Scaling laws under quantum Hall effect for a smooth disorder potential
We carried out the analysis of discovered experimental values of the critical parameter κ for the quantum Hall plateau-plateau transitions in modulation-doped GaAs/AlGaAs heterostructures. It turned out that these values are in the main concentrated at the range of 0.5–0.7. We argue that within th...
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| Zitieren: | Scaling laws under quantum Hall effect for a smooth disorder potential / S.V. Gudina, A.S. Klepikova, V.N. Neverov, N.G. Shelushinina, M.V. Yakunin // Физика низких температур. — 2019. — Т. 45, № 2. — С. 204-209. — Бібліогр.: 39 назв. — англ. |
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| author | Gudina, S.V. Klepikova, A.S. Neverov, V.N. Shelushinina, N.G. Yakunin, M.V. |
| author_facet | Gudina, S.V. Klepikova, A.S. Neverov, V.N. Shelushinina, N.G. Yakunin, M.V. |
| citation_txt | Scaling laws under quantum Hall effect for a smooth disorder potential / S.V. Gudina, A.S. Klepikova, V.N. Neverov, N.G. Shelushinina, M.V. Yakunin // Физика низких температур. — 2019. — Т. 45, № 2. — С. 204-209. — Бібліогр.: 39 назв. — англ. |
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| container_title | Физика низких температур |
| description | We carried out the analysis of discovered experimental values of the critical parameter κ for the quantum Hall
plateau-plateau transitions in modulation-doped GaAs/AlGaAs heterostructures. It turned out that these values
are in the main concentrated at the range of 0.5–0.7. We argue that within the theoretical concepts for the largescale disorder potential, it corresponds to a borderland between quantum tunnelling processes and classical percolation regime. Just, the critical exponent value for the bandwidth of delocalized states, κ = 0.54 ± 0.01, obtained by us for HgTe-based heterostructure with inverted band spectrum, can be associated with a smooth character of impurity potential in our system
Проведено аналіз експериментальних значень критичного
параметра квантових холлівських переходів κ типу «платоплато» в селективно легованій гетероструктурі GaAs/AlGaAs.
Виявилося, що ці значення в основному зосереджені в діапазоні
κ = 0,5–0,7. Стверджується, що в рамках теоретичних уявлень
про великомасштабний потенціал безладу це відповідає межі
між процесами квантового тунелювання та класичним режимом перколяції. Так само величина критичної експоненти κ =
= 0,54 ±0,01 для ширини смуги делокалізованних станів, отримана для гетероструктури на основі HgTe з інвертованим спектром, може бути пов'язана з плавним характером домішкового
потенціалу в дослідженій системі.
Проведен анализ экспериментальных значений критического параметра κ квантовых холловских переходов типа
плато–плато в селективно легированной гетероструктуре
GaAs/AlGaAs. Оказалось, что эти значения в основном сосредоточены в диапазоне κ = 0,5–0,7. Утверждается, что в рамках
теоретических представлений о крупномасштабном потенциале беспорядка это соответствует границе между процессами квантового туннелирования и классическим режимом
перколяции. Точно так же величина критической экспоненты
κ = 0,54 ±0,01 для ширины полосы делокализованных состояний, полученная для гетероструктуры на основе HgTe с инвертированным спектром, может быть связана с плавным характером примесного потенциала в исследованной системе.
|
| first_indexed | 2025-12-07T15:58:05Z |
| format | Article |
| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 2, pp. 204–209
Scaling laws under quantum Hall effect for
a smooth disorder potential
S.V. Gudina, A.S. Klepikova, V.N. Neverov, N.G. Shelushinina, and M.V. Yakunin
M.N. Miheev Institute of Metal Physics of Ural Branch of Russian Academy of Sciences,
18 S. Kovalevskaya Str., Ekaterinburg 620990, Russia
E-mail: klepikova@imp.uran.ru
Received October 3, 2018, published online December 20, 2018
We carried out the analysis of discovered experimental values of the critical parameter κ for the quantum Hall
plateau-plateau transitions in modulation-doped GaAs/AlGaAs heterostructures. It turned out that these values
are in the main concentrated at the range of 0.5–0.7. We argue that within the theoretical concepts for the large-
scale disorder potential, it corresponds to a borderland between quantum tunnelling processes and classical per-
colation regime. Just, the critical exponent value for the bandwidth of delocalized states, κ = 0.54 ± 0.01, ob-
tained by us for HgTe-based heterostructure with inverted band spectrum, can be associated with a smooth char-
acter of impurity potential in our system.
