Anisotropic temperature dependence of normal state resistivity in underdoped region of a layered electron-doped superconductor Nd₂−xCexCuO₄
The aim of this work is to investigate the temperature dependences both in CuO₂ plane and out-of plane resistivities in electron-doped Nd₂–xCexCuO₄ for x from 0.135 up to 0.15 in order to analyze the anisotropy of the electrical transport in the process of the evolution from antiferromagnetic orde...
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| Zitieren: | Anisotropic temperature dependence of normal state resistivity in underdoped region of a layered electron-doped superconductor Nd₂−xCexCuO₄ / A.S. Klepikova, T.B. Charikova, N.G. Shelushinina, M.R. Popov, A.A. Ivanov // Физика низких температур. — 2019. — Т. 45, № 2. — С. 251-257. — Бібліогр.: 31 назв. — англ. |
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irk-123456789-1759622021-02-04T01:30:46Z Anisotropic temperature dependence of normal state resistivity in underdoped region of a layered electron-doped superconductor Nd₂−xCexCuO₄ Klepikova, A.S. Charikova, T.B. Shelushinina, N.G. Popov, M.R. Ivanov, A.A. Спеціальний випуск. «XXII Уральська міжнародна зимова школа з фізики напівпровідників» (20–23 лютого, 2018) The aim of this work is to investigate the temperature dependences both in CuO₂ plane and out-of plane resistivities in electron-doped Nd₂–xCexCuO₄ for x from 0.135 up to 0.15 in order to analyze the anisotropy of the electrical transport in the process of the evolution from antiferromagnetic order in the underdoped region to superconducting order in optimally doped region. Досліджено температурні залежності як внутрішньоплощинних CuO₂, так і позаплощинних питомих опорів в електронно-легованих Nd₂−xCexCuO₄ в діапазоні х = 0,135–0,15 для аналізу анізотропії електричного транспорту в процесі еволюції від антиферомагнітного, в області недодопування, до надпровідного упорядкування, в області оптимального допування. Исследованы температурные зависимости как внутриплоскостных CuO₂, так и внеплоскостных удельных сопротивлений в электронно-легированных Nd₂−xCexCuO₄ в диапазоне х = 0,135–0,15 для анализа анизотропии электрического транспорта в процессе эволюции от антиферромагнитного, в области недодопирования, до сверхпроводящего упорядочения, в области оптимального допирования. 2019 Article Anisotropic temperature dependence of normal state resistivity in underdoped region of a layered electron-doped superconductor Nd₂−xCexCuO₄ / A.S. Klepikova, T.B. Charikova, N.G. Shelushinina, M.R. Popov, A.A. Ivanov // Физика низких температур. — 2019. — Т. 45, № 2. — С. 251-257. — Бібліогр.: 31 назв. — англ. 0132-6414 http://dspace.nbuv.gov.ua/handle/123456789/175962 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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English |
| topic |
Спеціальний випуск. «XXII Уральська міжнародна зимова школа з фізики напівпровідників» (20–23 лютого, 2018) Спеціальний випуск. «XXII Уральська міжнародна зимова школа з фізики напівпровідників» (20–23 лютого, 2018) |
| spellingShingle |
Спеціальний випуск. «XXII Уральська міжнародна зимова школа з фізики напівпровідників» (20–23 лютого, 2018) Спеціальний випуск. «XXII Уральська міжнародна зимова школа з фізики напівпровідників» (20–23 лютого, 2018) Klepikova, A.S. Charikova, T.B. Shelushinina, N.G. Popov, M.R. Ivanov, A.A. Anisotropic temperature dependence of normal state resistivity in underdoped region of a layered electron-doped superconductor Nd₂−xCexCuO₄ Физика низких температур |
| description |
The aim of this work is to investigate the temperature dependences both in CuO₂ plane and out-of plane
resistivities in electron-doped Nd₂–xCexCuO₄ for x from 0.135 up to 0.15 in order to analyze the anisotropy of
the electrical transport in the process of the evolution from antiferromagnetic order in the underdoped region to
superconducting order in optimally doped region. |
| format |
Article |
| author |
Klepikova, A.S. Charikova, T.B. Shelushinina, N.G. Popov, M.R. Ivanov, A.A. |
| author_facet |
Klepikova, A.S. Charikova, T.B. Shelushinina, N.G. Popov, M.R. Ivanov, A.A. |
| author_sort |
Klepikova, A.S. |
| title |
Anisotropic temperature dependence of normal state resistivity in underdoped region of a layered electron-doped superconductor Nd₂−xCexCuO₄ |
| title_short |
Anisotropic temperature dependence of normal state resistivity in underdoped region of a layered electron-doped superconductor Nd₂−xCexCuO₄ |
