Band spectrum transformation and temperature dependences of thermoelectric power of Hg₁-xRxBa₂Ca₂Cu₃ O₈+δ system
Temperature dependences of thermoelectric power S(T) at T>Tc of the Hg-based high temperature superconductors Hg₁-xRxBa₂Ca₂Cu₃O₈+δ (R=Re, Pb) have been analyzed with accounting for strong scattering of charge carriers. Transformation of parameters of a narrow conducting band in the region of the...
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irk-123456789-1199742017-06-11T03:04:39Z Band spectrum transformation and temperature dependences of thermoelectric power of Hg₁-xRxBa₂Ca₂Cu₃ O₈+δ system Babych, O. Gabriel, I. Lutsiv, R. Matviyiv, M. Vasyuk, M. Temperature dependences of thermoelectric power S(T) at T>Tc of the Hg-based high temperature superconductors Hg₁-xRxBa₂Ca₂Cu₃O₈+δ (R=Re, Pb) have been analyzed with accounting for strong scattering of charge carriers. Transformation of parameters of a narrow conducting band in the region of the Fermi level was studied. The existence of correlation between the effective bandwidth and the temperature of a superconductive transition Tc is shown. З врахуванням сильного розсiювання носiїв заряду проведено аналiз температурних залежностей коефiцiєнта термоелектрорушiйної сили S(T)при Т>Tc ртутьвмiсних високотемпературних над-провiдникiв (ВТНП) Hg₁−xRxBa₂Ca₂Cu₃O₈+(R=Re, Pb).Розглянута трансформацiя параметрiв вузької провiдної зон в дiлянцi рiвня Фермi. Показано iснування кореляцiї мiж ефективною шириною зони та температурою надпровiдного переходу Tc. 2011 Article Band spectrum transformation and temperature dependences of thermoelectric power of Hg₁-xRxBa₂Ca₂Cu₃ O₈+δ system / O. Babych, I. Gabriel, R. Lutsiv, M. Matviyiv, M. Vasyuk // Condensed Matter Physics. — 2011. — Т. 14, № 1. — С. 13702: 1-6. — Бібліогр.: 13 назв. — англ. 1607-324X PACS: 74.25.Fy, 74.62.Dh, 74.72.Jt DOI:10.5488/CMP.14.13702 arXiv:1106.6163 http://dspace.nbuv.gov.ua/handle/123456789/119974 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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Temperature dependences of thermoelectric power S(T) at T>Tc of the Hg-based high temperature superconductors Hg₁-xRxBa₂Ca₂Cu₃O₈+δ (R=Re, Pb) have been analyzed with accounting for strong scattering of charge carriers. Transformation of parameters of a narrow conducting band in the region of the Fermi level was studied. The existence of correlation between the effective bandwidth and the temperature of a superconductive transition Tc is shown. |
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Article |
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Babych, O. Gabriel, I. Lutsiv, R. Matviyiv, M. Vasyuk, M. |
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Babych, O. Gabriel, I. Lutsiv, R. Matviyiv, M. Vasyuk, M. Band spectrum transformation and temperature dependences of thermoelectric power of Hg₁-xRxBa₂Ca₂Cu₃ O₈+δ system Condensed Matter Physics |
| author_facet |
Babych, O. Gabriel, I. Lutsiv, R. Matviyiv, M. Vasyuk, M. |
| author_sort |
Babych, O. |
| title |
Band spectrum transformation and temperature dependences of thermoelectric power of Hg₁-xRxBa₂Ca₂Cu₃ O₈+δ system |
| title_short |
Band spectrum transformation and temperature dependences of thermoelectric power of Hg₁-xRxBa₂Ca₂Cu₃ O₈+δ system |
| title_full |
Band spectrum transformation and temperature dependences of thermoelectric power of Hg₁-xRxBa₂Ca₂Cu₃ O₈+δ system |
| title_fullStr |
Band spectrum transformation and temperature dependences of thermoelectric power of Hg₁-xRxBa₂Ca₂Cu₃ O₈+δ system |
| title_full_unstemmed |
Band spectrum transformation and temperature dependences of thermoelectric power of Hg₁-xRxBa₂Ca₂Cu₃ O₈+δ system |
| title_sort |
band spectrum transformation and temperature dependences of thermoelectric power of hg₁-xrxba₂ca₂cu₃ o₈+δ system |
| publisher |
Інститут фізики конденсованих систем НАН України |
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2011 |
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http://dspace.nbuv.gov.ua/handle/123456789/119974 |
| citation_txt |
