ab-plane tunneling and Andreev spectroscopy of superconducting gap and pseudogap in (Bi,Pb)₂Sr₂Ca₂Cu₃O₁₀₊β and Bi₂Sr₂CaCu₂O₈₊δ
We have measured the temperature dependence of gap features revealed by Andreev reflection (Ds) and by tunneling (D) in the ab-plane of optimally and slightly overdoped microcrystals of (BiPb)₂Sr₂Ca₂Cu₃O₁₀₊δ (Bi2223) with critical temperature Tc = 110-115 K, and Bi₂Sr₂CaCu₂O₈₊δ (Bi2212) with Tc = 80...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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| Cite this: | ab-plane tunneling and Andreev spectroscopy of superconducting gap and pseudogap in (Bi,Pb)₂Sr₂Ca₂Cu₃O₁₀₊β and Bi₂Sr₂CaCu₂O₈₊δ / A.I. D`yachenko, V.Yu. Tarenkov, R. Szymczak, H. Szymczak, A.V. Abal`oshev, S.J. Lewandowski, L. Leonyuk // Физика низких температур. — 2003. — Т. 29, № 2. — С. 149-155. — Бібліогр.: 27. назв. — англ. |
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D`yachenko, A.I. Tarenkov, V.Yu. Szymczak, R. Szymczak, H. Abal`oshev, A.V. Lewandowski, S.J. Leonyuk, L. 2018-01-13T20:04:57Z 2018-01-13T20:04:57Z 2003 ab-plane tunneling and Andreev spectroscopy of superconducting gap and pseudogap in (Bi,Pb)₂Sr₂Ca₂Cu₃O₁₀₊β and Bi₂Sr₂CaCu₂O₈₊δ / A.I. D`yachenko, V.Yu. Tarenkov, R. Szymczak, H. Szymczak, A.V. Abal`oshev, S.J. Lewandowski, L. Leonyuk // Физика низких температур. — 2003. — Т. 29, № 2. — С. 149-155. — Бібліогр.: 27. назв. — англ. 0132-6414 PACS: 74.25.Jb, 74.50.+r, 74.72.-h https://nasplib.isofts.kiev.ua/handle/123456789/128786 We have measured the temperature dependence of gap features revealed by Andreev reflection (Ds) and by tunneling (D) in the ab-plane of optimally and slightly overdoped microcrystals of (BiPb)₂Sr₂Ca₂Cu₃O₁₀₊δ (Bi2223) with critical temperature Tc = 110-115 K, and Bi₂Sr₂CaCu₂O₈₊δ (Bi2212) with Tc = 80-84 K. The tunneling conductance of a Bi2223-insulator-Bi2223 junction shows peaks at the 2D gap voltage, as well as dips and broad humps at other voltages. In Bi2223, similarly to the well-known Bi2212 spectra, the energies corresponding to 2D, to the dip, and to the hump structure are in the ratio 2:3:4. This confirms that the dip and hump features are generic to the high-temperature superconductors, irrespective of the number of CuO₂ layers or the BiO superstructure. On the other hand, in both compounds the D(T) and Ds(T) dependences are completely different, and we conclude that the two entities are of different natures. This work was supported by Polish Government (KBN) Grant No PBZ-KBN-013/T08/19. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Свеpхпpоводимость, в том числе высокотемпеpатуpная ab-plane tunneling and Andreev spectroscopy of superconducting gap and pseudogap in (Bi,Pb)₂Sr₂Ca₂Cu₃O₁₀₊β and Bi₂Sr₂CaCu₂O₈₊δ Article published earlier |