| title_full |
Anisotropic temperature dependence of normal state resistivity in underdoped region of a layered electron-doped superconductor Nd₂−xCexCuO₄ |
| title_fullStr |
Anisotropic temperature dependence of normal state resistivity in underdoped region of a layered electron-doped superconductor Nd₂−xCexCuO₄ |
| title_full_unstemmed |
Anisotropic temperature dependence of normal state resistivity in underdoped region of a layered electron-doped superconductor Nd₂−xCexCuO₄ |
| title_sort |
anisotropic temperature dependence of normal state resistivity in underdoped region of a layered electron-doped superconductor nd₂−xcexcuo₄ |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2019 |
| topic_facet |
Спеціальний випуск. «XXII Уральська міжнародна зимова школа з фізики напівпровідників» (20–23 лютого, 2018) |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/175962 |
| citation_txt |
Anisotropic temperature dependence of normal state resistivity in underdoped region of a layered electron-doped superconductor Nd₂−xCexCuO₄ / A.S. Klepikova, T.B. Charikova, N.G. Shelushinina, M.R. Popov, A.A. Ivanov // Физика низких температур. — 2019. — Т. 45, № 2. — С. 251-257. — Бібліогр.: 31 назв. — англ. |
| series |
Физика низких температур |
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2025-07-15T13:34:30Z |
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| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 2, pp. 251–257
Anisotropic temperature dependence of normal state
resistivity in underdoped region of a layered
electron-doped superconductor Nd2–xCexCuO4
A.S. Klepikova1, T.B. Charikova1, 2, N.G. Shelushinina1, M.R. Popov1, and A.A. Ivanov3
1M.N. Mikheev Institute of Metal Physics Ural Branch of RAS, Ekaterinburg, Russia
2Ural Federal University, Ekaterinburg, Russia
3National Research Nuclear University MEPhI, Moscow, Russia
E-mail: Popov_mr@imp.uran.ru
Received November 19, 2018, published online December 20, 2018
The aim of this work is to investigate the temperature dependences both in CuO2 plane and out-of plane
resistivities in electron-doped Nd2–xCexCuO4 for x from 0.135 up to 0.15 in order to analyze the anisotropy of
the electrical transport in the process of the evolution from antiferromagnetic order in the underdoped region to
superconducting order in optimally doped region.
Keywords: electron-doped superconductor, anisotropy of transport properties, superconducting films.
1. Introduction
The problem of the resistivity anisotropy in the normal
state of copper oxide systems has long attracted the attention
of researchers. A strong anisotropy of the conducting prop-
erties ( / 1c abρ ρ >> ) when a nonmetallic conductivity along
the c axis is combined with a metallic conductivity in the ab
plane was repeatedly observed in underdoped and optimally
doped hole-type HTSCs [1,2]. This is evidence of the quasi-
two-dimensionality of oxide systems that consist of highly
mobile 2CuO layers separated by buffer layers [3,4]. The
nonmetallic character of cρ in most superconducting high-Tc
compounds suggests an unconventional conduction mecha-
nism between 2CuO planes.
One of the most fundamental concepts in solid state
physics is that in most metallic crystals the electronic con-
duction occurs through the coherent motion of electrons in
band states associated with well-defined wave vectors [5].
There is currently a great deal of interest in whether this
concept is valid for interlayer transport in high-Tc supercon-
ductors [6]. Incoherent transport means that the motion from
layer to layer is diffusive and band states and a Fermi veloci-
ty perpendicular to the layers cannot be defined. The Fermi
surface is then not three-dimensional and Boltzmann
transport theory cannot describe the interlayer transport [7].
The cerium-doped cuprate of 2 4Nd Ce CuOx x− +δ has a
layered quasi-two-dimensional perovskite-like crystal struc-
ture [4]. As compared to other cuprate superconductors,
2 4Nd Ce CuOx x− +δ has many unique properties that make
it an attractive subject for investigations. This is a super-
conductor with an electron-type conductivity whose struc-
ture contains a single 2CuO plane per unit cell. In optimal-
ly annealed crystals, there are no apical oxygen atoms
between neighboring conducting 2CuO planes. Therefore,
2 4Nd Ce CuOx x− crystals have clearly pronounced two-
dimensional properties.