Keywords: quantum Hall effect, scaling hypothesis, quantum wells, semiconductors, disorder potential.
1. Introduction
The plateau-plateau transition (between neighboring
quantum Hall liquids through an intermediate metal phase)
was considered as an electron localization-delocalization-
localization quantum phase transition already in the first
papers on quantum Hall effect (QHE) interpretation [1,2]
and is widely treated at present within the framework of a
scaling hypothesis (see, e.g., the reviews [3–7]).
The scaling hypothesis is based on a concept that at the
absolute zero of temperature the localization length diverges
at the critical energy Ec of the phase transition at the center
of the broadened Landau level with a universal exponent γ
(the critical exponent of the localization length) [4,8]:
/2
( )
| |
c
N
c
E
E E γ
ω
ξ = ξ
−
, (1)
where cω is the cyclotron frequency and the constant Nξ
depends on microscopic details of the randomness and on
the Landau band index N. For a short-range random poten-
tial Nξ is of the order of cyclotron radius cR [9].
At finite temperatures, the region of delocalized states
at the Landau level center can be described by an energy
range where the localization length ( )Eξ increases to a
characteristic length ( )E Lϕξ > . Here /2~ pL T −
ϕ is the
phase coherence length and the dynamical exponent p de-
pends on the inelastic scattering mechanism. At ( )E Lϕξ <
electronic states remain localized and the bandwidth, ,δν
of delocalized states is determined from the condition
( )E Lϕξ ≅ [1–4]. Thus the width of the transition between
neighboring QHE plateaus, as well as the width of the cor-
responding peak in the magnetic-field dependence ( )xx Bσ
should tend to zero by the power-law dependence ,Tκ
where /2pκ = γ .
2. The current concepts of scaling in the QHE regime
2.1. Short-range random potential
The theoretical investigations of the critical behavior of
noninteracting electrons in the quantum Hall system with
the short-ranged disorder potentials led to the conclusion
about a single diverging length scale and the results of ex-
tensive efforts on numerical simulations for the critical
exponent gave the value 2.35 0.03γ = ± (see, for exam-
ple, reviews [3,4] and the detailed table in the review [5]).
In terms of the dimensionless filling numbers, ν (= n/nB,
nB being the degeneracy of the Landau level and n is the
carrier concentration), Eq. (1) takes the form
( ) N cv v v −γξ = ξ − . (2)
A schematic representation of localization length diver-
gences with |ν – νc|, where the critical filling factor νc is a
half-integer value of ν, is provided in Fig. 1(a) for a short-
range impurity potential according to theoretical consider-
ations described above.
The critical exponent κ = 0.42 experimentally deter-
mined for the first time in the classical study [10] for
© S.V. Gudina, A.S. Klepikova, V.N. Neverov, N.G. Shelushinina, and M.V. Yakunin, 2019
Scaling laws under quantum Hall effect for a smooth disorder potential
InGaAs/InP systems (κ = 0.42 ± 0.04) is in excellent
agreement with the conclusions of new unique studies of
AlxGa1–xAs/Al0.33Ga0.67As systems in the region of alloy
scattering (κ = 0.42 ± 0.01) [11] and with the results of
recent studies of the first and second Landau levels (both
for electrons and holes) in single layer graphene [12,13].
