively. We fitted the MDC curves to a Lorentz
function to determine the peak position. The thus extracted dispersion is superimposed by
white small circles on Figs. 2(a) and (c). The momentum where the dispersion curve crosses
the Fermi energy EF corresponds to the Fermi wave vector kF on the (π,0)-(π,π) cut, and
-2002040
S(290) (µV/K)
-2002040
S(290) (µV/K)
FIG. 1: (color online) The critical temperature Tc as a function of S(290), the thermopower at
290 K. Tc was determined from the temperature dependence of resistivity, which was measured
simultaneously with thermopower. Data are based on our previous work,4 and some new data
points are included. Inset: Lattice constant c plotted as a function of S(290).
Fig. 2(e) shows the energy distribution curves (EDCs) of the two samples at kF . Obviously,
the R=La sample has a larger spectral weight at EF , although the doping level of the two
samples is very similar.
Figure 3 shows the EDCs of the two samples of Fig. 2 at various temperatures. To
remove the effects of the Fermi function on the spectra, we applied the symmetrization
method Isym(ω) = I(ω) + I(−ω), where ω denotes the energy relative to EF .
12 As shown in
Figs. 3(a) and (b), the symmetrized spectra of both samples show clearly a gap structure at
the lowest measured temperature, 100 K. Because we are probing the antinodal direction at
a temperature that is higher than Tc, we attribute this gap structure to the pseudogap. With
increasing the temperature, the gap structure fills up without an obvious change in the gap
size. At 250 K, only a small suppression of the spectral weight was observed for the R=La
-0.08
-0.06
-0.04
-0.02
Momentum
T=100KR=Eu
-0.08
-0.06
-0.04
-0.02
Momentum
R=La T=100K
(0,0)
(π,π)
Momentum
−40meV
E-EF=−80meV
Momentum
−40meV
E-EF=−80meV
-0.4 -0.3 -0.2 -0.1 0.0 0.1
E-EF (eV)
(a) (c)
(e) (f)
(b) (d)
FIG. 2: (color online) Intensity plots in the energy-momentum plane of the ARPES spectra at
100 K of slightly underdoped Bi2Sr2−xRxCuOy samples that have a similar doping level with (a)
R=La and (c) R=Eu along the momentum line indicated by the arrow in (f). (b), (d) Momentum
distribution curves (MDCs) of the two samples. (e) The energy distribution curves (EDCs) of the
two samples at kF . (f) Schematic drawing of the underlying Fermi surface.
sample. On the other hand, a clear pseudogap structure can be observed for the R=Eu
sample even at 250 K. This means that the temperature T ∗ up to which the pseudogap
structure can be observed is certainly different despite the closeness of the doping level.
The thin solid lines Ifit(ω) of Figs. 3(a) and (b) are the results of fitting a Lorentz function
to the symmetrized spectrum in the energy range of EF ± 150 meV. The dashed lines are,
on the other hand, the background spectra Ibkg(ω), which were determined by making a
similar fit in the energy range of 150 meV≤ |ω| ≤400 meV. It can be seen that the difference
between the two fitted curves at EF increases with decreasing the temperature, reflecting
the growth of the pseudogap. To quantify how much the spectral weight at EF is depressed,
we define IPG as the difference between unity and the spectral weight of the fitted spectrum
at EF divided by that of the background curve (1 − Ifit(0)/Ibkg(0)). Figure 3(c) shows the
temperature dependence of IPG of the two samples. Obviously, the depression of the spectral
weight is larger for the R=Eu sample at all measured temperatures, and T ∗ is higher. IPG is
roughly linear temperature dependent for both samples with a very similar slope. Therefore,
we extrapolated the data with the same slope as shown by the dashed lines, and estimated
T ∗ to be 282 K and 341 K for the R=La and Eu samples, respectively.
We also measured ARPES spectra of four other samples at 150 K. Assuming that the
temperature dependence of IPG is the same as that of Fig. 3(c), we can estimate T
∗ from
the IPG value at 150 K. The thus estimated T
∗ values are included in Fig. 4(a), which shows
T ∗ of all samples studied in this work as a function of S(290). It can be seen that T ∗ is
higher for R=Eu than R=La when compared at the same S(290) value. Because Tc at the
same hole doping decreases with changing the R element to one with a smaller ionic radius
(Fig. 1), it is clear that Tc and T
∗ have an opposite R dependence. This important finding
is summarized on the schematic phase diagram shown in Fig. 4(b). As shown, both Tmaxc
and the carrier range where superconductivity takes place on the phase diagram decrease
with decreasing the ionic radius of R, while T ∗ at the same hole concentration increases.11
One of the most important issues of pseudogap has been whether such state is a compet-
itive one or a precursor state of high-Tc superconductivity.
14 Figure 4(b) clearly shows that
whatever the microscopic origin of the pseudogap is, it is competing with high-Tc supercon-
ductivity. In contrast, some other studies have concluded that pseudogap is closely related
to the superconducting state because the momentum dependence of the gap is the same
above and below Tc and the evolution of the gap structure through Tc is smooth.