Band spectrum transformation and temperature dependences of thermoelectric power of Hg₁-xRxBa₂Ca₂Cu₃ O₈+δ system / O. Babych, I. Gabriel, R. Lutsiv, M. Matviyiv, M. Vasyuk // Condensed Matter Physics. — 2011. — Т. 14, № 1. — С. 13702: 1-6. — Бібліогр.: 13 назв. — англ. |
| series |
Condensed Matter Physics |
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2025-07-08T16:57:47Z |
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2025-07-08T16:57:47Z |
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| fulltext |
Condensed Matter Physics 2011, Vol. 14, No 1, 13702: 1–6
DOI:10.5488/CMP.14.13702
http://www.icmp.lviv.ua/journal
Band spectrum transformation and temperature
dependences of thermoelectric power of
Hg1−xRxBa2Ca2Cu3O8+δ system
O. Babych∗, I. Gabriel, R. Lutsiv, M. Matviyiv, M. Vasyuk
Ivan Franko National University of Lviv, 50 Dragomanov Str., 79005 Lviv, Ukraine
Received September 28, 2009, in final form May 31, 2010
Temperature dependences of thermoelectric power S(T) at T > Tc of the Hg– based high temperature super-
conductors Hg1−xRxBa2Ca2Cu3O8+δ (R=Re, Pb) have been analyzed with accounting for strong scattering
of charge carriers. Transformation of parameters of a narrow conducting band in the region of the Fermi level
was studied. The existence of correlation between the effective bandwidth and the temperature of a super-
conductive transition Tc is shown.
Key words: high-temperature superconductivity, superconductive transition temperature, thermoelectric
power, narrow conduction band, peak of density of states, Fermi level
PACS: 74.25.Fy, 74.62.Dh, 74.72.Jt
1. Introduction
When studying high temperature superconductors (HTSC), it is important to identify correla-
tion between major peculiarities of the transport process of charge carriers in normal phase T > Tc
and the calculated or model densities of states in the vicinity of the Fermi level.
According to the band calculations, the Fermi level for YBaCuO, HgBaCuO and other cuprates
is near (on a slope) the narrow peak of the density of states (DOS) formed by overlapping of the p –
and d– bands [1, 2]. Therefore, the usage of the narrow band phenomenological model to explain
peculiarities in the behavior of the HTSC materials (see for example [3]) is understandable. There
are considerable discrepancies concerning the role of various atoms and their positions in the
elementary cell in the formation of the conductive band. The data of band-structure calculations
show that the peak in the density of states exists against the background of a considerably wider
band. However, if the Fermi level is located within this narrow energy interval, where the value of
the density of states is larger than beyond this interval, then this peak plays a dominat role in the
properties of the normal state and possibly of the superconductive state as well. The width of this
band is of the order of kBT . Therefore, all its levels can make a considerable contribution to the
transport of electrons.
It should be noted that absolute values, slopes of curves of temperature dependences of the
Hall coefficient Rx and resistivity ρ in particular, vary depending on structure defects, microcracks,
and granularity of the medium. Contribution of the component that is related to imperfections,
to thermoelectric power is considerably smaller. Experimental data on S(T ) obtained by different
authors for samples with equal compositions are close to each other and good reproducibility of
the results is observed. Therefore, differences in values and dependences with the change of compo-
sition should be explained by specific features of electronic structure. Moreover, using theoretical
expressions, one can calculate the absolute values of thermoelectric power, whereas resistivity and
the Hall coefficient can be calculated with an accuracy to a constant because of the lack of nec-
essary data on the material parameters. Due to the aforementioned features, the analysis in the
present study was based on the temperature dependences of thermoelectric power.