The observable exponent 0.42κ = is compatible with a
numerical short-ranged potential value 2.3γ ≈ for the
Fermi-liquid dynamical exponent 2p = as it is believed to
be the case by Li et al. [11] along with the pioneering work
of Wei et al. [10]. Although the value of the parameter κ is
currently the subject of discussion, there is a consensus
that 0.42κ = indeed describes transitions in the QHE re-
gime (when they are not masked by macroscopic
inhomogeneities) for systems with short-range scattering
potentials [14,15].
2.2. Large-scale random potential
However, in sharp contrast to the short range alloy po-
tential scattering in InGaAs/InP samples [10], the most
perfect and the most studied AlGaAs/GaAs heterostructure
has long range Coulomb scattering on remote (by a spacer)
ionized impurities which results in nonuniversality of the
temperature exponent κ (see both the early [16–19] and the
recent works [20–26]).
In modulation-doped GaAs/AlGaAs heterostructures the
values κ > 0.42 ± 0.01 are regularly observed (see Table 1 in
Appendix). In the Table 1 results for critical exponent (κ)
values in modulation-doped GaAs/AlGaAs heterostructures
from the works of the years 1991–2016 have been collected,
and the “nonuniversal” values of parameter κ in the range
of 0.5−0.75 come to light.
The fact that a slowly varying potential turned out to be
the generic type of disorder in the standard AlGaAs/GaAs
heterostructure has led historically to semiclassical consid-
erations (percolation picture) of delocalization near the
Landau band center. The ideas, which relate localization to
the classical percolation in the context of the integer quan-
tum Hall effect, have been developed intensively by a
number of authors (see the article of Prange [27] for ex-
haustive information).
In the theoretical calculations, an exponent 4/3γ =
was obtained within a model of classical percolation
[28,29]. On the other hand, after including the effect of
quantum tunneling, the universal critical exponent 7/3γ =
results from a model of quantum percolation [29,30] (see a
clear exposition of arguments in a number of reviews
[3,31,32]).
The percolation model for QHE supplemented by the
quantum effects [29,30] provides a physical background
for the Chalker–Coddington network model [33] — a ge-
neric model, which is assumed to describe the universal
quantum mechanical properties of noninteracting electrons
in two dimensions in the presence of a random potential
subject to a strong perpendicular magnetic field. An over-
view of the random network model, invented by Chalker
and Coddington, and its generalizations is provided, for
example, in [3].
In a seminal paper on percolation and quantum tunnel-
ing in the integer quantum Hall effect [33] a network mod-
el for localization in the QHE regime has been introduced
that made it possible to numerically simulate a system
where the disorder potential varies slowly on the magnetic
length scale. Using the simplifying features of a slowly
varying potential in the model the quantum tunneling and
interference effects were incorporated. It turned out that
the network model contains the features necessary for a
qualitative understanding of the integer quantum Hall ef-
fect: localized states in the Landau band tails and extended
Fig. 1. (Color online) Localization length, ξ, dependences on the filling factor, ν, in the vicinity of critical value ν = νc within a modern
theoretical conception for a short-range (a) or a large-scale (b) impurity potential in QHE regime.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 2 205
S.V. Gudina, A.S. Klepikova, V.N. Neverov, N.G. Shelushinina, and M.V. Yakunin
states in the band center, existing only at one energy. To
this extent, the classical picture survives the introduction of
quantum tunneling.
There are, however, quantitative changes. In the classical
picture, as was shown earlier [28,29], the localization length
diverges with an exponent 4/3γ = . For the network model
[33] the value 2.5 0.5γ = ± was found in a reasonable
agreement with estimates for a rapidly varying potential.
The modern theoretical network models for the large-
scale impurity potential with the quantum tunneling give a
numerical value of the critical exponent 2.3γ ≈ in the
immediate vicinity of the critical energy ( )c cE E v v= =
(see [3,4] and references therein) in accordance with the
findings of Ref. 33. On the other hand, far from the critical
energy, dependence of ξ on | |– cE E (on | |)cν − ν is
determined by the model of classical percolation with
4/3γ = (see Fig. 1(b)).
Let’s turn our attention on the results of Wei et al.