In bulk 2 4Nd Ce CuOx x− +δ single crystals, a very strong
anisotropy of the resistivity is observed, 4/ ~ 10c abρ ρ [8–10],
however, the nonmetallic temperature dependence of ( )c Tρ
is quite rare. This, apparently, is due to the special sensitivity
of the transport properties of the Nd-system to the content of
non-stoichiometric oxygen (δ) and difficulties in achieving
an optimal annealing regime ( 0)δ → for bulk samples. On
the other hand, single-crystal 2 4 3Nd Ce CuO / SrTiOx x−
films (up to 500 nm thick) are well suited for different an-
nealing procedures.
High-quality single-crystal 2 4 3Nd Ce CuO / SrTiOx x− +δ
films with the c axis perpendicular (orientation (001) [11])
and parallel (orientation (110) [12]) to the substrate plane
were obtained and investigated by us earlier. In [13] a com-
parative analysis of ( )ab Tρ and ( )c Tρ temperature depend-
ences for single-crystal films 2 4 3Nd Ce CuO / SrTiOx x− +δ
with 0.12x = (nonsuperconducting underdoped films),
0.15x = (optimally doped films with maximal cT ) and
© A.S. Klepikova, T.B. Charikova, N.G. Shelushinina, M.R. Popov, and A.A. Ivanov, 2019
A.S. Klepikova, T.B. Charikova, N.G. Shelushinina, M.R. Popov, and A.A. Ivanov
0.17, 0.20x = (overdoped films) at orientations (001) and
(110) were done. An emphasis has been placed on the
overdoped region, the “damping” region of superconduc-
tivity (gradual decrease in cT , down to 0cT → for 0.22)x ≈
in comparison with optimal doping one.
In the Nd-system (the n-type HTSC) we have found a
transition from a quasi-2D ( / 0, / 0)c abd dT d dTρ < ρ > to
3D anisotropic system with metallic conductivity both in
the ab-plane and in the c-axis directions ( / 0,cd dTρ >
/ 0)abd dTρ > with increasing of doping, x, as it was
found previously in the La-system (the p-type HTSC) [2].
From the works [2,13] the conclusion about the correlation
of quasi-two-dimensionality of the system with the imple-
mentation of superconductivity in copper oxide compounds
can be done.
Thus the region of the appearance of superconductivity
with increasing cerium doping (at 0.13 0.14x ≈ − ) remained
unexplored. Presently, the advances in technology have al-
lowed us to grow the high-quality 2 4 3Nd Ce CuO / SrTiOx x− +δ
single-crystal films with 0.135x = and 0.145x = in which
the c axis was both normal ((100) films) and parallel ((110)
films) to the substrate plane to study the carrier charge
transfer processes in the region of the antiferromagnetic
(AFM) – superconducting (SC) quantum phase transition.
Study of the properties just of these samples under an
optimal annealing in conjunction with the optimally doped
( 0.15)x = samples is the subject of this work. We are the
first to detect experimentally the ( )c Tρ dependences with
nonmetallic behavior for samples with 0.135x = and
0.145 near the threshold values of x for AFM–SC phase
transition. A comparison of the results obtained for the two
types of films allowed us to demonstrate the quasi-two-
dimensional character of carrier transport in them.
2. Materials and method
The superconductor 2 4Nd Ce CuOx x− +δ with an electron-
type conductivity has a body-centered crystal lattice and
corresponds to a tetragonal T ′-phase. Lattice parameters:
0.39a b= = nm, 1.208c = nm. As a result of doping and
annealing ( 0δ → ), the crystal structure is a set of 2CuO
conducting planes separated by a distance of / 2 0.6d c= =
nm in the direction of the c axis [14]. The compound has
pronounced two-dimensional properties including quasi-
two-dimensional character of the carrier transport.
We have synthesized 2 4 3Nd Ce CuO / SrTiOx x− +δ epi-
taxial films with 0.135x = , 0.145 and 0.15 by pulsed laser
deposition [15,16] of two types:
1. Orientation of the film (001) — the c axis of the
2 4Nd Ce CuOx x− +δ lattice is perpendicular to the 3SrTiO
substrate plane.
2. Orientation of the film (110) — the c axis of the
2 4Nd Ce CuOx x− +δ lattice is directed along the long side of
the 3SrTiO substrate.
In the process of pulsed laser deposition, an excimer KrF
laser was used with a wavelength of 248 nm, with an energy
of 80 mJ/pulse. The energy density at the target surface was
1.5 J/cm2. The pulse duration was 15 ns, the repetition rate
of pulses was from 5 to 20 Hz. Further, the synthesized films
were subjected to heat treatment (annealing) under various
conditions to obtain samples with a maximum superconduct-
ing transition temperature. X-ray diffraction analysis (Co-K
radiation) showed that all films were of high quality and
were single crystal.