∗E-mail: orestbabych@gmail.com
c© O. Babych, I. Gabriel, R. Lutsiv, M. Matviyiv, M. Vasyuk 13702-1
http://dx.doi.org/10.5488/CMP.14.13702
http://www.icmp.lviv.ua/journal
O. Babych et al.
Figure 1. Temperature dependences of thermopower HgBa2Ca2Cu3O8+δ annealed under various
conditions [12], solid lines — calculation results:
1. E0=−6.40 meV, W=45.9 meV, W1/W2=0.70, D(EF)=21.58 eV−1, F=0.474, Tc=128.7 K;
2. E0=−4.60 meV, W=45.0 meV, W1/W2=0.80, D(EF)=21.96 eV−1, F=0.488, Tc=130.0 K;
3. E0=−1.18 meV, W=43.0 meV, W1/W2=0.96, D(EF)=23.23 eV−1, F=0.499, Tc=133.0 K;
4. E0=−1.61 meV, W=44.1 meV, W1/W2=0.87, D(EF)=22.72 eV−1, F=0.484, Tc=131.6 K;
In insert: experimental (o) and calculation (−) data of thermopower Hg0.8Pb0.2Ba2Ca2Cu3O8+δ:
E0=−4.7 meV, W=47.5 meV, W1/W2=0.67, D(EF)=21.50 eV−1, F=0.453, Tc=126.5 K.
The use of the band densities of states does not always make it possible to explain the transport
properties of the HTSC. This can be attributed to the fact that correlation effects are not taken
into account in the one electron approximation of the band theory. Furthermore, there is frequently
no information on electronic structure of compounds with deviations of their compositions from
stoichiometry. That is why we have used a model presentation of the density of states in the Lorentz
form:
D(E) =
1
π
W
(E − E0)2 +W 2
, (1)
where E0 — is the distance of the peak of DOS from the Fermi level, W — is the width of DOS
peak. Thermoelectric power temperature depedence in the phenomenological model term of narrow
band using reference [4] has been calculated:
S(T ) = −
1
|e|T
I1
I0
, (2)
where
I1 =
∫
σE
(
−
df
dE
)
(E − EF) dE, (3)
I0 =
∫
σE
(
−
df
dE
)
dE , (4)
where σE — is the conductivity at T → 0, sensitive to the fine structure of the density of states
near EF , f(E − EF) — the Fermi distribution function. Resistivity is inversely proportional to:
ρ(T ) ∼ 1/I0 = 1/
∫
σE
(
−
df
dE
)
dE. (5)
13702-2
Band spectrum transformation and temperature dependences . . .
To analyse the results obtained we estimated the degree of band filling by electrons:
F (T ) =
∫
f(E − EF)D(E)dE
∫
D(E)dE
. (6)
When selecting the type of scattering of carriers, one ought to note that during the interpretation
of analogous dependences of S(T ) in intermetallic systems with intermediate valence and heavy
fermions on the base of the 4f– , 3d– transition elements, logical results can be obtained by as-
suming σE ∼ D−1(E) (the Mott model – rather weak scattering, attributed mainly to the p − d
transitions) [5, 6]. Values of the mobility of carriers and conductivity for samples of HTSC are com-
paratively small [7, 8], and thus we have used the dependence on the basis of the Kubo-Greenwood
formula σE ∼ D2(E) (general case of a strong scattering).
2. Technical data-out
Members of the mercury homological series HgBa2Can−1CunO2n+n+δ , which demonstrate the
highest currently known temperature of transition in a superconductive state Tc (n = 3), of the
order of 130 K and 160 K both at atmospheric [9] and increased pressures [10, 11], correspondingly,
were selected as objects for the study. There is a large amount of published experimental data
for these superconductive ceramics on temperature dependences of thermoelectric power during
cationic substitutions and anionic doping.
