Quantum Hall effect in p-Ge/Ge₁₋xSix heterostructures with low hole mobility
The apparent insulator—quantum Hall—insulator (I—QH—I) transition for filling factor 1 has been investigated in p-type Ge/Ge₁₋xSix heterostructures with εFτ/h ≈ 1. Scaling analysis is carried out for both the low- and high-field transition point. In low magnetic fields ωcτ < 1 pronounced QH...
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| Cite this: | Quantum Hall effect in p-Ge/Ge₁₋xSix heterostructures with low hole mobility / Yu.G Arapov, G.I. Harus, I.V. Karskanov, V.N. Neverov, N.G.Shelushinina, M.V. Yakunin // Физика низких температур. — 2007. — Т. 33, № 2-3. — С. 207-210. — Бібліогр.: 22 назв. — англ. |
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Arapov, Yu.G. Harus, G.I. Karskanov, I.V. Neverov, V.N. Shelushinina, N.G. Yakunin, M.V. 2017-12-23T21:28:25Z 2017-12-23T21:28:25Z 2007 Quantum Hall effect in p-Ge/Ge₁₋xSix heterostructures with low hole mobility / Yu.G Arapov, G.I. Harus, I.V. Karskanov, V.N. Neverov, N.G.Shelushinina, M.V. Yakunin // Физика низких температур. — 2007. — Т. 33, № 2-3. — С. 207-210. — Бібліогр.: 22 назв. — англ. 0132-6414 PACS: 73.40.–c, 73.43.–f https://nasplib.isofts.kiev.ua/handle/123456789/127532 The apparent insulator—quantum Hall—insulator (I—QH—I) transition for filling factor 1 has been investigated in p-type Ge/Ge₁₋xSix heterostructures with εFτ/h ≈ 1. Scaling analysis is carried out for both the low- and high-field transition point. In low magnetic fields ωcτ < 1 pronounced QH-like peculiarities for ν = 1 are also observed in both the longitudinal and Hall resistivities. Such behavior may be evidence of a localization effect in the mixing region of Landau levels and is inherent for two-dimensional structures in a vicinity of the metal—insulator transition. The work was supported by: Russian Foundation for Basic Research RFBR, grants 05-02-16206 and 04-02-16614; program of Russian Academy of Sciences «Low-dimensional quantum heterostructures»; CRDF and Ministry of Education and Science of Russian Federation, grant Y1-P-05-14 (Ek-05 [X1]); Ural Division of Russian Academy of Sciences, grant for young scientists; Russian Science Support Foundation. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Электронные свойства низкоразмерных систем Quantum Hall effect in p-Ge/Ge₁₋xSix heterostructures with low hole mobility Article published earlier |
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Quantum Hall effect in p-Ge/Ge₁₋xSix heterostructures with low hole mobility |
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Quantum Hall effect in p-Ge/Ge₁₋xSix heterostructures with low hole mobility Arapov, Yu.G. Harus, G.I. Karskanov, I.V. Neverov, V.N. Shelushinina, N.G. Yakunin, M.V. Электронные свойства низкоразмерных систем |
| title_short |
Quantum Hall effect in p-Ge/Ge₁₋xSix heterostructures with low hole mobility |
| title_full |
Quantum Hall effect in p-Ge/Ge₁₋xSix heterostructures with low hole mobility |
| title_fullStr |
Quantum Hall effect in p-Ge/Ge₁₋xSix heterostructures with low hole mobility |
| title_full_unstemmed |
Quantum Hall effect in p-Ge/Ge₁₋xSix heterostructures with low hole mobility |
| title_sort |
quantum hall effect in p-ge/ge₁₋xsix heterostructures with low hole mobility |
| author |
Arapov, Yu.G. Harus, G.I. Karskanov, I.V. Neverov, V.N. Shelushinina, N.G. Yakunin, M.V. |
| author_facet |
Arapov, Yu.G. Harus, G.I. Karskanov, I.V. Neverov, V.N. Shelushinina, N.G. Yakunin, M.V. |
| topic |
Электронные свойства низкоразмерных систем |
| topic_facet |
Электронные свойства низкоразмерных систем |
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2007 |
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English |
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Физика низких температур |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Article |
| description |
The apparent insulator—quantum Hall—insulator (I—QH—I) transition for filling factor 1
has been investigated in p-type Ge/Ge₁₋xSix heterostructures with εFτ/h ≈ 1. Scaling analysis is
carried out for both the low- and high-field transition point. In low magnetic fields ωcτ < 1 pronounced
QH-like peculiarities for ν = 1 are also observed in both the longitudinal and Hall
resistivities. Such behavior may be evidence of a localization effect in the mixing region of Landau
levels and is inherent for two-dimensional structures in a vicinity of the metal—insulator transition.