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| title |
ab-plane tunneling and Andreev spectroscopy of superconducting gap and pseudogap in (Bi,Pb)₂Sr₂Ca₂Cu₃O₁₀₊β and Bi₂Sr₂CaCu₂O₈₊δ |
| spellingShingle |
ab-plane tunneling and Andreev spectroscopy of superconducting gap and pseudogap in (Bi,Pb)₂Sr₂Ca₂Cu₃O₁₀₊β and Bi₂Sr₂CaCu₂O₈₊δ D`yachenko, A.I. Tarenkov, V.Yu. Szymczak, R. Szymczak, H. Abal`oshev, A.V. Lewandowski, S.J. Leonyuk, L. Свеpхпpоводимость, в том числе высокотемпеpатуpная |
| title_short |
ab-plane tunneling and Andreev spectroscopy of superconducting gap and pseudogap in (Bi,Pb)₂Sr₂Ca₂Cu₃O₁₀₊β and Bi₂Sr₂CaCu₂O₈₊δ |
| title_full |
ab-plane tunneling and Andreev spectroscopy of superconducting gap and pseudogap in (Bi,Pb)₂Sr₂Ca₂Cu₃O₁₀₊β and Bi₂Sr₂CaCu₂O₈₊δ |
| title_fullStr |
ab-plane tunneling and Andreev spectroscopy of superconducting gap and pseudogap in (Bi,Pb)₂Sr₂Ca₂Cu₃O₁₀₊β and Bi₂Sr₂CaCu₂O₈₊δ |
| title_full_unstemmed |
ab-plane tunneling and Andreev spectroscopy of superconducting gap and pseudogap in (Bi,Pb)₂Sr₂Ca₂Cu₃O₁₀₊β and Bi₂Sr₂CaCu₂O₈₊δ |
| title_sort |
ab-plane tunneling and andreev spectroscopy of superconducting gap and pseudogap in (bi,pb)₂sr₂ca₂cu₃o₁₀₊β and bi₂sr₂cacu₂o₈₊δ |
| author |
D`yachenko, A.I. Tarenkov, V.Yu. Szymczak, R. Szymczak, H. Abal`oshev, A.V. Lewandowski, S.J. Leonyuk, L. |
| author_facet |
D`yachenko, A.I. Tarenkov, V.Yu. Szymczak, R. Szymczak, H. Abal`oshev, A.V. Lewandowski, S.J. Leonyuk, L. |
| topic |
Свеpхпpоводимость, в том числе высокотемпеpатуpная |
| topic_facet |
Свеpхпpоводимость, в том числе высокотемпеpатуpная |
| publishDate |
2003 |
| language |
English |
| container_title |
Физика низких температур |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| format |
Article |
| description |
We have measured the temperature dependence of gap features revealed by Andreev reflection (Ds) and by tunneling (D) in the ab-plane of optimally and slightly overdoped microcrystals of (BiPb)₂Sr₂Ca₂Cu₃O₁₀₊δ (Bi2223) with critical temperature Tc = 110-115 K, and Bi₂Sr₂CaCu₂O₈₊δ (Bi2212) with Tc = 80-84 K. The tunneling conductance of a Bi2223-insulator-Bi2223 junction shows peaks at the 2D gap voltage, as well as dips and broad humps at other voltages. In Bi2223, similarly to the well-known Bi2212 spectra, the energies corresponding to 2D, to the dip, and to the hump structure are in the ratio 2:3:4. This confirms that the dip and hump features are generic to the high-temperature superconductors, irrespective of the number of CuO₂ layers or the BiO superstructure. On the other hand, in both compounds the D(T) and Ds(T) dependences are completely different, and we conclude that the two entities are of different natures.