The optimum annealing conditions were as follows:
– for the composition onset0.15 ( 23.5 K,cx T= = cT =
22 K)= — 60 min,t = 780 C,T = 510 Torrp −= ;
– for the composition onset0.145 ( 15.7 K,cx T= = cT =
10.7 K)= — 60 min, t = 600 C, T = 510 Torrp −= ;
– for the composition onset0.135 ( 13.7 K,cx T= = cT =
9.6 K)= — 60 min,t = 600 C,T = 510 Torrp −= .
The thickness of the films was 140–520 nm.
The temperature dependences of the resistivity for both
types of 2 4 3Nd Ce CuO / SrTiOx x− +δ films were carried out
in the Quantum Design PPMS 9 and in the solenoid “Oxford
Instruments” (Center for Nanotechnologies and Advanced
Materials, IFM UrB RAS). The electric field was always
applied parallel to the 3SrTiO substrate plane. Depending on
the type of samples we were able to measure the temperature
dependences of the resistivity in the conducting planes of
2CuO and between planes (along the c axis).
3. Experimental results and discussion
The results for both in-plane, abρ (for films with (001)
orientation), and out-of-plane, cρ (films with (110) orienta-
tion), resistivities as functions of the temperature in the sam-
ples 2 4 3Nd Ce CuO / SrTiOx x− with 0.135x = , 0.145 and
0.15, optimally annealed in vacuum, are shown in Fig. 1.
Let us discuss in more detail the temperature depend-
ences of abρ and cρ and their relation in terms of the aniso-
tropic model for a quasi-two-dimensional system with
good metallic conductivity in 2CuO planes in combination
with incoherent transfer between the planes.
3.1. Temperature dependence of resistivity in CuO2 planes
for Nd2–xCexCuO4/SrTiO3 (001) films
It is seen from Fig. 1 that the normal state conductivity
in the ab plane is metallic with a dominant quadratic tem-
perature dependence of ( )Tρ at T > 25–70 K for different
samples up to room temperature. A manifestation of weak
2D localization effects with ( ) ~ lnT Tρ takes place at
50 KT < for 0.145x = and at 70 KT < for 0.135x = .
The resistance in the 2CuO plane is described by the
standard formula [5,17]:
2 ,ab
m
ne
ρ =
τ
(1)
252 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 2
Anisotropic temperature dependence of normal state resistivity in Nd2–xCexCuO4
where n is the concentration and τ is the relaxation time of
the carriers. Let us represent the total scattering probability
in the form 0 in/ ,/ /+τ = τ τ where 0/ τ describes the
elastic scattering probability due to impurities and in )(Tτ is
the inelastic scattering time responsible for the temperature
dependence of the in-plane resistivity. Then we have
( ) (0) ( )ab ab abT Tρ = ρ + ∆ρ (2)
with 2
0(0) ( ) /ab m neρ = τ being the residual resistivity and
2
in( ) / ( ( ))ab T m ne T∆ρ = τ .
In a paper of Kontani et al. [18] the authors give the ex-
planation of a summary of the experimental relations on
quadratic temperature dependence of the normal state in-
plane resistivity ( )ab Tρ for NdCeCuO in the underdoped
region from the standpoint of the nearly antiferromagnetic
(AF) Fermi liquid. The typical spin-fluctuation theories
(see [19] and references therein) give 2~ CTρ and thus
may reproduce the experimental results.
On the other hand, Seng et al. [20] made a conclusion
that quadratic temperature dependence of the zero-field re-
sistivity ( )ab Tρ in the normal state of 1.85 0.15 4Nd Ce CuO −δ,
observed by them, is generated by electron-e1ectron (e-e)
scattering in a two-dimensional metal, i.e. in eeτ ≡ τ .
For electron-electron scattering in a three-dimensional
(3D) metal the 2T dependence of the zero-field resistivity
should take place [17]. For a two-dimensional (2D) metal
the 2T law is modified by a logarithmic correction [21] and
the dependence of Δ )(ab Tρ takes the form
2
) ( / ln ( / )( )ab ee eeT K T T T T∆ρ = . (3)
Seng et al. [20] and also Tsuei et al. [22], in a first step,
fitted a 2T law to their data on the normal state resistivity
of 1.85 0.15 4Nd Ce CuO −δ films. But next they found that
their experimental results are better described by Eqs. (2)
and (3) with the residual resistivity, (0)abρ , the factor K
and the effective temperature, eeT , as fitting parameters.