|
| issn |
0132-6414 |
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https://nasplib.isofts.kiev.ua/handle/123456789/127532 |
| citation_txt |
Quantum Hall effect in p-Ge/Ge₁₋xSix heterostructures with low hole mobility / Yu.G Arapov, G.I. Harus, I.V. Karskanov, V.N. Neverov, N.G.Shelushinina, M.V. Yakunin // Физика низких температур. — 2007. — Т. 33, № 2-3. — С. 207-210. — Бібліогр.: 22 назв. — англ. |
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2025-11-26T01:39:33Z |
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2025-11-26T01:39:33Z |
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| fulltext |
Fizika Nizkikh Temperatur, 2007, v. 33, Nos. 2/3, p. 207–210
Quantum Hall effect in p-Ge/Ge1–xSix heterostructures
with low hole mobility
Yu.G. Arapov, G.I. Harus, I.V. Karskanov, V.N. Neverov,
N.G. Shelushinina, and M.V. Yakunin
Institute of Metal Physics RAS, Ekaterinburg 620041, Russia
E-mail: arapov@imp.uran.ru
O.A. Kuznetsov
Physico-Technical Institute at Nizhnii Novgorod State University, Nizhnii Novgorod, Russia
L. Ponomarenko and A. de Visser
Van der Waals—Zeeman Institute, University of Amsterdam, The Netherlands
Received July 31, 2006
The apparent insulator—quantum Hall—insulator (I—QH—I) transition for filling factor � � 1
has been investigated in p-type Ge/Ge1–xSix heterostructures with � �F � �� 1. Scaling analysis is
carried out for both the low- and high-field transition point. In low magnetic fields � �c � 1 pro-
nounced QH-like peculiarities for � � 1 are also observed in both the longitudinal and Hall
resistivities. Such behavior may be evidence of a localization effect in the mixing region of Landau
levels and is inherent for two-dimensional structures in a vicinity of the metal—insulator transi-
tion.
PACS: 73.40.–c Electronic transport interface structures;
73.43.–f Quantum Hall effects.
Keywords: Quantum Hall effects, heterostructures.
Introduction
A magnetic-field-induced transition from an Ander-
son insulator to quantum Hall effect (QHE) conduc-
tor has been reportedly observed both for low-elec-
tron-mobility GaAs/AlGaAs heterostructures [1–4]
and low-hole-mobility Ge/SiGe quantum wells [5,6],
which at magnetic field B = 0 exhibit insulating be-
havior with a divergent resistance �( )T h e� �� �0 2.
An initial very large decrease of diagonal resistivity
�xx(giant negative magnetoresistence [7]) is followed
by a clear critical point at B = BC where the �xx value
is temperature independent. At higher fields the QHE
minima for filling factor either � � 2 or � � 1 are deve-
loped. The insulator to QHE boundary points at
B = BC are characterized by the equality of the diago-
nal and Hall resistivities, � �xxc xyc� , within experi-
mental uncertainty [5]. Just the T-independent point
BC is identified by the authors of [1–6] as the quan-
tum phase transition point between the insulator and
QHE conductor.
In contrast to that, Huckestein [8] identifies the
apparent low-field insulator—QHE transition as a
crossover due to weak localization and a strong reduc-
tion of the conductivity when Landau quantization be-
comes dominant at � �c 1, �c being the cyclotron fre-
quency and � being the elastic mean free time.
On the other hand, for well-conducting 2D systems
with k lF �� 1(kF is Fermi quasimomentum and l is the
mean free path) the interplay of classical cyclotron
motion and the quantum correction
� ee due to elec-
tron—electron interaction (EEI) to the Drude con-
ductivity �D Fe h k l� �( )( )2 leads to a parabolic nega-
tive magnetoresistance [9–11]:
�
�
� �
�
�
xx
D
c
ee
D
B T
T
( , ) [ ( ) ]
( )
� �
1
1 2
2
. (1)
© Yu.G. Arapov, G.I. Harus, I.V. Karskanov, V.N. Neverov, N.G. Shelushinina, M.V. Yakunin, O.A. Kuznetsov, L. Ponomarenko, and
A. de Visser, 2007
The temperature independent point at � �c � 1 (for
� �xx xy� ) predicted by Eq. (1) has been observed in
various experiments and used for the estimation of the
�D value (see, for example, [12–15]).
It seems for us that the results of the paper [16] of
C.F. Huang et al. are an especially beautiful experi-
mental demonstration just of this (EEI) physical pic-
ture in a gated GaAs/AlGaAs heterostructure (our es-
timations give 4 13� �k lF for five Vg values on your
Fig. 2), but the authors of [16] treated the low-field
T-independent point as a kind of quantum phase tran-
sition (see also [17]).
