Weak localization and interaction effects in acceptor graphite intercalation compounds
The presented work is devoted to investigations of manifestation of quantum effects of weak localization and interaction of charge carriers in electrical conductivity of acceptor graphite intercalation compounds (CICs). As shown by studies intercalation leads to a decrease in the resistivity and to...
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Prokopov, O.I. Ovsiienko, I.V. Matzui, L.Yu. Len, T.A. Naumova, D.D. Berkutov, I.B. Mirzoiev, I.G. Le Normand, F. 2018-01-19T20:36:40Z 2018-01-19T20:36:40Z 2017 Weak localization and interaction effects in acceptor graphite intercalation compounds / O.I. Prokopov, I.V. Ovsiienko, L.Yu. Matzui, T.A. Len, D.D. Naumova, I.B. Berkutov, I.G. Mirzoiev, F. Le Normand // Физика низких температур. — 2017. — Т. 43, № 6. — С. 884-888. — Бібліогр.: 22 назв. — англ. 0132-6414 PACS: 72.20 Ee, 72.30.+q https://nasplib.isofts.kiev.ua/handle/123456789/129518 The presented work is devoted to investigations of manifestation of quantum effects of weak localization and interaction of charge carriers in electrical conductivity of acceptor graphite intercalation compounds (CICs). As shown by studies intercalation leads to a decrease in the resistivity and to change the resistivity temperature coefficient from negative sign in the source graphite on a positive sign in intercalated graphite. At the low temperature for all GICs specimens the minimum in the temperature dependence of resistivity is observed. In terms of the model of charge carrier's weak localization and interaction for two-dimensional systems temperature dependence of phase relaxation time, localization radius and charge carriers screening constant for all GICs are estimated. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Электронные свойства проводящих систем Weak localization and interaction effects in acceptor graphite intercalation compounds Article published earlier |
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Weak localization and interaction effects in acceptor graphite intercalation compounds |
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Weak localization and interaction effects in acceptor graphite intercalation compounds Prokopov, O.I. Ovsiienko, I.V. Matzui, L.Yu. Len, T.A. Naumova, D.D. Berkutov, I.B. Mirzoiev, I.G. Le Normand, F. Электронные свойства проводящих систем |
| title_short |
Weak localization and interaction effects in acceptor graphite intercalation compounds |
| title_full |
Weak localization and interaction effects in acceptor graphite intercalation compounds |
| title_fullStr |
Weak localization and interaction effects in acceptor graphite intercalation compounds |
| title_full_unstemmed |
Weak localization and interaction effects in acceptor graphite intercalation compounds |
| title_sort |
weak localization and interaction effects in acceptor graphite intercalation compounds |
| author |
Prokopov, O.I. Ovsiienko, I.V. Matzui, L.Yu. Len, T.A. Naumova, D.D. Berkutov, I.B. Mirzoiev, I.G. Le Normand, F. |
| author_facet |
Prokopov, O.I. Ovsiienko, I.V. Matzui, L.Yu. Len, T.A. Naumova, D.D. Berkutov, I.B. Mirzoiev, I.G. Le Normand, F. |
| topic |
Электронные свойства проводящих систем |
| topic_facet |
Электронные свойства проводящих систем |
| publishDate |
2017 |
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English |
| container_title |
Физика низких температур |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| format |
Article |
| description |
The presented work is devoted to investigations of manifestation of quantum effects of weak localization and interaction of charge carriers in electrical conductivity of acceptor graphite intercalation compounds (CICs). As shown by studies intercalation leads to a decrease in the resistivity and to change the resistivity temperature coefficient from negative sign in the source graphite on a positive sign in intercalated graphite. At the low temperature for all GICs specimens the minimum in the temperature dependence of resistivity is observed. In terms of the model of charge carrier's weak localization and interaction for two-dimensional systems temperature dependence of phase relaxation time, localization radius and charge carriers screening constant for all GICs are estimated.