|
| issn |
0132-6414 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/128786 |
| citation_txt |
ab-plane tunneling and Andreev spectroscopy of superconducting gap and pseudogap in (Bi,Pb)₂Sr₂Ca₂Cu₃O₁₀₊β and Bi₂Sr₂CaCu₂O₈₊δ / A.I. D`yachenko, V.Yu. Tarenkov, R. Szymczak, H. Szymczak, A.V. Abal`oshev, S.J. Lewandowski, L. Leonyuk // Физика низких температур. — 2003. — Т. 29, № 2. — С. 149-155. — Бібліогр.: 27. назв. — англ. |
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2025-11-26T00:18:49Z |
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2025-11-26T00:18:49Z |
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| fulltext |
Fizika Nizkikh Temperatur, 2003, v. 29, No. 2, p. 149–155
ab-plane tunneling and Andreev spectroscopy
of superconducting gap and pseudogap
in (Bi,Pb)2Sr2Ca2Cu3O10+� and Bi2Sr2CaCu2O8+�
A.I. D’yachenko1, V.Yu. Tarenkov1, R. Szymczak2, H. Szymczak2,
A.V. Abal’oshev2, S.J. Lewandowski2, and L. Leonyuk 3
1A. Galkin Donetsk Physical and Technical Institute of the National Academy of Sciences of Ukraine
72 R. Luxemburg Str., Donetsk 83114, Ukraine
2Institute of Physics, Polish Academy of Sciences,
32/46 Al. Lotnik�w, 02-668 Warsaw, Poland
E-mail: abala@ifpan.edu.pl
3Moscow State University, Moscow, 118899 Russia
Received May 7, 2002, revised July 29, 2002
We have measured the temperature dependence of gap features revealed by Andreev reflection
(�s) and by tunneling (�) in the ab-plane of optimally and slightly overdoped microcrystals of
(BiPb)2Sr2Ca2Cu3O10+� (Bi2223) with critical temperature Tc = 110–115 K, and Bi2Sr2CaCu2O8+�
(Bi2212) with Tc = 80–84 K. The tunneling conductance of a Bi2223—insulator—Bi2223 junction
shows peaks at the 2� gap voltage, as well as dips and broad humps at other voltages. In Bi2223,
similarly to the well-known Bi2212 spectra, the energies corresponding to 2�, to the dip, and to
the hump structure are in the ratio 2:3:4. This confirms that the dip and hump features are generic
to the high-temperature superconductors, irrespective of the number of CuO2 layers or the BiO su-
perstructure. On the other hand, in both compounds the �(T) and �s(T) dependences are com-
pletely different, and we conclude that the two entities are of different natures.
PACS: 74.25.Jb, 74.50.+r, 74.72.–h
1. Introduction
Along with the usual coherence gap �s, in the spec-
trum of quasiparticle excitations in high-Tc supercon-
ductors there appears a gap �p (pseudogap), which
persists above the superconducting transition tempera-
ture Tc [1,2]. The pseudogap has the same d symmetry
as �s, but disappears (more accurately: becomes indis-
tinct) at some temperature T* > Tc [3]. The relation-
ship between the pseudogap and superconductivity is
far from clear [1,2]. One of the reasons appears to be
that the most popular methods of investigating the ex-
citation spectrum in cuprates, like tunneling and an-
gle-resolved photoemission (ARPES), cannot distin-
guish between �p and �s without recourse to various
theoretical models. However, it is known that in the
process of Andreev reflection of an electron from a
normal metal–superconductor (N–S) interface, a Coo-
per pair is created in the superconductor [4]. This oc-
curs only in the presence of a nonzero energy gap �s in
the superconductor. In other words, the process of
Andreev transformation of an electron–hole pair into
a Cooper pair is possible only for a reflection from the
superconducting order parameter �s. In marked con-
trast, the tunneling effect is sensitive to any singu-
larity in the quasiparticle excitation spectrum [5].
Therefore, the tunneling characteristics at T < Tc in
general depend on joint contributions of the energy
gap and pseudogap.
d-wave symmetry of the energy gap introduces
some additional complications. The dominant con-
tribution to the junction conductivity in classical
(Giaever) tunneling comes from electrons with wave
vectors forming a narrow, only a few degrees wide,
cone [5]. Accordingly, tunnel junctions yield informa-
tion on the gap anisotropy �( )k , and the gap revealed
in tunneling experiments can be expressed as
� � �( ) [ ) )]k k k� �s p
/2 2 1 2( ( [6]. In the case of And-
reev reflection from a clean N–S interface, the situa-
© A.I. D’yachenko, V.Yu. Tarenkov, R. Szymczak, H. Szymczak, A.V. Abal’oshev, S. J. Lewandowski and L. Leonyuk, 2003
tion is different. The incident electron is not scat-
tered, but reflected back along the same trajectory.
This is true for any angle of incidence. It can be said
that all incident electrons participate in Andreev re-
flection on an equal footing. Therefore, measurement
of a single Andreev N–S junction is in principle suffi-
cient to determine the maximal value of the supercon-
ducting gap �s(k).