Here we report and analyze the results of
magnetotransport measurements for low-mobility
p-Ge/Ge1–xSix heterostructures, where the low-field
temperature-independent point on the �xx B( ) depend-
ence is clearly observed.
Experimental results and discussion
Experimental data are presented for two samples
A and B of a multilayered Ge Ge Si1�
�x x p-type he-
terostructures. The hole density and Hall mobili-
ty, as obtained from zero field resistivity �0 and
low field Hall coefficient at T � 4 2. K, are p �
� � �1 3 11 1011. ( . ) cm 2 and � � � � �3 6 4 0 103 2. ( . ) (cm V s)
( ( )�0 16 15� �k� �). From the relation � �0
1 2� � � �( )e �
� �( )� �F � the important parameter, connecting the
Fermi energy �F and elastic mean free time � may be
estimated: � �F � �� 0 8 0 85. ( . ). Thus for the samples
investigated � �F � �� 1, and we are in a region of con-
jectural metal-insulator transition, which is seen ex-
perimentally in a variety of two-dimensional semicon-
ductor systems [18].
The dependencies of longitudinal �xx and Hall �xy
resistivities on magnetic field B at T = 1.7–4.2 K up to
B = 12 T for sample A are shown in Fig. 1. The quan-
tum Hall effect (QHE) plateau number one with cor-
responding �xx minimum at B � 3 5. T are well seen
in the pictures. The estimation of the hole mobility
from the condition �BC1 1� , where BC1(= 2.7 T)
is the field where � �xx xy� (see Fig. 1,a), gives
� � � � �3 7 103 2. (cm V s) in reasonable accordance with
the low-field estimate.
We take notice that at B < 0.5 T positive
magnetoresistance due to the effect of Zeeman split-
ting [19] is observed for all temperatures. At fields
B > 0.5 T up to QHE �xx minimum a background nega-
tive magnetoresistance takes place with the following
peculiarities observed: i) Shubnikov—de Haas (SdH)
oscillation structure with maximum at B � 2 T, and
ii) the �xx temperature-independent point at B BC� 1
(Fig. 1,b). In the high-field region the transition from
the QHE regime to the insulator takes place in the vi-
cinity of BC2 7 5� . T (Fig. 1,a).
In a great deal of work [1–6,16,17] the low-field
temperature-independent point at B BC� on the
�xx B( ) dependence is interpreted as a point of insula-
tor—QHE quantum phase transition. A criterion of
existence of a phase transition is a scaling dependence
of � �
xx CB T f B B /T( , ) (( ) )�
in the vicinity of BC
with � being a critical exponent [20]. By plotting
ln ( )d dBxx B BC
� �
�
versus ln T, one could obtain �.
Such a situation may be realized in a system with
genuine (strong) localization, e.g., with variable
range hopping conduction at B = 0.
But for a system with weak localization we think
that it is not the case. The weak localization regime at
k lF �� 1 (� �F � ��� 1) is in fact the regime of the elec-
tron diffusion from one scattering event on an impu-
rity to another, with some mean free path l. Here the
notion of insulating behavior is valid only in the sense
that d dT� � � 0. For such a system there exists another
reason for a temperature-independent point on the
208 Fizika Nizkikh Temperatur, 2007, v. 33, Nos. 2/3
Yu.G. Arapov et al.
2 4 6 8 100
50
100
150
0 2 4 6
12
14
16
6
5
4
3
21a
B, T
5
4
3
2
1
b
B, T
�
�
�
xx
xy
,
, k
�
�
xx
, k
Fig. 1. Longitudinal resistivity (1–5) and Hall resistivity (6) as functions of magnetic field for sample A. T, K: 1, 6 —
1.7; 2 — 2.3; 3 — 2.9; 4 — 3.7; 5 — 4.2.
�xx B( ) dependence at � �c � 1 (B mc eC1 � � �): it is a
consequence of the interplay of classical cyclotron mo-
tion and the EEI correction
� ee to the Drude con-
ductivity (see Eq. (1)). According to Eq. (1) the de-
rivative ( )d dT B BC
� �
�
should be proportional to
ln T as
� ee is proportional to ln ( )kT� � � .