[16] who have found that the T dependence of
max( / )xyd dBρ behaves like 0.42T − in two low-mobility
GaAs/AlxGa1–xAs heterostructures from the experiments
down to T = 200 mK (see Table 1 in Appendix). It is si-
milar to their earlier reported result for the
1In Ga As/InPx x− heterostructure [10] but at more lower
temperatures. The 2DEG in the InxGa1–xAs/InP hetero-
structure is in the alloy InxGa1–xAs layer and the potential
fluctuations are therefore short ranged compared to the
cyclotron radius (typically 100 Å). On the other hand, the
2DEG in the GaAs/AlxGa1–xAs heterostructures is in the
GaAs layer, and the dominant scattering mechanism at
low T is the remote ionized impurities away from the
2DEG layer. One should then expect smooth, long-range
potential fluctuations [34,35]. The necessity to lower the
temperature for detecting the “universal” scaling in
GaAs/AlxGa1–xAs is attributed just to the dominance of
the long-range random potential.
Recently Li et al. [11] studied the dependence of the
exponent κ on x for AlxGa1–xAs/Al0.33Ga0.67As hetero-
structures in a wide Al concentration range and have dis-
tinguished three regimes.
For samples in the first regime (x < 0.0065), where the
long-range potential for scattering on remote ionized impuri-
ties is the main one, κ reaches 0.56−0.58. For the second
regime (0.0065 < x < 0.016), the probability of short-range
alloy scattering becomes significantly higher, the transport
has a quantum nature, and 0.42κ = for all samples. Finally,
at x > 0.016, κ again increases to 0.57−0.59 because of
Al-atom clusterization resulting in a change in the charac-
ter of disorder in the system (macroscopic inhomoge-
neities), thus breaking the universal scaling.
It is assumed in Ref. 11 that quantum tunnelling pro-
cesses (for the short-range impurity potential) are followed
by classical processes (for the large-scale potential) with
increasing disorder range. Due to the quantum-classical
crossover effect the exponent κ increases from 0.42 to-
wards the classical value of 0.75. The fact that the κ val-
ues obtained in the first and third regimes, which are still
well below 0.75, show that the system is still away from an
ideal classical percolation regime. In their subsequent work
[25], extending temperature range from 1.2 K down to
1 mK for AlxGa1–xAs/Al0.32Ga0.68As heterostructures in a
region of long-range disorder (for x = 0 and 0.0021) Li et
al. have observed a crossover behavior from the high-
temperature nonuniversal scaling regime to the low-
temperature universal scaling regime with the temperature
exponent κ changing from 0.58κ = to 0.42, respectively
(see Table 1 in Appendix).
3. Diagrams of scaling
As first pointed out by Chalker and Coddington [33] (see
above), the tunneling through saddle points should be taken
into account for a disorder potential, smooth on the scale of
magnetic length ( )1/2 /Bl eB= . The tunneling becomes
determinative in an energy band of the width t∆ around the
critical energy Ec. By assuming a quadratic form for the
potential near saddle points, the estimate for the band of
tunneling has been obtained [36] (see also [37] or [38]):
2( / )t Bl a∆ ≈ Γ . (3)
Here a is the correlation length of the random potential,
which one has taken to be much larger than ,Bl Γ equals
the disorder-induced width of the Landau level. As
,Ba l we have from (3) that .t∆ Γ
In dimensionless units Eq. (3) takes the form
( ) ( ) 12/t B cl a −δ = ω τ , (4)
where / ,t t cδ = ∆ ω and a simple relation / (Γ = τ τ is
the elastic relaxation time) is used to estimate the broaden-
ing of the Landau level due to disorder.
Figure 1 schematically shows the diagrams of scaling
(2): theoretically assumed dependences of QHE localiza-
tion length on the filling factor, ( )ξ ν , when counting from
the critical value of cν = ν at the center of a Landau level,
both for a short-range (a) and for a large-scale impurity
potential (b) (see a description in the text).