|
| issn |
0132-6414 |
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https://nasplib.isofts.kiev.ua/handle/123456789/129518 |
| citation_txt |
Weak localization and interaction effects in acceptor graphite intercalation compounds / O.I. Prokopov, I.V. Ovsiienko, L.Yu. Matzui, T.A. Len, D.D. Naumova, I.B. Berkutov, I.G. Mirzoiev, F. Le Normand // Физика низких температур. — 2017. — Т. 43, № 6. — С. 884-888. — Бібліогр.: 22 назв. — англ. |
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Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 6, pp. 884–888
Weak localization and interaction effects in acceptor
graphite intercalation compounds
O.I. Prokopov1, I.V. Ovsiienko1, L.Yu. Matzui1, T.A. Len1, D.D. Naumova2, I.B. Berkutov3,
I.G. Mirzoiev3, and F. Le Normand4
1Taras Shevchenko National University of Kyiv, Departments of Physics
64/13 Volodymyrska Str., Kyiv 01601, Ukraine
E-mail: matzui@univ.kiev.ua
2Taras Shevchenko National University of Kyiv, Departments of Chemistry
64/13 Volodymyrska Str., Kyiv 01601, Ukraine
3B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy Sciences of Ukraine
47 Nauky Ave., Kharkiv 61103, Ukraine
E-mail: iberkutov@gmail.com
4Institut de Physique et Chimie des Matériaux, 23 rue du Loess BP 43, Strasbourg 67037, France
Received August 12, 2016, published online April 25, 2017
The presented work is devoted to investigations of manifestation of quantum effects of weak localization and in-
teraction of charge carriers in electrical conductivity of acceptor graphite intercalation compounds (CICs). As
shown by studies intercalation leads to a decrease in the resistivity and to change the resistivity temperature coeffi-
cient from negative sign in the source graphite on a positive sign in intercalated graphite. At the low temperature for
all GICs specimens the minimum in the temperature dependence of resistivity is observed. In terms of the model of
charge carrier’s weak localization and interaction for two-dimensional systems temperature dependence of phase re-
laxation time, localization radius and charge carriers screening constant for all GICs are estimated.
PACS: 72.20 Ee Mobility edges; hopping transport;
72.30.+q High-frequency effects; plasma effects.
Keywords: graphite intercalation compounds, studies intercalation, weak localization.
Introduction
The theory of charge carriers weak localization and in-
teractions was developed for disordered metals, semimetals
and degenerate semiconductors [1–3]. As expected in Mott
theory the transition metal–insulator occurs abruptly. The
theory of weak localization assumed that the transition
from metallic to insulator state, in which the electron wave
function decreases exponentially, is not abrupt. There is an
intermediate region of structures in which the electron
wave function decreases slowly. A charge carriers weak
localization is due to interference of direct and elastically
scattered backwards on the inhomogeneities of structure
electronic waves. In the theory of electron–electron inter-
action inelastic interactions of electrons with each other
and with phonons or other degrees of freedom is taken into
account. If the condition 1Fk L occurs the character of
electron-electron interaction is qualitatively changed, be-
cause during the interaction time electrons are scattered
repeatedly at impurities or defects. Quantum effects of
charge carriers weak localization and interactions lead to
the appearance of abnormal temperature and magnetic field
dependences of transport properties. In first abnormal low-
temperature dependence of electrical resistance is observed
for fine crystalline graphite in [4,5]. It was shown that a
sharp proportional to 1/2T increase of electrical resistance
for fine crystalline graphite can be explained in the terms
of theory of weak localization and interaction of charge
carriers. As another manifestation of quantum effects in
this material negative magnetoresistance in fine crystalline
graphite was found.
As it was shown in several papers there are quantum ef-
fects of weak localization and interaction of charge carriers
in the multiwall carbon nanotubes [6–9]. More pronounced
weak localization and interaction effects are for two-
dimensional systems. Graphite intercalation compounds
(GICs) are natural two-dimensional electronic systems in
which carriers move mainly in a direction parallel to the
planes of graphite, so the charge carriers system in GICs of
© O.I. Prokopov, I.V. Ovsiienko, L.Yu. Matzui, T.A. Len, D.D. Naumova, I.B. Berkutov, I.G. Mirzoiev, and F. Le Normand, 2017
Weak localization and interaction effects in acceptor graphite intercalation compounds
low stages can be seen as degenerate dimensional electron
gas, two-dimensionality of which is associated with struc-
tural features of the electronic structure of GICs.
Abnormal transport properties were revealed for GICs
based on graphite fibers and high oriented pyrolitic graph-
ite (HOPG) also [10–13]. These anomalies authors are as-
sociated with the manifestation of the weak localization
and interaction effects.
However, despite a number of researches on these ef-
fects in GICs, question about the ratio between contribu-
tions of weak localization and interaction effects is open.