In this paper we employ the above discussed cha-
racteristic features of tunneling and Andreev spectro-
scopy to investigate the temperature dependence
of the energy gaps � and �s in Bi2Sr2CaCu2O8+�
(Bi2212) and (Bi,Pb)2Sr2Ca2Cu3O10+� [(BiPb)2223]
cuprates. The well-studied Bi2212 has two CuO2 lay-
ers per unit cell and strong incommensurate modu-
lation in the BiO layer [7], which complicates the
interpretation of tunneling and ARPES data. The sub-
stitution of Bi by Pb in the (BiPb)2223 compound
completely erases the superstructure in the BiO layers.
Tunneling measurements were carried out on
«break junctions» with the barrier surface practically
normal to the crystallographic axes in the base ab
plane of the material. In the c direction, the influence
of the BiO layer on the tunneling spectra is much
more pronounced. Andreev experiments were per-
formed on S–N–S junctions. In both cases we retained
only the samples showing pure tunneling or Andreev
characteristics. The temperature dependences of the
energy gaps obtained in the two types of experiments
are completely different and attest to fundamental dif-
ferences between the «superconducting» gap �s and
the a,b-axis quasiparticle gap �.
2. Sample preparation
The tunnel junctions were elaborated from Bi2223
and Bi2212 single crystals. Textured
(Bi1.6Pb0.4)Sr2Ca2Cu3O10+� and Bi2Sr2CaCu2O8 sam-
ples in the form of 10�1�0.1 mm rectangular bars were
prepared [8–10] by compacting powdered (BiPb)2223
and Bi2212 compounds, respectively, at 30–40 kbar
between two steel anvils. The powder was contained
between two thin copper wires, whose deformation
provided uniform pressure distribution in sample vo-
lume. In this manner the powder was compacted into
dense plane-parallel bars about 0.1 mm thick. The
bars were then pre-annealed at T = 845�C for 16 h,
compressed again, and finally annealed at T = 830�C
for 14 h, producing a well-pronounced texture. Usual-
ly the Bi2212 samples were slightly overdoped and ex-
hibited a critical temperature Tc = 80–84 K. The dop-
ing level of the oxygen content was controlled by
annealing optimally doped samples in flowing gas ad-
justed for different partial pressures of oxygen. The
samples emerging from this procedure were highly
textured, composed of tightly packed microcrystals
aligned in one direction. Sample quality was controlled
by transport measurements. We used for further pro-
cessing only those samples which were showing a criti-
cal current density Jc (T = 4.2 K) � 4�104 A/cm2. The
superconducting transition temperature Tc was deter-
mined from the midpoint of the resistive R(T) transi-
tion (see Fig. 1).
The S–I–S and S–N–S junctions were made by
breaking specially prepared Bi2212 and Bi2223 sam-
ples. Each sample was hermetically sealed by insula-
ting resin and glued to an elastic steel plate, which
was then bent until a crack occurred, running across
the sample width and detected by monitoring the sam-
ple resistance. The hermetic seal remained unbroken
in this process. After the external load was relieved,
the sample returned to its initial position with the
crack closed and the microcrystals once again tightly
pressed to each other along the line of the fracture.
The best alignment is expected in the sample region in
which the shear deformation was minimal. This is ap-
parently one of the reasons why such a procedure re-
sults in the realization of one effective junction of the
microcrystal–microcrystal type. The selection of a sin-
gle junction with minimal tunneling resistance from
among the competing junctions is further assisted by
the nature of the tunneling effect, which decreases ex-
ponentially with the barrier thickness. A small sample
thickness (< 100 �m) and a relatively large size of the
microcrystals (> 10 �m) are also important factors en-
hancing junction quality. Such break junctions on
microcrystals were found to be particularly effective
in the investigation of high-Tc superconductors [9].
The typical normal-state resistance of junctions used
150 Fizika Nizkikh Temperatur, 2003, v. 29, No. 2
A.I. D’yachenko et al.
�
�
Fig. 1. Temperature dependence of the ab-plane resistance
of (BiPb)2223 samples with different oxygen doping.
in the present study was between a few ohms and a
few tens of ohms, and were remarkably stable.