In Fig. 1(a) it is displayed that for a short-range poten-
tial the critical exponent of localization length should be
equal to 2.3qγ ≈ for the entire interval 0.5.cν − ν ≤
In Fig. 1(b) the solid lines are: the divergence law (2)
with 4/3pγ = γ = in regions of classical percolation
(thick blue lines) and with qγ = γ in regions of the quan-
tum tunnelling processes (thin red lines). Here 7/3qγ =
within a modified percolation model [30] and 2.3qγ ≈
within the modern network models [3,4]. The dash lines in
Fig. 1(b) show an intermediate region of Eq. (2) with
4/3 7/3< γ < (or 2.3) that gives 0.42 0.75< κ < (if the
exponent 2)p = in the interspace of crossover from a
206 Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 2
Scaling laws under quantum Hall effect for a smooth disorder potential
classical percolation to the quantum tunneling as pointed
out by Li et al. [11].
The dimensionless width of the tunneling band, ,tδ as
well as the value of 0 ,ξ = ξ corresponding to a condition
Table 1. The critical exponent κ values for modulation-doped GaAs/AlGaAs heterostructures (1991–2016 years)
Structure PPT Value of κ Method Ref. (year) Authors
GaAs/AlxGa1–xAs
2 → 1
3 → 2
4 → 3
0.42 [T < 2 K]
0.72 ± 0.2
[T > 0.75 K]
max
xyd
dB
ρ [0.02–5 K] [16]
(1992)
Wei et al.
GaAs/AlxGa1–xAs
3 → 2
4 → 3
5 → 4
0.68 ± 0.04
0.72 ± 0.05
0.67 ± 0.06
∆B ∼ T
κ
max
xyd
dB
ρ [0.025–1 K]
[17]
(1991)
Koch et al.
GaAs/AlxGa1–xAs
3 → 2
4 → 3
5 → 4
6 → 5
0.5 ± 0.03
0.5 ± 0.03
∆B ∼ T
κ [0.3–1.2 K]
max
xyd
dB
ρ
[18]
(1994)
Yoo et al.
GaAs/AlxGa1–xAs 4 → 3
0.62 ± 0.04
0.59 ± 0.04
∆B ∼ T
κ [0.05–1 K]
∆B ∼ J
κ/2
[19]
(1995)
Koch et al.
GaAs/AlxGa1–xAs 2 → 1
0.66 ± 0.02 S1
0.60 ± 0.02 S2
0.62 ± 0.02 S3
∆B ∼ T
κ [0.05–1 K]
[20]
(2002)
Hohls et al.
GaAs/AlxGa1–xAs 2 → 1 0.64 ± 0.09
max
xyd
dB
ρ [0.3–1 K] [21]
(2004)
Huang et al.
AlxGa1–xAs/Al0.32Ga0.68As
x < 0.0085
6 → 5
5 → 4
4 → 3
0.58–0.49
0.58–0.50
0.57–0.49
∆B ∼ T
κ [0.03–1 K]
max
xyd
dB
ρ
[11]
(2005)
Li et al.
GaAs/Al0.35Ga0.65As
3 → 2
4 → 3
0.66–0.77
∆B ∼ T
κ [1.7–4 K]
max
xyd
dB
ρ
[22]
(2007)
Tao Tu et al.
GaAs/AlxGa1–xAs
6 → 5
7 → 6
8 → 7
10 → 8
0.72 (0.74)
0.72 (0.80)
0.75 ± 0.05
∆ν ∼ T
κ [0.05–1.2 K]
max
xyd
dB
ρ
[23]
(2008)
Zhao et al.
GaAs/AlxGa1–xAs
mesoscopic system
1 → 0
3 → 2
0.79
0.54
∆ν ∼ T
κ [0.05–5 K]
[24]
(2007)
Nakajima et al.
AlxGa1–xAs/Al0.32Ga0.68As
x = 0
4 → 3
0.42 [T < 120 mK]
0.58 [T > 150 mK]
∆B ∼ T
κ [0.03–1.2 K]
max
xyd
dB
ρ
[25]
(2010)
Li et al.