Also conclusion on observation of weak localization and
interaction effects in the GIC based on HOPG is ambigu-
ous. So, the aim of this work is to investigate the low-
temperature anomalies in resistivity of GICs based on
graphites with different structure perfection and to estab-
lish the nature of these anomalies.
Experimental results and discussion
As source for intercalation two types of graphite with
different structure perfection were used. These are highly
oriented pyrolytic graphite (HOPG) (distance between lay-
ers 002d = 0.335 nm, crystallite size L = 100 nm) and fine
crystalline pyrolytic graphite (FPG) ( 002d = 0.340 nm,
L = 30nm). For both types of graphite there is a significant
anisotropy of crystalline structure.
The specimens of graphite intercalation compounds
with antimony chloride (SbCl5), iodine chloride (ICl),
aluminum chloride (AlCl3) and bromine (Br2) were ob-
tained with standard two-temperature method [2]. As it is
known, intercalation of graphite results in orderly ar-
rangement of intercalates layers in the graphite matrix and
the formation of ordered structure of intercalates layer.
Investigations of structural characteristics of obtained
GICs were carried out with x-ray diffraction method. The
identity parameters SI were determined from 00l-dif-
fraction patterns of each GICs specimens and then com-
pounds stages S were calculated with use Eq. (1):
( ) 0021S SI d S d= + − , 002S id d d= + (1)
where id is the thickness of intercalates layer.
Table 1 presents the synthesis conditions, composition;
stages number s and identity period SI for the obtained
GICs. In Table 1 also ratios of resistivity at room tempera-
ture to resistivity at T = 4.2 K 4.2 300( / )a aρ ρ are shown.
The resistivity along graphite planes ( )aρ in GICs
specimens was measured in temperature interval from 4.2 K
to 293 K by standard for-probe method. Resistivity meas-
urement error was 0.05%.
Figure 1 presents the temperature dependences of resis-
tivity aρ for obtained GICs. As it is seen at the Figures
intercalation leads to a decrease of the resistivity and to
change the resistivity temperature coefficient from nega-
tive sign in the source graphite on a positive sign in inter-
calated graphite. For all specimens of GICs based on FPG
in temperature dependence ( )a Tρ there is a wide mini-
mum. The exact position and value of minimum vary for
different specimens. So for second stage GIC with SbCl5
minimum is observed at T = 38 K, for GIC with ICl mini-
mum is observed at T = 20 K, while for GIC with AlCl3
minimum is at T = 87 K and for GIC with bromine mini-
mum is at T = 150 K. Note, that for GICs based on HOPG
in dependence ( )a Tρ minimum is not observed at any
temperature.
Let us analyze the main mechanisms that determine the
temperature dependence of resistivity in the GICs of ac-
ceptor type. As you know GICs of acceptor type are two-
dimensional electronic systems, two-dimensionality of
which is due to features of their electronic structure.
In the terms of two-dimensional GICs electron structure
model of Blinowski and Rigaux [14] two-dimensional re-
sistivity for two stage compound can be written as
2 2
ef
1
Sa
F Le k
π
ρ = ⋅
, (2)
where, Fk is the Fermi wave vector, efL is the effective
mean free path. In approaching of independence of differ-
ent mechanisms of charge carriers scattering
ef
1 1 1
b TL L L
= + , (3)
Table 1. Synthesis conditions, composition, stages number s, identity period IS and ratio 4.2 300/a aρρ for GICs specimens.
Source graphite Intercalate Тemperature of intercalation, K SI S 4.2 300( / )a aρρ
HOPG – – 0.335 – 1.27
HOPG SbCl5 493 1.278 2 0.56
HOPG ICl 313 1.045 2 0.62
FPG – – 0.340 – 1.63
FPG SbCl5 493 1.280 2 0.96
FPG ICl 317 1.052 1 0.92
FPG ICl 317 0.712 2 0.96
FPG AlCl3 483 1.306 2 0.94
FPG Br2 317 0.717 2 1.01
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 6 885
O.I. Prokopov, I.V. Ovsiienko, L.Yu. Matzui, T.A. Len, D.D. Naumova, I.B. Berkutov, I.G. Mirzoiev, and F. Le Normand
where bL is the free path of the charge carriers scattering
on the boundaries of crystallites and TL is the mean free
path in the temperature-dependent charge carriers scatter-
ing mechanisms. Consider the main carrier scattering
mechanisms, that cause the temperature dependence of the
electrical resistivity ( )a Tρ in GICs. In first, this is elec-
tron–electron scattering, which leads to the quadratic tem-
perature dependence of electrical resistivity [15]. However,
according to estimates, resulted in a number of works for
the second stage GICs with SbF5 [16], the mean free path
of carriers scattering each other is 7⋅10–5 m at 100 K. This
value is significantly greater than the mean free paths at
scattering of charge carriers on phonons and boundaries of
crystallites. In secondly, this is carrier scattering on pho-
nons, which includes scattering on different modes of graph-
ite and intercalate. Thus, in a first approximation the sum-
marized temperature dependence of charge carriers mean
free path is determined by the temperature dependence of
the phonon scattering mean free path, because all other tem-
perature-dependent scattering mean free paths are much
larger: ph ( )TL L T= . Mean free path of carriers scattering on
phonons is inversely proportional to temperature and can be
written as:
ph 0
cL L T −= , (4)
where 0L and C are constants.