The surface of our Bi2212 and (BiPb)2223 break
junctions was perpendicular to the CuO2 plane, and
the direction of tunneling formed only a very small an-
gle with one of the crystallographic axes (a or b) in
this plane, as is attested to by the presence of Andreev
bound states, seen in the tunneling S–I–S characteris-
tics as a characteristic peak of conductivity at zero
bias (cf. Fig. 2). Numerical calculations based on a
simplified theoretical model [9,11] and taking into ac-
count the d-wave mechanism of pairing show that the
appearance of such a narrow zero-bias peak in the tun-
neling conductance occurs at
6�. In high-quality
break junctions the zero-bias conductance peak
(ZBCP) was reported to coexist with the Josephson
effect [12], but we have to rule out this possibility be-
cause of the wrong signature: the ZBCP was insensi-
tive to magnetic field and did not reflect on the I–V
characteristics. The spectra �(V) = dI/dV show the
quasiparticle peaks at 2�, where � is defined as a quar-
ter of the peak-to-peak separation (Fig. 2). We use
this � value as a measure of the gap, since there is no
exact method of extracting the energy gap from the
tunneling spectra, given that the exact functional
form of the density of states for high-Tc superconduc-
tors is not known.
In general, the type of the junction was determined
ex post facto from their conductance �(V) spectra.
We retained for further investigation only the junc-
tions conforming to either S–I–S or S–N–S types. For
example, the �(V) curve in Fig. 2 reveals all the cha-
racteristic features of a superconducting tunnel S–I–S
junction: an almost flat region around zero bias fol-
lowed by a sharp increase in the tunneling current,
peaking around � 60 meV (2�); at still higher bias
voltages V the conductance depends parabolically
on V. The junction shown in Fig. 3, on the other
hand, behaves as a typical Andreev S–N–S junction.
First, there is a low-resistance region at low bias volt-
ages, seen as a broad pedestal spanning the coordinate
origin. The next indication is the excess current,
which was observed in all S–N–S junctions included
in this study. Finally, the differential conductivity
of the junction at eV > 2�s coincides with the nor-
mal-state conductivity at T > Tc [see inset in
Fig. 3,b], i.e., for T > Tc practically all of the bias
voltage is applied directly to the junction.
ab-plane tunneling and Andreev spectroscopy
Fizika Nizkikh Temperatur, 2003, v. 29, No. 2 151
Fig. 2. Tunneling conductance of a Bi2223–I–Bi2223
junction at T = 77.4 K. The zero-bias peak is due to the
Andreev bound state. The spectra clearly show dip and
hump structures. Arrows indicate the 3� and 4� positions.
C
o
n
d
u
ct
an
ce
,
ar
b
.
u
n
it
s
c
�
�
(T
)
/
S
m
ax
a
b
Fig. 3. Conductance � of S–N–S (Andreev)
Bi2212–N–Bi2212 break junction. (a) Temperature depen-
dence of �. The individual plots are shifted vertically for
clarity. (b) Temperature dependence of the energy gap �s.
The inset shows the � plots in their original position.
One may inquire about the mechanism which might
produce in an apparently random manner either S–I–S
or S–N–S junctions. The insulating layer in S–I–S
junctions is most probably caused by oxygen deple-
tion. As to the normal barrier, we speculate that the
CuO2 planes are harder to fracture than the buffer
layers. After the sample is broken, they penetrate
slightly into the buffer layers (see left inset in Fig. 4).
In this manner, the coupling between the CuO2 planes
belonging to the separated sample parts would be
stronger than the normal coupling across the buffer
layers, and it could assist in creating a constriction,
which would act as a normal 3D metal. This hypothe-
sis is in agreement with the scanning microscope study
of the fracture surfaces of Bi2212 single-crystal break
junctions, which revealed rough, but stratified frac-
ture surfaces [13].