AlxGa1–xAs/Al0.32Ga0.68As
x = 0.0021
4 → 3
0.42 [T < 250 mK]
0.58 [T > 250 mK]
∆B ∼ T κ [0.03–1.2 K]
max
xyd
dB
ρ
[25]
(2010)
Li et al.
p-GaAs/AlxGa1–xAs
3 → 2
4 → 3
5 → 4
0.52 ± 0.01
0.52 ± 0.02
0.53 ± 0.02
∆ν ∼ T κ [0.05–1 K]
[26]
(2016)
Wang et al.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 2 207
S.V. Gudina, A.S. Klepikova, V.N. Neverov, N.G. Shelushinina, and M.V. Yakunin
/2c tν − ν = δ are also marked on Fig. 1(b). For
/2c tν − ν < δ (i.e., for | | /2)c tE E− < ∆ the bandwidth of
delocalized states, ,δν becomes less than the width of tun-
neling strip. In these and only in these circumstances the
genuine “universal” scaling
( ) ,~ q
c
−γξ ν ν − ν (5)
corresponding to the quantum tunneling, should be ob-
served. In reality, it is a condition of sufficiently low tem-
peratures, 0Lϕ > ξ (for example, (1)L Lϕ ϕ= in Fig. 1(b)).
We believe that the critical exponent value for the band-
width of delocalized states, 0.54 0.01,κ = ± obtained by us
in [39] for HgTe-based heterostructure with inverted band
spectrum, as well as a number of results with κ = 0.5–0.75
for systems with large-scale impurity potentials (see Table 1)
are driven by a situation schematically represented on
Fig. 1(b) with ( )2
0 :L Lϕ ϕ= < ξ the line ( )2 constLϕ = crosses
the curves ( )vξ just at the intermediate region of γ values
that (for 2)p = gives 0.42 0.75< κ < . This situation, quite
possibly, is typical for modulation-doped GaAs/AlGaAs
heterostructures [16–26] manifesting itself in supervision of
“nonuniversal” values of parameter κ .
Conclusions
Thus, the analysis of the available in the literature a
great amount of experimental results on critical exponent
κ values, extracted from the temperature dependences of
the QHE plateau-plateau transition width in modulation-
doped GaAs/AlGaAs heterostructures, led us to the con-
clusion that in most experiments one is dealing with an
intermediate situation between quantum tunnelling pro-
cesses (genuine scaling, 0.42)κ = and classical percola-
tion regime ( 0.75).κ =
This work was done in frames of the state task on the
topic “Electron” No. AAAA-A18-118020190098-5, pro-
ject No. 18-10-2-6 of the Ural Branch Program of the Rus-
sian Academy of Sciences and partly by the Russian Foun-
dation for Basic Research (project Nos. 18-02-00172 and
18-02-00192).
Appendix
Here is a table of experimental results for critical expo-
nent κ values extracted from the temperature dependences
of QHE plateau-plateau transition (PPT) width in modula-
tion-doped GaAs/AlGaA heterostructures [11,16–26].
In the Table 1 the following abbreviations for a method
of determination of the critical exponent from the experi-
mental data on the Hall, xyρ , and the longitudinal, xxρ ,
resistivities are used. The values of κ have been found
from the temperature dependences both of the slope of the
steps between adjacent quantum Hall plateaus:
max
~
c
xy xy
B B
d d
T
dB dB
−κ
=
ρ ρ
≡ , (11)
and of the longitudinal resistance peak width at the PPT:
Δ ~B Tκ . (12)
In Ref. 19 a scaling analysis of the current (J) depend-
ence of the resistance peak width was also carried out:
/2Δ ~B J −κ . (13)
It is seen from the Table 1 that the discovered values of
parameter κ are in the main concentrated at the range of
0.5–0.75. Within the theoretical concepts for the large-scale
impurity potential (see the text) it corresponds to a border-
land between quantum tunnelling processes (genuine scaling,
0.42)κ = and classical percolation regime ( 0.75).κ =
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___________________________
Скейлінг в режимі квантового
ефекту Холла для плавного потенціалу безладу
С.В. Гудина, А.С. Клепікова, В.Н. Неверов,
Н.Г. Шелушініна, М.В. Якунін
Проведено аналіз експериментальних значень критичного
параметра квантових холлівських переходів κ типу «плато-
плато» в селективно легованій гетероструктурі GaAs/AlGaAs.