The solid lines in Fig. 1 are the best fits of Eqs. (2)
and (3) to our experimental data from 25 K for sample with
0.15x = (c), from 50 K for sample with 0.145x = (b) and
from 70 K for sample with 0.135x = (a) up to room tem-
perature with the parameters (0)abρ , K and eeT given in
the Table 1.
Table 1. The values of parameters obtained from a fitting of
Eqs. (2), (3), (4) and (10) to the corresponding experimental data
Sample,
x
ρab(0),
mOhm·cm
K,
mOhm·cm
Tee,
10–3 K Aε , meV ∆ , meV
0.135 0.47 37.85 3.17 1.7 28.6 (8.1*)
0.145 0.34 56.06 4.43 2.4 17.4 (7.2*)
0.15 0.03 328.16 36.8 2.2 12.6 (6.4*)
* The values from a fitting of σc (T) by Eq. (8).
The conclusion is that temperature dependence of zero-
field resistivity )(ab Tρ in the normal state is generated by
electron-e1ectron scattering and that the good fit to the loga-
rithmically corrected 2T law (3) expresses the quasi-2D na-
ture of the conductivity in our specimens.
3.2. The temperature dependence of resistivity across
the CuO2 planes for Nd2–xCexCuO4/SrTiO3 (110) films
It is seen from Fig. 1 that the normal state out-of-plane
resistivity across the blocking layers, cρ , is large with re-
spect to the in-plane resistivity, abρ , and a nonmetallic
Fig. 1. (Color online) Temperature dependences of in-plane, abρ ,
and out-of-plane, cρ , resistivities of 2 4 3Nd Ce CuO / SrTiOx x−
films at different doping and optimal annealing for x = 0.135 (a);
0.145 (b) and 0.15 (c). The solid lines are the best fits of Eqs. (2)
and (3) to our experimental data on ( )ab Tρ . The dashed lines are
fitting of the data on )(c Tρ by function /a b T+ . Insets: coeffi-
cient of resistivity anisotropy, c / abρ ρ , as a function of T for each
of the films.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 2 253
A.S. Klepikova, T.B. Charikova, N.G. Shelushinina, M.R. Popov, and A.A. Ivanov
temperature dependence ( / 0cd dTρ < ) is observed for all
the investigated films up to 300 K.
Two regions can be distinguished in the ( )c Tρ depend-
ence (see Fig. 1): the high-temperature region, 100 KT > ,
where T dependence can be empirically described as
( ) ~ 1/c T Tρ , and the low-temperature region, where out-
of-plane resistivity exibits the activation-type temperature
dependence.
The dashed lines in Fig. 1 are the best fits of function
( ) /T a b Tρ = + to the experimental data from 100 K up to
300 K for each sample. At 100 KT < the dependences of
ln cρ on 1/ T may be described by straight lines corre-
sponding to a function
*) exp( A
c cT
kT
ε ρ = ρ −
(4)
with the values of activation energy Aε given in Table 1.
First the systematic data for ( )c Tρ in a number of well
characterized single high- cT crystals were presented by Ito
et al. [1]. They find that ( )c Tρ is nonmetallic ( / 0)cd dTρ <
in most superconducting compounds, suggesting an un-
conventional conduction mechanism between 2CuO planes
in the normal state of superconducting cooper oxides.
The nonmetallic ( )c Tρ dependences that Ito et al. ob-
served do not fit activation- or hopping-type laws, but ex-
hibit the power law T dependence, c T −αρ ∝ − , with α in
range 0 2< α < . The authors arise a question whether the
measured cρ contains a contribution from abρ due to im-
perfect alignment of layers in the crystal.
Band calculations can explain the large anisotropy of re-
sistivity in high- cT systems but predict that the out-of-plane
conduction is always metallic, in sharp contrast to the exper-
imental facts. As the simplest one-dimensional Kronig–
Penny model with its ideal periodicity (and thus coher-
ence) can only lead to a metallic nature of the interlayer
conductivity, a number of microscopic models for devia-
tion from coherence in c-axis transport have been proposed
[7,12,23–27]).
The effect of incoherent interlayer transport on the re-
sistance of a layered metal was theoretically considered by
McKenzie and Moses [7] wherein the Fermi surface appear-
ance relevant to coherent and incoherent interlayer transport
in a quasi-two-dimensional system was presented.
If the transport between layers is coherent then one can
define a three-dimensional Fermi surface which is a
warped cylinder. For the incoherent interlayer transport a
Fermi surface is defined only within the layers (“a stack of
pancakes”) and the interlayer conductivity is determined
by the interlayer tunneling rate (see Fig. 1 in [7]).