3. Experimental results
The temperature dependence of the energy gap
�s(T) obtained from Andreev S–N–S measurements
for Bi2212 exhibited a BCS-like form (see Fig. 3). We
used two methods to determine �s for Andreev junc-
tions. The first one is shown in Fig. 4 and relies on
measuring the distance between the points of maximal
slope changes of the �(V) plot, which is taken as the
measure of 4�s. The details of the second one are
shown in top inset in Fig. 4. The rationale for both
methods is in recent calculations [14], based on the
Klapwijk, Blonder, and Tinkham [15] treatment of
multiple Andreev reflections between two supercon-
ductors, which indicate that 2�s is determined by the
separation of the extrema in d�/dV. The results ob-
tained by both methods are plotted together in
Fig. 3,b. It is seen that these results differ slightly,
but both outline essentially the same �s(T) depen-
dence.
The �(T) gap dependence determined from tunnel-
ing measurements performed on the same compounds
diverged considerably from the BCS relation (Fig. 5).
In fact, �(T) depends on temperature very weakly for
T
Tc. According to an ARPES investigation [16],
such behavior of �(T) in Bi2212 near optimal doping
is expected for the a (or b) direction in the CuO2
plane. This result agrees with our assumption about
the direction of tunneling in our Bi2212–I–Bi2212
junctions. As mentioned above, further confirmation
is provided by the presence of an Andreev bound state,
152 Fizika Nizkikh Temperatur, 2003, v. 29, No. 2
A.I. D’yachenko et al.
Fig. 4. Geometrical construction for the determination of
�s from Andreev measurements. The top inset shows the
corresponding d�/dV plot. The left inset shows the hypo-
thetical inner structure of the Andreev break junction.
Fig. 5. Conductance of S–I–S (tunneling)
Bi2223–I–Bi2223 break junction. The inset shows the tem-
perature dependence of the tunneling gap �(T). Some struc-
tural details of the spectra have been blurred by the speed
of recording needed to overcome temperature instabilities
of the experimental setup.
seen in the spectra of S–N–S and S–I–S junctions as a
characteristic peak of conductivity at zero bias
(cf. Fig. 3 and Fig. 5). According to the ARPES data
[16], near optimal doping the �(T) gap becomes tem-
perature dependent only when is of the order of 15�.
For technological reasons, the formation of break
junctions with the crystal broken at such an angle is
improbable. As a result, the tunneling characteristics
at T > Tc relate to the gap in (100) or (010) direction.
In full agreement with the ARPES results [16],
with increasing temperature the gap � of Bi2212 be-
comes filled with quasiparticle excitations, and the
conductance peaks at 2� become less distinct. The dis-
tance between the still-discernible conductance peaks
does not decrease, and the �(T) gap is seen to persist
into the region T > Tc. Similar behavior is also ob-
served for the (BiPb)2223 compound.
The temperature dependence of the proper coherent
gap �s(T) behaves in a completely different manner
(Fig. 3). The gap narrows with increasing tempera-
ture and at T = Tc it closes completely. The high cur-
vature of the Andreev conductance dip at eV � 2�s is
evidence both of the good quality of the investigated
junctions and of the long lifetime of quasiparticles in
the gap region. This was confirmed by the analysis of
spectra of the normal metal–constriction–supercon-
ductor (N–c–S) junctions [9]. For Bi2212 Andreev
N–c–S junctions, the Blonder—Tinkham—Klapwijk
[17] parameter Z used to obtain the theoretical fit was
small, Z � 0.5, a value characteristic for very clean
N–S contacts.
For energies beyond the gap � value, tunneling in
the ab plane of (BiPb)2223 S–I–S junction revealed
the so-called dip and hump structures, as shown in
Fig. 2 and Fig. 6. In Fig. 6, the voltage axis is norma-
lized to the voltage eVp = �, and the conductance axis
is normalized to the background; the spectra are
shifted vertically for clarity. The dip and hump fea-
tures roughly scale with the gap � for different oxygen
doping levels (see Fig. 7). There is, however, a slight
deviation of the data from a straight line.
4. Theoretical implications
The considerable interest in pseudogap investiga-
tion is stimulated to a great extent by the theoretical
models of high-Tc superconductivity, in which a pseu-
dogap appears as a precursor of the superconducting
gap [18,19], e.g., the bipolaron model [20]. In ano-
ther group of models, the appearance of pseudogap is
related to some sort of magnetic pairing [21]. How-
ever, the domains of applicability of these models are
not very strictly defined and it is quite possible that
the pseudogap (like high-temperature superconducti-
vity) is caused by several simultaneously acting me-
chanisms.