Thus, the two-dimensional resistivity for second stage
GICs in terms of two-dimensional model of the electronic
structure can be written as:
0
2 2 2
ph ph
31 1 1 1 ,
( ) ( )2
Sa
b bF F
b
L L T L L Te k e E
π γπ
ρ = ⋅ + = +
(5)
where b is thedistance between neighboring atoms in a
graphite layer, 0γ is the wave functions overlap integral for
neighboring atoms in a graphite layer, FE is the Fermi
energy level.
To analyze the temperature dependences of electrical
resistivity expression for aρ taking into account the rela-
tions (4) and (5) conveniently presented as:
C
a AT Bρ = + ,
2
0
S
F
I
A
Le k
π
= ⋅
,
2
S
bF
I
B
Le k
π
= ⋅
. (6)
From experimental data on electrical resistivity ( )a Tρ
for GICs based on structurally different graphites with dif-
ferent intercalates coefficients A, B, C and Fermi energy
FE have been calculated. The values of coefficients A, B,
C and Fermi energy FE are given in Table 2.
As it is shown from Table 2 the experimentally deter-
mined value of C = 1.6 for both GIC based on FPG and
HOPG. The temperature-independent term B is in 2.5–3.5
times higher for GICs-based on FPG in comparison with
GICs based on HOPG while as factor A (factor at T) is in
10–20 times greater for GICs based in HOPG compared
with GICs based on FPG.
Thus, the main mechanisms that determine the tempera-
ture dependence of the resistivity ρa in the temperature
range 60–300 K for both the GICs based on VOPH and for
the GICs based on FPG are the same. These compounds
are characterized by positive resistivity temperature coeffi-
cient, which weakly depends on the type of intercalate and
significantly decreases with decreasing of crystallite size of
the source graphite.
Figure 2 presents the calculated with Eq. (6) tempera-
ture dependences of resistivity ( )a Tρ .
As it is revealed from Figure equation (6) very well de-
scribes the experimental dependence ( )a Tρ at the high
temperature. While at low temperatures significant devia-
tion from dependence (6) is observed. The minimum on
Fig. 1. Experimental dependences ρa for GICs: FPG+Br2 (1);
FPG+ICl (2); FPG+AlCl3 (3); FPG+ SbCl5 (4); HOPG+SbCl5 (5).