The experimental data for HgBa2Ca2Cu3O8+δ (figure 1) and Hg0.82Re0.18Ba2Ca2Cu3O8+δ (fig-
ure 2) are available from [12, 13]. Temperature dependences of thermoelectric power features with
Figure 2. Temperature dependences of thermopower Hg0.82Re0.18Ba2Ca2Cu3O8+δ annealed un-
der various conditions [13], solid lines — calculation results:
1. E0=−1.08 meV, W=43.3 meV, W1/W2=0.99, D(EF)=23.06 eV−1, F=0.506, Tc=132.6 K;
2. E0=−0.63 meV, W=42.8 meV, W1/W2=1.00, D(EF)=23.36 eV−1, F=0.504, Tc=133.2 K;
3. E0=−0.20 meV, W=43.2 meV, W1/W2=0.99, D(EF)=23.16 eV−1, F=0.500, Tc=132.7 K.
clearly visible maximum at temperatures above the superconductive transition, are presented as
a section of practically linear fall-off with temperature increasing up to 290 K. Authors of this
paper synthesized the samples and measured ρ(T ), Tc and S(T ) when Hg is substituted for Pb
(see figure 1, insert). Introduction of Re, Pb and some other elements results in an improvement of
chemical stability without considerable losses of initial value for Tc . Values of the thermoelectric
13702-3
O. Babych et al.
power decrease up to possible sign inversion for certain compositions with an increase of oxygen
content both in pure and doped samples.
3. Results and discussion
Analyzing the temperature dependences of thermoelectric power in the model of a narrow
band and reaching a qualitative matching between the calculated and experimental data, it is
possible to estimate the band spectrum parameters and trace their transformation with variations
of composition of the samples.
Representation of the peak of the density of states in the form of a symmetric Lorentzian (1) does
not yield satisfactory results. Good agreement of the calculation with experimental dependences
at T > Tc , in particular inversion of the thermoelectric conductivity sign, can be obtained using
a asymmetric peak of the density of states, which is defined by a position of the E0 maximum
relatively to the Fermi level and the two half band widths W1 at E < E0 and W2 at E > E0. The
average value of W = (W1 +W2)/2 is presented in the paper. Let us note the following point: if
the band filling degree F > 1/2, then symmetric Lorentz distribution is below EF and S > 0; if
F < 1/2, it is higher than EF and S < 0, and if F = 1/2 — S = 0. In the case of an asymmetric
band, positive values of S can be also observed at F 6 1/2.
Figure 3. Band broadening, increase of the part of localized states at the band edges (shaded
areas), fall of the density of states at the Fermi level D(EF) as a function of structure disordering.
The results of the calculations using the approach described above for HgBa2Ca2Cu3O8+δ
in the region of optimal oxygen doping are shown in figure 1. Here, the degree of band filling
13702-4
Band spectrum transformation and temperature dependences . . .
decreases in the whole range when the oxygen index δ grows, which corresponds to the acceptor
type of additional ions of oxygen introduced in the system. When the bandwidth increases in the
vicinity of the optimal doping region (curves 2 and 4 in figure 1), the density of states at the Fermi
level D(EF) decreases, which correlates with a decrease of Tc . This can be related to the lattice
disordering (increase of structural defects) when oxygen content deviates from the optimal one
(curve 3) both downwards (curve 2) and upwards (curve 4). This is confirmed by an increase of the
band asymmetry (W1/W2) for compositions 2, 4 as compared with composition 3. Consequently,
the largest Tc (maximal ordering degree) corresponds to sample 3.
An analogous type of the band spectrum transformation was obtained during the analysis of
temperature dependences of thermoelectric power of the Hg0.82Re0.18Ba2Ca2Cu3O8+δ system with
variation of the oxygen index δ (figure 2). Here, correlation between the conducting band width and
correspondingly density of states on the EF and the temperature of transition in superconductive
state is also observed, i.e., larger values of Tc for composition 2 as compared to the 1 and 3.
The relationships obtained correspond to the Anderson model: band broadening, increase of the
part of localized states at the band edges, the drop of the density of states at the Fermi level D(EF)
as a function of disordering structure (figure 3), which corresponds to a type of transformation of
the band spectrum and temperatures of superconductive transition obtained from calculation.
Comparing the dependences S(T ) for pure Hg–1223 samples and those optimally doped with
oxygen (figure 1) with the experimental obtained data for Hg0.8Re0.2Ba2Ca2Cu3O8+δ (insert in the
figure 1), it is found that the inversion is only observed for the (Hg,Pb)–1223 samples for one level
αmax
∼= 3 µV/K with the increase of temperature, which points to additional introduction of holes
due to cationic substitution. This is confirmed by the calculation results: with such substitution of
mercury by lead, there takes place a decrease of the degree of band filling by electrons, a growth
of its symmetry and width, and correspondingly a decay of the D(EF), which corresponds to the
change of Tc (figure 1).
The results of calculations enabled us to assess an impact of various cationic and anionic
substitutions in Hg– containing HTSC not only on the band spectrum parameters, but also on
critical temperature, as well as to trace the relationship between them. Figure 4 graphically depicts
the correlation between Tc and the bandwidth W . Reduction of the density of states value at the
Fermi level due to the band broadening can be caused by a decrease of the Tc .
Figure 4. Correlative dependence between critical temperature and effective conducting band-
width Tc(W ) in the system of Hg1−xRxBa2Ca2Cu3O8+δ (R=Re, Pb).
13702-5
O. Babych et al.
4. Conclusion
Using a representation of the peak of the density of states in the region of the Fermi level in the
form of an asymmetric Lorentz distribution, good agreement of the calculated temperature depen-
dences of the thermoelectric power with experimental data at T > Tc has been obtained. The type
of the behaviour of thermoelectric power of the Hg– containing high temperature superconductors
being studied, with cationic substitution and anionic doping, is defined by such parameters of the
narrow conduction band in the region of the Fermi level as its width W , population by electrons F
and values of the density of states D(EF). Existence of correlation between the effective band width
and the temperature of superconductive transition has been shown during establishing interrelation
between properties of the normal state and superconductive characteristics.
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Трансформацiя зонного спектру та температурнi залежностi
коефiцiєнта термоелектрорушiйної сили в системi
Hg1−xRxBa2Ca2Cu3O8+δ
О. Бабич, I. Габрiєль, Р. Луцiв, М. Матвiїв, М. Васюк
Львiвський нацiональний унiверситет iменi Iвана Франка, вул. Драгоманова, 50, Львiв, Україна
З врахуванням сильного розсiювання носiїв заряду проведено аналiз температурних залежностей
коефiцiєнта термоелектрорушiйної сили S(T) при Т>Tc ртутьвмiсних високотемпературних над-
провiдникiв (ВТНП) Hg1−xRxBa2Ca2Cu3O8+δ (R=Re, Pb). Розглянута трансформацiя параметрiв
вузької провiдної зони в дiлянцi рiвня Фермi. Показано iснування кореляцiї мiж ефективною
шириною зони та температурою надпровiдного переходу Tc.
Ключовi слова: високотемпературна надпровiднiсть, температура надпровiдного переходу,
коефiцiєнт термоелектрорушiйної сили, вузька провiдна зона, пiк густини станiв, рiвень Фермi.
13702-6
http://dx.doi.org/10.1016/0038-1098(87)91136-7
http://dx.doi.org/10.1016/0921-4534(93)90509-O
http://dx.doi.org/10.1016/0921-4534(88)90190-6
http://dx.doi.org/10.1016/S0925-8388(01)01007-6
http://dx.doi.org/10.1134/1.1477479
http://dx.doi.org/10.1103/PhysRevB.35.7124
http://dx.doi.org/10.1103/PhysRevB.51.1330
http://dx.doi.org/10.1038/363056a0
http://dx.doi.org/10.1038/365323a0
http://dx.doi.org/10.1103/PhysRevB.50.4260
Introduction
Technical data-out
Results and discussion
Conclusion
|