For example, in the Emerson—Kilverson—Zachar
(EKZ) theory [19] the crucial role in the formation of
high temperature superconductivity is ascribed to the
separation of spin and charge, arising as a result of
partitioning of the CuO2 planes into narrow conduct-
ing and dielectric stripes. «Pairing» at T* > Tc in the
EKZ model means the formation of a spin gap. A wide
ab-plane tunneling and Andreev spectroscopy
Fizika Nizkikh Temperatur, 2003, v. 29, No. 2 153
Fig. 6. S–I–S tunneling conductance in the ab plane for
the Bi2223 samples of Fig. 1 at T = 77.4 K. The voltage
axis has been rescaled in units of �. Each curve has been
rescaled and shifted for clarity.
�
Fig. 7. � (dip) and Ep (hump) positions as a function
of energy gap �, determined from the tunneling data
of Figs. 2 and 6.
spin gap (or pseudogap �p) is indeed formed in a spa-
tially limited hole-free region, such as the region
between the conducting stripes. A phase-coherent
(i.e., actually superconducting) state is created only
at T < Tc. The model explains well the smooth transi-
tion of the pseudogap into the tunneling gap � when
the temperature decreases below Tc. However, the ob-
served temperature dependence of the order parameter
gap �(T) at T < Tc is fundamentally different from
that of the gap �s(T), as is seen in Figs. 3 and 5. It is
not clear how the BCS-like �s(T) dependence arises in
the phase-fluctuation picture. Such a situation would
be possible, e.g., in the generation of charge (and
spin) density waves, with the superconducting gap
and pseudogap competing for the same region of the
Brillouin zone [22]. Then the transition to the super-
conducting state could occur in the presence of a
pseudogap in normal excitations, opening, e.g,. in the
electron–hole channel (i.e., a pseudogap, which would
not transform directly into the superconducting gap,
as in the Emery—Kivelson model).
There are numerous experiments that confirm the
essentially different nature of the superconducting
gap �s and the gap (pseudogap) � [23–25]. The most
convincing are intrinsic c-axis tunneling experiments
(in stacked layers) [26]. However, they yield diffe-
rent results from the point contact, scanning tunne-
ling spectroscopy (STM), and break junction experi-
ments: the hump was observed at an energy of 2�
instead of 4�. The authors note a similarity between
the observed c-axis pseudogap and Coulomb pseu-
dogap for tunneling into a two-dimensional electron
system. In our case, the tunneling and Andreev reflec-
tion were realized in the ab plane, and together with
the �(T) dependence (Fig. 4), we clearly observed the
peak–dip–hump structure (Figs. 2 and 3). The posi-
tion of the dip and hump for S–I–S junctions was at
3� and 4� (Fig. 2). This suggests that the observed
dip–hump structure may originate from short-range
magnetic correlations in the ab plane [27]. Then the
gap � would be the fermionic excitation gap and �s —
the mean-field order parameter. It should be empha-
sized, finally, that the observed �s(T) dependence ex-
hibits non-BCS behavior at T � 0 (Fig. 3).
In summary, our ab-plane tunneling and Andreev
spectroscopy studies of normal and slightly overdoped
(BiPb)2223 and Bi2212 compounds show the presence
of both a superconducting energy gap �s, corres-
ponding to d-wave Cooper pairing, and a dip–hump
structure at 3� and 4� (for the S–I–S junction). This
suggests that the high-energy pseudogap, which is as-
sociated with the dip and hump, could be magnetic in
origin. The gap � is nearly temperature independent
and becomes blurred above Tc, being continuously
transformed with increasing temperature into the
pseudogap. In contrast, the order parameter gap �s(T)
has a strong temperature dependence and for T � 0 re-
veals a non-BCS mean field behavior. Our findings are
in general agreement with those of Deutscher [25], al-
though it must be emphasized again that we have con-
sidered the slightly overdoped case.
Acknowledgments
This work was supported by Polish Government
(KBN) Grant No PBZ-KBN-013/T08/19.
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