Table 2. Calculated coefficients A, B, C and Fermi energy FE for GICsAs
GICs A, Ohm⋅m/К B, Оhm⋅m C FE , eV
FPG — SbCl5 4.37·10–12 6.60·10–7 1.63 0.24
HOPG — SbCl5 15.5·10–11 2.27·10–7 1.55 0.75
FPG — ICl 1.80·10–11 2.12·10–6 1.64 0.11
FPG — IСl 4.55·10–11 1.83·10–6 1.59 0.13
FPG — AlCl3 8.50·10–12 1.21·10–6 1.60 0.19
886 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 6
Weak localization and interaction effects in acceptor graphite intercalation compounds
the curves ( )a Tρ indicates that for GICs in low-tem-
perature interval conductivity mechanism is different from
the classic. Such abnormal temperature dependence of re-
sistivity may be related with effect of weak localization
and electron–electron interaction charge carriers that occur
for weekly disordered systems ef .Fk L= The electrical
conductivity with additions due to quantum effects can be
written as:
( ) ( ) ( )
( ) ( ) ( )
cl
loc int ,
q
q
T T T
T T T
σ = σ + δσ
δσ = δσ + δσ
(7)
where clσ is the classic conductivity, qδσ — addition to
conductivity due to quantum effects, qδσ consists the addi-
tion due to carriers weak localization effects locδσ and
addition due to carriers interaction effects intδσ . For two-
dimensional systems weak localization addition to conduc-
tivity 2locδσ is [17–20]:
2
0
2loc 2 ln
2
e
ϕ
τ
δσ = α τπ
, (8)
and interaction addition 2intδσ is
2
0
2int 2
2
ln
2
k Te π τ δσ = γ
π
, (9)
where 0τ is the charge carriers relaxation time, ϕτ is wave
function phase relaxation time, * PA T −
ϕτ = , ( /2p d= , d
is dimensionality of system [21,22]); α is numerical coef-
ficient that depends on the ratio between ϕτ and 0τ ; γ is
numerical coefficient that reflects the degree of carriers
screening. With use equations (7)–(9) addition to two-
dimensional conductivity is:
2 2loc 2intqδσ = δσ + δσ =
( )
2
0 0
2 *
2
ln ln ln
2
bke p T
A
π τ τ = α + γ + γ + α
π
(10)
or in simplified form:
2 lnq K T Eδσ = + , (11)
where
( )
2
22
eK p= α + γ
π
;
2
0 0
2 *
2
ln ln
2
bkeE
A
π τ τ = γ + α
π
.
Thus, for two-dimensional system additions to
conductivity related with manifestation of quantum effects
of charge carriers weak localization and interaction are
proportional to lnT.
Figure 3 presents the temperature dependence ( )Tδσ =
2exp cl( ) ( )T T= δσ − δσ for GICs specimens, where
2exp exp/(2 )S aIσ = ρ according to simple two-dimensional
model of GICs electron structure, clσ is calculated with
use equation (7).
As it is shown Fig. 3, linear dependence of δσ from
lnT is observed. Such dependence (ln )Tδσ indicates the
possibility of realization of quantum effects of weak local-
ization and interaction in GICs and the two-dimensional
character of conductivity in them. From dependences
(ln )Tδσ the coefficients K and E were determined (Table 3)
and with use Eq. (11) the constants ,γ α and 0τ were cal-
culated. For calculation the value of *A is taken as in [9].
Values of constants are in the Table 3. In Table 3 also the
values of Fermi energy FE and resistivity in minimum
minaρ are presented.
Fig. 2. Experimental ρa(T) and calculated ρcalc (corresponding
solid lines) dependences for GICs based on FPG with AlCl3 (1),
SbCl5 (2) and ICl (3).
Fig. 3. Dependences 2exp cl( ) ( ) ( )T T Tσ = δσ − σδ δ for GICs
with ICl (1), AlCl3 (2) and SbCl5 (3).
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 6 887
O.I. Prokopov, I.V. Ovsiienko, L.Yu. Matzui, T.A. Len, D.D. Naumova, I.B. Berkutov, I.G. Mirzoiev, and F. Le Normand
As can be seen from the table, for all specimens of
GICs constant γ , which is related with shielding of charge
carriers at the interaction, exceeds the constant α that is
responsible for weak localization, about 6–7 times.
Figure 4 presents the calculated according to (9) addi-
tion to conductivity 2qδσ with use calculated parameters ,γ
α and 0τ .
As is shown at the Fig. 4 calculated addition 2qδσ well
coincides with the experimentally determined ( )Tδσ =
2exp cl( ) ( )T T= δσ − δσ .
Conclusions
Thus, the revealed low-temperature anomalies in the
resistivity of acceptor type GICs based on FPG can be
explained as for source for intercalation FPG in the terms of
theory of charge carriers weak localization and interaction
effects. For GICs the additions to conductivity due to weak
localization and interaction are two-dimensional in contrast to
the three-dimensional additions to conductivity for source for
intercalation GPG. The comparative analysis of the calculated
values of shielding constants γ and weak localization
constants α for GICs with different acceptor intercalates
allows us to conclude that for low stage GICs based on FPG
low-temperature peculiarities in the conductivity caused
mainly by effect of the charge carriers interaction. For GICs
based on HOPG the low-temperature anomalies in the
conductivity were not revealed.
1. B.L. Al’tshuler, D. Khmel’nitzkii, A.I. Larkin, and P.A. Lee,
Phys. Rev. B 22, 5142 (1980).