12,15,16 We
point out, however, that several recent experiments revealed the existing of two energy gaps
at a temperature well below Tc for underdoped cuprate superconductors
17,18 as well as for
optimally doped and overdoped (Bi,Pb)2(Sr,La)2CuO6+δ.
19,20 The energy gap observed in
the antinodal region was attributed to the pseudogap while the one near the nodal direction
0 100 200 300
T (K)
-0.2 0 0.2
E-EF (eV)
-0.2 0 0.2
E-EF (eV)
R=La(a)
FIG. 3: (color online) Temperature dependence of the symmetrized ARPES spectrum at the antin-
odal point for the (a) R=La and (b) R=Eu crystals of Fig. 2. (c) Temperature dependence of the
amount of spectral weight suppression IPG.
to the superconducting gap. We think that the conflict encountered in the pseudogap issue
arose because distinguishing these two gaps would be not easy when their magnitudes are
similar.
We next discuss why Tc decreases when T
∗ increases. We think that the ungapped
Carrier Concentration
(a) (b)
S(290) (µV/K)
carrier doping
FIG. 4: (color online) (a) Pseudogap temperature T ∗ plotted as a function of S(290). (b) A
schematic phase diagram of Bi2Sr2−xRxCuOy based on the results of Figs. 1 and 4(a).
portion of the Fermi surface above Tc is smaller for R=Eu when compared at the same
doping and at the same temperature because pseudogap opens at a temperature that is
higher than R=La. Indeed, the results of our ARPES experiment on optimally doped
Bi2Sr2−xRxCuOy confirmed this assumption by demonstrating that the momentum region
where a quasiparticle or a coherence peak was observed was narrower for the R=Eu sample
than the R=La sample.10 In other words, the Fermi arc shrinks with changing the R element
from La to Eu, which mimics the behavior observed when doping is decreased.8,13 Because
the superfluid density ns decreases with underdoping,
21 it is reasonable to assume that
only the states on the Fermi arc can participate to superconductivity. If we can think in
analogy to the carrier underdoping case therefore, ns would be smaller forR=Eu than R=La,
and the decrease of Tc is quite naturally explained from the Uemura relation.
21 The faster
disappearance of superconductivity with carrier underdoping for R=Eu (see Fig. 1) is also
a straightforward consequence of this model. Furthermore, the opening of the pseudogap at
the antinodal direction would not increase much the residual in-plane resistivity because the
in-plane conduction is mainly governed by the nodal carriers.7,8,9 Hence, the observation that
out-of-plane disorder largely suppresses Tc with only a slight increase in residual resistivity
can also be immediately understood.
Finally, we discuss our results in conjunction with the reported data of scanning tunneling
microscopy/spectroscopy (STM/STS) experiments, which unveiled a strong inhomogeneity
in the local electronic structure for Bi2Sr2CaCu2Oy.
22,23,24 It was demonstrated that the
volume fraction of the pseudogapped region increases with underdoping. The ARPES ex-
periments, on the other hand, show that the spectral weight at the chemical potential of the
antinodal region decreases with carrier underdoping.14 Hence, the antinodal spectral weight
at EF is likely to correlate with the volume fraction of the pseudogap region. In the present
work, we increased the degree of out-of-plane disorder while the hole doping was unaltered,
and observed that the spectral weight at the chemical potential is lower for the R=Eu sample
when compared at the same temperature, as shown in Fig. 3(c). We thus expect that the
fraction of superconducting region in real space is smaller for R=Eu. Indeed, quite recent
STM/STS experiments on optimally doped Bi2Sr2−xRxCuOy report that the averaged gap
size is larger when the ionic radius of R is smaller,25 which is attributable to an increase of
the pseudogapped region. Moreover, our results complement the STM/STS data and indi-
cate that not only the area where a pseudogap is observed at low temperature but also T ∗
increases with disorder which means that the pseudogap state is stabilized and persists up to
higher temperatures. Further, while the STM/STS studies on Bi2Sr2−xRxCuOy investigated
only optimally doped samples,25,26 we have varied hole doping, which further corroborates
the conclusion that the pseudogap state competes with high-Tc superconductivity.
In summary, we have studied the mechanism why Tmaxc and the carrier range where
high-Tc superconductivity occurs strongly depend on the R element in the Bi2Sr2−xRxCuOy
system by investigating the electronic structure at the antinodal direction of the Fermi sur-
face of R=La and Eu samples. We observed a pseudogap structure in the ARPES spectrum
up to a higher temperature for R=Eu samples when samples with a similar hole doping are
compared, which clearly indicates that the pseudogap state is competing with high-Tc su-
perconductivity. This result suggests that out-of-plane disorder increases the pseudogapped
region and reduces the superconducting fluid density, which explains its strong influence
on high-Tc superconductivity. We stress that the present results are relevant to all high-Tc
superconductors because they are more or less suffered from out-of-plane disorders.
We would like to thank T. Ito of UVSOR and T. Kitao and H. Kaga of Nagoya University
for experimental assistance.
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