To distinguish between the two cases in our sam-
ples with � �F � �� 1 an analysis of dependence
( )d dBxx B BC
� �
�
on T has been carried out. Figure
2,a shows the nonscaling behavior of �xx B T( , ) near
the low-field critical point BC1: it is not possible to
extract consistently any power law from the tempera-
ture dependence of derivative ( )d dBxx B BC
� �
� 1
. On
the other hand, rather good linear dependence of
( )d dB B BC
� �
� 1
on ln T is observed up to T � 3 K
that is an argument in favor of the EEI version. In
contrast to it, real scaling behavior of �xx B T( , ) with
critical exponent � � 0 38. (compare with theoretical
value � � 0 42. for the spin-split case [21]) takes place
in a vicinity of high-field critical point BC2 (Fig. 3).
The experimental data for sample B at T = 0.4 K
are presented on Fig. 4. The QHE plateau number one
and corresponding minimum at B = 5.6 T are clearly
seen on �xy B( ) and �xx B( ) dependencies. The estima-
tion of the hole mobility from the � �xx xy� point
BC1 2 5� . T gives � � � � �4 0 103. (cm V s)2 . The con-
dition for the field of QHE �xx B( ) minima,
p i e hc Bi� �( ) , where i is the number of the plateau,
gives p � � �12 1011 2. cm .
It is seen from Fig. 4 that in low-field region
B BC� 1 (� �c � 0 7. ) minimum in �xx B( ) at B4 1 4� . T
(see inset of this figure) and precursor of �xy B( ) pla-
teau number four are observed. Really, Fig. 5 shows
pronounced QHE-like structures on the dependence of
first derivative d dBxy� � on filling factor for � � 1, 2,
and 4.
In complete QHE regime at � �c �� 1 the appear-
ance of quantized plateaus in the �xy B( ) dependences
with vanishing values of �xx is commonly accepted to
be caused by the existence of disorder-induced mobil-
ity gaps (stripes of localized states) between the nar-
Quantum Hall effect in p-Ge/Ge
1–x
Si
x
heterostructures with low hole mobility
Fizika Nizkikh Temperatur, 2007, v. 33, Nos. 2/3 209
8
8
6
6
4
4
a b
d
/d
B
, k
�
�
�
xx
T
d
/d
B
, k
�
�
�
xx
T
0.4 0.41.0 1.04.0 4.0
T, K T, K
2
Fig. 2. The first derivative d dBxx � as a function of
temperature in a vicinity of low-field critical point in
log—log scale (a) and linear—log scale (b). Dashed line
on Fig. 2,a is a guide for eye.
d
/d
B
, k
�
�
�
xx
T
30
20
10
0.4 1.0 4.0
T, K
Fig. 3. The first derivative d dBxx � as a function of tem-
perature in a vicinity of high-field critical point (log—log
scale).
�
�
�
xx
xy
,
, k
xx
,
k
�
30
20
10
0 2 4 6 8
B, T
B, T
i = 4
i = 2
i = 1
16
15
1 2
Fig. 4. Longitudinal and Hall resistivities as functions of
magnetic field for sample B at T = 0.4 K.
d
/d
B
, a
rb
. u
n
its
�
xx
1 2 3 4 5
Fig. 5. The first derivative d dBxy � as a function of fil-
ling factor � for sample B at T = 0.4 K.
row bands of extended states of width � presented
close to the center of each of the Landau subbands
[22]. The existence of QHE-like structures at � �c � 1
then should be a manifestation of localization of elec-
tron states in mixing regions for adjacent Landau
subbands so that the width of extended state bands is
less than the collision broadening of Landau level:
� � �� �. We think that realization of such a situation
is more preferable just for � �F � �� 1 when the locali-
zation effect is more essential than for � �F � ��� 1 but
is not yet too strong as for � �F � ��� 1.
Conclusions
Both low-field (BC1) and high-field (BC2) T-inde-
pendent points on �xx B( ) dependence with the � � 1
QHE state between them have been observed for
p-type Ge/Ge1–xSix heterostructures with low hole
mobility (k lF � 16. ). In contrast to series of works
[1–6] and [16,17] where the low-field point is treated
as the critical point of an insulator � QHE phase
transition, we speculate that in our 2D systems with
k lF 1 such a point at � �c � 1 is a manifestation of
quantum e—e interaction correction in the diagonal
component of the magnetoresistivity tensor.
On the other hand, in accordance with [1–6] the
high-field BC2 point is a point of genuine quantum
phase transition between the � � 1 QHE phase and the
high-field insulator and corresponds to passing of the
Fermi level through the lowest Landau level.
Acknowledgment
The work was supported by: Russian Foundation
for Basic Research RFBR, grants 05-02-16206 and
04-02-16614; program of Russian Academy of Sciences
«Low-dimensional quantum heterostructures»; CRDF
and Ministry of Education and Science of Russian
Federation, grant Y1-P-05-14 (Ek-05 [X1]); Ural Di-
vision of Russian Academy of Sciences, grant for
young scientists; Russian Science Support Founda-
tion.
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