Виявилося, що ці значення в основному зосереджені в діапазоні
κ = 0,5–0,7. Стверджується, що в рамках теоретичних уявлень
про великомасштабний потенціал безладу це відповідає межі
між процесами квантового тунелювання та класичним режи-
мом перколяції. Так само величина критичної експоненти κ =
= 0,54 ± 0,01 для ширини смуги делокалізованних станів, отри-
мана для гетероструктури на основі HgTe з інвертованим спек-
тром, може бути пов'язана з плавним характером домішкового
потенціалу в дослідженій системі.
Ключові слова: квантовий ефект Холла, скейлiнг, квантові
ями, напівпровідники, потенціал безладу.
Скейлинг в режиме квантового эффекта Холла для
плавного потенциала беспорядка
С.В. Гудина, А.С. Клепикова, В.Н. Неверов,
Н.Г. Шелушинина, М.В. Якунин
Проведен анализ экспериментальных значений критиче-
ского параметра κ квантовых холловских переходов типа
плато–плато в селективно легированной гетероструктуре
GaAs/AlGaAs. Оказалось, что эти значения в основном сосре-
доточены в диапазоне κ = 0,5–0,7. Утверждается, что в рамках
теоретических представлений о крупномасштабном потен-
циале беспорядка это соответствует границе между процес-
сами квантового туннелирования и классическим режимом
перколяции. Точно так же величина критической экспоненты
κ = 0,54 ± 0,01 для ширины полосы делокализованных состоя-
ний, полученная для гетероструктуры на основе HgTe с инвер-
тированным спектром, может быть связана с плавным харак-
тером примесного потенциала в исследованной системе.
Ключевые слова: квантовый эффект Холла, скейлинг, кванто-
вые ямы, полупроводники, потенциал беспорядка.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2019, v. 45, No. 2 209
https://doi.org/10.1103/PhysRevB.78.233301
https://doi.org/10.1143/JPSJ.76.094703
https://doi.org/10.1143/JPSJ.76.094703
https://doi.org/10.1103/PhysRevB.81.033305
https://doi.org/10.1103/PhysRevB.93.075307
https://doi.org/10.1103/PhysRevB.27.7539
https://doi.org/10.1103/PhysRevLett.70.4130
https://doi.org/10.1016/0038-1098(88)90077-4
https://doi.org/10.1063/1.101176
https://doi.org/10.1103/PhysRevB.36.7969
https://doi.org/10.1103/PhysRevLett.75.1368
https://doi.org/10.1103/PhysRevB.60.16838
https://doi.org/10.1103/PhysRevB.60.16838
https://doi.org/10.1134/S1063782615120039
1. Introduction
2. The current concepts of scaling in the QHE regime
2.1. Short-range random potential
2.2. Large-scale random potential
3. Diagrams of scaling
Conclusions
Appendix
|
| id | nasplib_isofts_kiev_ua-123456789-175849 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-12-07T15:58:05Z |
| publishDate | 2019 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Gudina, S.V. Klepikova, A.S. Neverov, V.N. Shelushinina, N.G. Yakunin, M.V. 2021-02-02T20:03:03Z 2021-02-02T20:03:03Z 2019 Scaling laws under quantum Hall effect for a smooth disorder potential / S.V. Gudina, A.S. Klepikova, V.N. Neverov, N.G. Shelushinina, M.V. Yakunin // Физика низких температур. — 2019. — Т. 45, № 2. — С. 204-209. — Бібліогр.: 39 назв. — англ. 0132-6414 https://nasplib.isofts.kiev.ua/handle/123456789/175849 We carried out the analysis of discovered experimental values of the critical parameter κ for the quantum Hall plateau-plateau transitions in modulation-doped GaAs/AlGaAs heterostructures. It turned out that these values are in the main concentrated at the range of 0.5–0.7. We argue that within the theoretical concepts for the largescale disorder potential, it corresponds to a borderland between quantum tunnelling processes and classical percolation regime. Just, the critical exponent value for the bandwidth of delocalized states, κ = 0.54 ± 0.01, obtained by us for HgTe-based heterostructure with inverted band spectrum, can be associated with a smooth character of impurity potential in our system Проведено аналіз експериментальних значень критичного параметра квантових холлівських переходів κ типу «платоплато» в селективно легованій гетероструктурі GaAs/AlGaAs. Виявилося, що ці значення в основному зосереджені в діапазоні κ = 0,5–0,7. Стверджується, що в рамках теоретичних уявлень про великомасштабний потенціал безладу це відповідає межі між процесами квантового тунелювання та класичним режимом перколяції. Так само величина критичної експоненти κ = = 0,54 ±0,01 для ширини смуги делокалізованних станів, отримана для гетероструктури на основі HgTe з інвертованим спектром, може бути пов'язана з плавним характером домішкового потенціалу в дослідженій системі. Проведен анализ экспериментальных значений критического параметра κ квантовых холловских переходов типа плато–плато в селективно легированной гетероструктуре GaAs/AlGaAs. Оказалось, что эти значения в основном сосредоточены в диапазоне κ = 0,5–0,7. Утверждается, что в рамках теоретических представлений о крупномасштабном потенциале беспорядка это соответствует границе между процессами квантового туннелирования и классическим режимом перколяции. Точно так же величина критической экспоненты κ = 0,54 ±0,01 для ширины полосы делокализованных состояний, полученная для гетероструктуры на основе HgTe с инвертированным спектром, может быть связана с плавным характером примесного потенциала в исследованной системе. This work was done in frames of the state task on the topic “Electron” No. AAAA-A18-118020190098-5, project No. 18-10-2-6 of the Ural Branch Program of the Russian Academy of Sciences and partly by the Russian Foundation for Basic Research (project Nos. 18-02-00172 and 18-02-00192). en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Спеціальний випуск. «XXII Уральська міжнародна зимова школа з фізики напівпровідників» (20–23 лютого, 2018) Scaling laws under quantum Hall effect for a smooth disorder potential Скейлінг в режимі квантового ефекту Холла для плавного потенціалу безладу Скейлинг в режиме квантового эффекта Холла для плавного потенциала беспорядка Article published earlier |
| spellingShingle | Scaling laws under quantum Hall effect for a smooth disorder potential Gudina, S.V. Klepikova, A.S. Neverov, V.N. Shelushinina, N.G. Yakunin, M.V. Спеціальний випуск. «XXII Уральська міжнародна зимова школа з фізики напівпровідників» (20–23 лютого, 2018) |
| title | Scaling laws under quantum Hall effect for a smooth disorder potential |
| title_alt | Скейлінг в режимі квантового ефекту Холла для плавного потенціалу безладу Скейлинг в режиме квантового эффекта Холла для плавного потенциала беспорядка |
| title_full | Scaling laws under quantum Hall effect for a smooth disorder potential |
| title_fullStr | Scaling laws under quantum Hall effect for a smooth disorder potential |
| title_full_unstemmed | Scaling laws under quantum Hall effect for a smooth disorder potential |
| title_short | Scaling laws under quantum Hall effect for a smooth disorder potential |
| title_sort | scaling laws under quantum hall effect for a smooth disorder potential |
| topic | Спеціальний випуск. «XXII Уральська міжнародна зимова школа з фізики напівпровідників» (20–23 лютого, 2018) |
| topic_facet | Спеціальний випуск. «XXII Уральська міжнародна зимова школа з фізики напівпровідників» (20–23 лютого, 2018) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/175849 |
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