In [7,25–27] the nonmetallic behavior of ( )c Tρ in the
layered oxides was attributed to the incoherent tunneling of
charge carriers in the c-axis direction. Incoherent transport
between 2CuO layers occurs when the probability of carrier
scattering in the plane ( / τ ) is much larger than the inter-
layer hopping integral esc( / )ct ≡ τ between the planes.
Here τ is the carrier relaxation time in the plane, and escτ is
the escape time from the given plane to the neighboring one.
If an electron experiences many collisions before moving
to another plane, the subsequent tunneling processes between
the planes are uncorrelated. The interlayer conductivity,
tun
cσ , is then proportional to the tunneling rate between just
two adjacent layers and can be represented in the following
form (see, for example, [7,25] and references therein):
2
tun 2
22 ,c
c
t
de g
τ
σ =
(5)
where 2/g m= π is the density of states for unit area at the
Fermi energy of the two-dimensional conducting planes.
In the simplified model of square barriers of the height
∆, the tunneling matrix element ct can be calculated as
0exp ( / )ct d r= − , (6)
where r0 is a radius of carrier localization, which is less
than the distance between adjacent 2CuO planes, and
1 2
0 2 /r m− = ∆ .
Thus the c-axis resistivity for the tunneling process is
found to be
tun
tun( (
(
1) )
)
c ab
c
T A T
T
ρ ≡ = ρ
σ
, (7)
with constA = . The second equality in the right side of
Eq. (7) can be obtained by expressing 1/ τ in terms of abρ
using Eq. (1) (see [25] for more details on the relation of
( )c Tρ and ( )ab Tρ ).
Giura et al. [27] proposed the model for the )(c Tρ
based on a submission that the crystal structure along the c
axis induces a stack of energy barriers between the nearly
two-dimensional sheets where the carriers are mostly con-
fined ( 2CuO layers). They assumed that two comple-
mentary processes determine the c-axis transport: incoher-
ent tunneling and thermal activation across the barriers.
For the first mechanism Giura et al. adopted the model
introduced in [7,25–27] (see Eqs. (5) or (7)) which de-
scribes the transport across a barrier trough incoherent tun-
neling process. For the second term, they used the general
expression for thermal activation across the barrier:
th ) exp ( / )( ,c T kTσ = β −∆ (8)
where β is a prefactor which may be weakly dependent on
temperature.
The overall c-axis conductivity is then obtained as the
combination of both contributions:
tun th( () ) )(c c cT T Tσ = σ + σ . (9)
In Fig. 1 we have described the behavior of c-axis resis-
tivity at 100 300 KT = − by the empirical dependence
( ) ~ 1/c T Tρ in accordance with the Ito et al. approach [1].
As far as it is known no theoretical models have predicted
254 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 2
Anisotropic temperature dependence of normal state resistivity in Nd2–xCexCuO4
such a behavior of the out-of-plane conduction in high- cT
copper oxides.
We have attempted to describe the high-temperature
part of ( )c Tρ dependences in the framework of the Giura
et al. [27] model with the help of Eq. (9). Using expres-
sions (7) and (8), we have found
( )( ) ( ) exp exp ( / )c T T q kTσ = α − ∆ +β −∆ , (10)
with 0( ) / ( ), abT Tα = α ρ 0 constα = and 22 2 /q d m= ,
where the formula (6) for ct is used.
Figure 2 shows the experimental dependences of
( ) 1/ ( ),c cT Tσ ≡ ρ as well as the best fitting of these curves
by the expression (10) with the adjustable parameters
0 , and α β ∆ (see Table 1).
The possibility of describing the experimental ( )c Tσ
dependence at 100 KT > by the activation law (8) was
verified on the insets of Fig. 2. It is seen that this law is
valid only in the range of 100–150 KT = for all the three
samples with 8.1 meV∆ = for 0.135x = , 7.2 meV∆ = for
0.145x = and 6.4 meV∆ = for 0.15x = .
On the other hand, the description of c-axis conductivi-
ty, )(c Tσ , by means of Eq. (10) is possible over a wide
temperature ranges of T = 150–300 K with 28.6 meV∆ =
for 0.135x = , of T = 100–300 K with 17.4 meV∆ = for
0.145x = , and of T = 75–250 K with 12.6 meV∆ = for
0.15x = (see the main parts of Figs. 2(a),(b),(c)).
It is seen from Table 1 that the values of ∆, found from
the fitting procedure, decrease with increasing of x. This
pattern is understandable if we take into account that, in
the spirit of the Giura et al. model [27], the barrier height
∆ in Eq. (8) is counted off from the Fermi level, FE , in
each system. The model can explain most of the qualitative
features of observed resistivity, by assuming that an in-
crease of x results in an increase of the carrier density in
the ab planes and thus of the Fermi energy.