2. B.L. Al’tshuler, A.G. Aronov, A.I. Larkin, and D.E.
Khmel’nitskii, Z. Eksp. Teor. Fiz. 81, 768 (1981) [Sov. Phys.
JETP 54, 411 (1981)].
3. B.L. AI’tshuler and A.G. Aronov, Z. Eksp. Teor. Fiz. 77,
2028 (1979) [Sov. Phys. JETP 50, 968 (1979)].
4. Ye.Yo. Charkov, L.L. Kolesnichenko, and L.Yu. Matzui,
Solid State Phys. 25, 594 (1983).
5. L.Yu. Matzui and A.M. Katsiuba, Bull. Kiev University,
Ser.: Phys. Math. 1, 342 (1999).
6. I.V. Ovsienko, T.A. Len, L.Yu. Matzui, Yu.I. Prylutskyy,
I.B. Berkutov, V.V. Andrievskii, Yu.F. Komnik, I.G. Mirzoiev,
G.E. Grechnev, Yu.A. Kolesnichenko, R. Hayn, and P. Scharff,
Phys. Status Solidi 252, 1402 (2015).
7. I.V. Ovsienko, L.Yu. Matzui, I.V. Yatsenko, S.V. Khrapatiy,
Yu.I. Prylutskyy, U. Ritter, P. Scharff, and F. Normand,
Materialwiss. Werkst. 44, 161 (2013).
8. L.Yu. Matzui, I.V. Ovsienko, T.A. Len, Yu.I. Prylutskyy,
and P. Scharff, Fuller. Nanotubes Carbon Nanostruct. 13,
259 (2005).
9. T.A. Len, L.Yu. Matzui, I.V. Ovsienko, Yu.I. Prylutskyy,
V.V. Andrievskii, I.B. Berkutov, G.E. Grechnev, and Yu.А.
Kolesnichenko, Fiz. Nizk. Temp. 37, 1027 (2011) [Low
Temp. Phys. 37, 819 (2011)].
10. L. Piraux, V. Bayot, J.P. Michenaud, and J.P. Issi, Solid
State Commun. 59, 711 (1986).
11. L. Piraux and V. Bayot, Phys. Rev. B 36, 9045 (1987).
12. L. Piraux, V. Bayot, and M.S. Dresselhaus, Phys. Rev. B 45,
14315 (1992).
13. L. Piraux, V. Bayot, J.P. Michenaud, and J.P. Issi, Phys.
Scripta 37, 942 (1988).
14. J. Blinowski and C. Rigaux, J. Physique 41, 667 (1980).
15. K. Matsubara, K. Sugihara, I.-S. Suzuki, and M. Suzuki,
J. Phys. Condens. Matter 11, 3149 (1999).
16. L. Piraux, K. Amine, V. Bayot, and J.P. Issi, Mater. Science
Forum 91–93, 481 (1992).
17. B.L. Al’tshuler and A.G. Aronov, Solid State Commun. 46,
429 (1983).
18. K. Shimakawa, K. Hayashi, and T. Kameyama, Philos. Mag.
Lett. 64, 375 (1991).
19. А.К. Savchenko, V.N. Lutskii, and A.S. Rypik, Lett. JETP
34, 367 (1981).
20. M. Kaveh, Can. J. Phys. 60, 746 (1982).
21. P.W. Anderson, Phys. Rev. 109, 1492 (1958).
22. D.J. Thouless, Physica B 109, 1523 (1982)
Table 3. Coefficients K, E and calculated constants γ, α and 0τ for GICs
Specimen K, (Ohm⋅K)–1 E, (Ohm)–1 γ α 0τ , s FE , eV minaρ , Ohm⋅m
FPG — SbCl5 3.48⋅10–6 –1.445⋅10–5 0.24 0.034 2.0⋅10–14 0.24 6.62⋅10–7
FPG — AlCl3 2.34⋅10–6 –1.069⋅10–5 0.16 0.024 1.8⋅10–14 0.19 1.21⋅10–6
FPG — ICl 2.64⋅10–7 –8.2⋅10–7 0.03 4.9⋅10–3 1.5⋅10–14 0.11 2.22⋅10–6
Fig. 4. Calculated temperature dependences of additions to two-
dimensional conductivity, 2exp cl( ) ( ) ( )T T Tσ = δσ − σδ δ and
calc( )Tσδ : FPG — SbCl5 (1) and FPG — AlCl3 (2).
888 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 6
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Introduction
Experimental results and discussion
Conclusions
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