The continuous decrease of ∆ as a function of x also
explains in a natural way the crossover from a semicon-
ducting behavior of the 2 4Nd Ce CuOx x− normal-state re-
sistivity at low doping ( 0.12 0.15x = − ) through almost
metallic at slightly overdoped system ( 0.17x = ) to strictly
metallic at highly overdoped region ( 0.20x = ) (see our
work [12] for details).
At low temperatures (kT << ∆) another mechanism of
incoherent transfer between the layers can occur. In the
model of a natural superlattice (when 2CuO layers are
quantum wells and Nd(Ce)O blocks serve as barriers of
the effective height ∆) [27–29], we can consider the disor-
der, that is undoubtedly inherent in this system (the chaotic
impurity potential), as a cause of the temperature depend-
ence of ct [30].
Then in Eq. (5) we have
0( ) exp ( / ) exp ( / )c ct t T d r kT→ = − −δ , (11)
where δ is the spread of electron energy in the wells due to
the fluctuations of ∆ values, the same as in the one-
dimensional Anderson model. The first factor in (11) (over-
lap integral) determines the dependence of the transition
probability between the layers on the barrier height, and the
Fig. 2. (Color online) Temperature dependences of c-axis con-
ductivity for x = 0.135 (a), 0.145 (b) and 0.15 (c). The dashed
lines are the best fits of Eq. (10) to the data. Insets: the fitting of
Eq. (8) to experimental ln ) on 1 /(c T Tσ dependences.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 2 255
A.S. Klepikova, T.B. Charikova, N.G. Shelushinina, M.R. Popov, and A.A. Ivanov
second one leads to a nonmetallic temperature dependence
of the conductivity at low temperatures (analog of the con-
ductivity within the impurity band of semiconductors [30]).
As tun 2~ c ctσ , in Eq. (4) the activation energy 2Aε = δ.
With increasing temperature, the contribution to the
conductivity (8), associated with the thermal activation of
carriers through the barrier, begins to play an increasingly
important role and at kTδ << < ∆ we return to the mecha-
nism of Giura et al. (see Eq. (10)).
3.3. Anisotropy of resistivity for optimally anneale
Nd2–xCexCuO4/SrTiO3 films with various
cerium contents
For the 2D diffusion coefficients along ( D
) and across
( D⊥ ) the layers (see [26], and references therein) one has:
2
/ 2 D l= τ
and 2 2
( / 2)( / )cD d t⊥ = τ , where l is the
mean free path in the ab plane. For the anisotropy coeffi-
cient of resistivity we then find
( ) ( )22/ /c
c
ab
D
l d t
D⊥
ρ
= = τ
ρ
(12)
and / 1c abρ ρ , since / 1l d and under incoherent
tunneling conditions ct τ .
Thus, the strong anisotropy of the resistivity in the
2 4Nd Ce CuOx x− +δ layered system can be explained by the
incoherent transport of charge carriers in the c direction
with good metallic conductivity in the 2CuO planes.
The insets of Figs. 1(a),(b),(c) show temperature depend-
ences of the resistivity anisotropy in the conducting 2CuO
planes and in a direction perpendicular to these planes for
each of the films studied. It is seen that the coefficient of
anisotropy of the resistivity is great even at room tempera-
ture: 2/ ~ 10 10c abρ ρ − . This parameter increases signifi-
cantly with decreasing of T , reaching values 3/ ~ 10c abρ ρ
for compounds with 0.145x = and 0.135 and / ~c abρ ρ
2~ 10 for an optimally doped compound with 0.15x = ,
due to a sharp increase of cρ at low temperatures.
We emphasize (see Fig. 1) that low-temperature anisot-
ropy coefficient is maximal for 0.145x = ( /c abρ ρ ≈
32 10 )≈ ⋅ and 0.135x = ( 3/ 10c abρ ρ ≈ ) and much less for
0.15x = ( 2/ 10c abρ ρ ≈ ) in contrast to the situation in the
overdoped region where the direct correlation between the
values of /c abρ ρ and cT takes place (see Fig. 6 in [12]).
4. Conclusions
The temperature dependences of both in-plane ( abρ )
and out-of-plane ( cρ ) resistivities in the normal state of
recently grown 2 4 3Nd Ce CuO / SrTiOx x− structures with
0.135x = and 0.145, in the region of superconductivity
emergence at the antiferromagnetic-superconductor transi-
tion boundary, have been studied. The results are compared
with the data for the optimally doped superconducting
2 4Nd Ce CuOx x− structure with 0.15x = .
The structures are single-crystal 2 4 3Nd Ce CuO / SrTiOx x−
films with the c axis both perpendicular to the plane of the
film (for measuring of abρ ) and parallel to the plane (for
measuring of cρ ).
The results obtained are successfully interpreted within
the concept of quasi-two-dimensionality of the systems
studied with high metallic conductivity along ab planes
( / 0)abd dTρ > and semiconducting behavior of the con-
ductivity in c-axis direction ( / 0abd dTρ < ) due to inco-
herent tunneling and thermal activation across the barriers
between the conducting 2CuO layers.
Acknowledgments
This work was carried out in the framework of the state
task by the theme “Electron” (No. AAAA-А18-
118020190098-5) and in part supported by the Russian
Foundation for Basic Research (project No. 18-02-00192)
and by the project “Fundamental Research” of Ural Branch
of the Russian Academy of Sciences, No. 18-10-2-6.
________
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___________________________
Анізотропна температурна залежність питомого
опору нормального стану шаруватого електронно-
легованого надпровідника Nd2−xCexCuO4
в області недодопування
А.С. Клепікова, Т.Б. Чарікова, Н.Г. Шелушініна,
М.Р. Попов, А.А. Іванов
Досліджено температурні залежності як внутрішньопло-
щинних CuO2, так і позаплощинних питомих опорів в елект-
ронно-легованих Nd2−xCexCuO4 в діапазоні х = 0,135–0,15
для аналізу анізотропії електричного транспорту в процесі
еволюції від антиферомагнітного, в області недодопування,
до надпровідного упорядкування, в області оптимального
допування.
Ключові слова: електронно-легований надпровідник, анізо-
тропія транспортних властивостей, надпровідні плівки.
Анизотропная температурная зависимость
удельного сопротивления нормального состояния
слоистого электронно-легированного
сверхпроводника Nd2−xCexCuO4
в области недодопирования
А.С. Клепикова, Т.Б. Чарикова, Н.Г. Шелушинина,
М.Р. Попов, А.А. Иванов
Исследованы температурные зависимости как внутрипло-
скостных CuO2, так и внеплоскостных удельных сопротив-
лений в электронно-легированных Nd2−xCexCuO4 в диапазоне
х = 0,135–0,15 для анализа анизотропии электрического
транспорта в процессе эволюции от антиферромагнитного, в
области недодопирования, до сверхпроводящего упорядоче-
ния, в области оптимального допирования.
Ключевые слова: электронно-легированный сверхпроводник,
анизотропия транспортных свойств, сверхпроводящие пленки.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 2 257
https://doi.org/10.1016/0921-4534(91)90638-F
https://doi.org/10.1016/j.physc.2012.09.001
https://doi.org/10.1103/PhysRevB.59.14723
https://doi.org/10.1103/PhysRevB.59.14723
https://doi.org/10.1103/PhysRevB.52.1297
https://doi.org/10.1103/PhysRevB.52.3071
https://doi.org/10.1080/00018738400101671
https://doi.org/10.1016/0921-4534(89)90354-7
https://doi.org/10.1103/PhysRevLett.60.132
https://doi.org/10.1209/0295-5075/15/6/016
https://doi.org/10.1103/PhysRevB.45.5001
https://doi.org/10.1103/PhysRevB.52.1984
https://doi.org/10.1103/PhysRevB.68.134505
https://doi.org/10.1134/1.567850
https://www.google.ru/search?newwindow=1&hl=ru&tbm=bks&tbm=bks&q=inauthor:%22B.I.+Shklovskii%22&sa=X&ved=0ahUKEwjOorbPgITeAhVGkywKHekwAJoQ9AgIKzAA
https://www.google.ru/search?newwindow=1&hl=ru&tbm=bks&tbm=bks&q=inauthor:%22A.L.+Efros%22&sa=X&ved=0ahUKEwjOorbPgITeAhVGkywKHekwAJoQ9AgILDAA
1. Introduction
2. Materials and method
3. Experimental results and discussion
3.1. Temperature dependence of resistivity in CuO2 planes for Nd2–xCexCuO4/SrTiO3 (001) films
3.2. The temperature dependence of resistivity across the CuO2 planes for Nd2–xCexCuO4/SrTiO3 films
3.3. Anisotropy of resistivity for optimally anneale Nd2–xCexCuO4/SrTiO3 films with various cerium contents
4. Conclusions
Acknowledgments
|