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NANO EXPRESSOpen Access

On the direct insulator-quantum Hall transition in

two-dimensional electron systems in the vicinity

of nanoscaled scatterers

Chi-Te Liang1*, Li-Hung Lin2, Kuang Yao Chen1, Shun-Tsung Lo1, Yi-Ting Wang1, Dong-Sheng Lou3, Gil-Ho Kim4,

Yuan-Huei Chang1, Yuichi Ochiai5, Nobuyuki Aoki5, Jeng-Chung Chen3, Yiping Lin3, Chun-Feng Huang6,

Sheng-Di Lin7, David A Ritchie8

Abstract

A direct insulator-quantum Hall (I-QH) transition corresponds to a crossover/transition from the insulating regime to

a high Landau level filling factor ν > 2 QH state. Such a transition has been attracting a great deal of both

experimental and theoretical interests. In this study, we present three different two-dimensional electron systems

(2DESs) which are in the vicinity of nanoscaled scatterers. All these three devices exhibit a direct I-QH transition,

and the transport properties under different nanaoscaled scatterers are discussed.

Introduction

The simultaneous presence of disorder and a strong

enough magnetic field B can lead to a wide variety of

interesting physical phenomena. For example, the inte-

ger quantum Hall effect is one of the most exciting

effects in two-dimensional electron systems (2DES), in

which the electrons are usually confined in layers of the

nanoscale [1]. In an integer quantum Hall (QH) state,

the current is carried by the one-dimensional edge

channels because of the localization effects. It has been

shown that with sufficient amount of disorder, a 2DES

can undergo a B-induced insulator to quantum Hall

transition [2-5]. Experimental evidence for such an insu-

lator-quantum Hall (I-QH) transition is an approxi-

mately temperature (T)-independent point in the

measured longitudinal resistivity of a 2DES [3-5]. The I-

QH transition continues to attract a great deal of inter-

est both experimentally and theoretically as it may shed

light on the fate of extended states [6-10], the true

ground state of a non-interacting 2DES [2], and a possi-

ble metal-insulator transition in 2D [11,12].

It is worth pointing out that in order to observe an I-

QH transition separating the zero-field insulator from

the QH liquid, one needs to deliberately introduce

strong disorder within a 2DES. The reason for this is

that the localization length needs to be shorter than the

sample size. In the study by Jiang and co-workers [2], a

2DES without a spacer layer in which strong Coulomb

scattering exists was used. Wang et al. utilized a 30-nm-

thick heavily doped GaAs layer so as to allow the posi-

tively charged Si atoms to introduce long-range random

potential in the 2DES [3]. Hughes et al. have shown that

when a Si-doped plane was incorporated into a 550-nm-

thick GaAs film, a deep potential well can form in

which the 2DES is confined close to the ionized donors

and is therefore highly disordered [4]. It has been shown

that by deliberately introducing nanoscaled InAs quan-

tum dots [13] in the vicinity of a modulation-doped

GaAs/AlGaAs heterostructure, a strongly disordered

2DES which shows an I-QH transition can be experi-

mentally realized [14,15].

The transition/crossover from an insulator to a QH

state of the filling factor ν > 2 in an ideal spinless 2DES

can be denoted as the direct I-QH transition [16-19].

Such a transition has been attracting a great deal of

interest and remains an unsettled issue. Experimental

[16-19] and theoretical results [9,10] suggest that such a

direct transition can occur, and it is a quantum phase

transition. However, Huckestein [20] has argued that

such a direct transition is not a quantum phase

* Correspondence: ctliang@phys.ntu.edu.tw

1Department of Physics, National Taiwan University, Taipei 106, Taiwan

Full list of author information is available at the end of the article

Liang et al. Nanoscale Research Letters 2011, 6:131

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© 2011 Liang et al; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution

License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium,

provided the original work is properly cited.

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transition, but a narrow crossover in B due to weak

localization to Landau quantization.

In this study, the authors compare three different elec-

tron systems containing nanoscaled scatterers which all

show a direct I-QH transition. The first sample is a

GaAs 2DES containing self-assembled nanoscaled InAs

quantum dots [13,14,21-23].

The second one is a 2DES in a nominally undoped

AlGaN/GaN heterostructure [24-33] grown on Si sub-

strate [33,34]. Such a GaN-based electron system can be

affected by nanoscaled dislocation and impurities [35].

Finally, experimental results on the third sample, a

delta-doped GaAs/AlGaAs quantum well with additional

modulation doping [36,37], will be presented. All the

experimental results on the three completely different

samples show that the direct I-QH transition does not

occur with the onset of strong localization due to

Landau quantization [20,38]. Therefore, in order to

obtain a thorough understanding of the direct I-QH

transition, further studies are required.

Experimental details

Figure 1a,b,c show the structures of the three devices,

Sample A, Sample B, and Sample C, considered in this

study. Sample A is a GaAs/AlGaAs 2DES containing

self-assembled InAs quantum dots. Sample B is an

AlGaN/GaN heterostructure grown on Si. Such a system

is fully compatible with Si CMOS technology and is thus

Figure 1 Schematic diagrams showing the structure of (a) Sample A, (b) Sample B, and (c) Sample C.

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of great potential applications. Sample C is a delta-

doped quantum well with additional delta-doping. Since

the electrons in the quantum well in sample B are in

close proximity of nanoscaled dislocation and impurities,

the 2DES is strongly influenced by these nanoscaled

scatterers. In fact, these scatterers provide scattering

which is required for observing the I-QH transition [16].

On the other hand, the scatterings in samples A and C

are mainly due to the self-assembled quantum dots and

the delta-doping in the quantum well, respectively.

Recent studies focussing on alloy disorder in AlxGa1-

xAs/GaAs heterostructure [39-41] have shown that

2DESs influenced by short-range disorder provides an

excellent opportunity to connect the Anderson localiza-

tion theory with real experimental systems [41]. More-

over, the nature of disorder may affect scaling behavior

in the plateau-plateau (P-P) transition at high B [39-41],

and the P-P and I-QH transitions may be considered as

the same universality class [42]. Therefore, it may be

interesting to investigate the direct I-QH transitions

under different scattering types at low magnetic fields.

In this article, such low-field direct transitions in sam-

ples A, B, and C are compared.

Figure 2 shows a TEM image of the wafer for fabricat-

ing Sample A. Very uniform nanoscaled InAs quantum

dots can be seen. These nano-scattering centers provide

strong scattering in the vicinity of the 2DES in the

GaAs. The dimensions of the quantum dot are esti-

mated to be 20 nm in diameter and 4 nm in height.

Experiments were performed in a top-loading He3 cryo-

stat equipped with a superconductor magnet. Four-

terminal resistance measurements were performed using

standard phase-sensitive lock-in techniques.

Results and discussions

Figure 3 shows the longitudinal magnetoresistivity mea-

surements on Sample A as a function of B at various

temperatures. It can be seen that at a crossing field Bc

= 0.9 T, rxxis approximately T-independent. For B <Bc,

rxxdecreases with increasing temperature, characteristics

of an insulating regime [16]. For B >Bc, rxxincreases

with increasing temperature, and therefore the 2DES is

in the quantum Hall regime. As the 2DES enters the ν =

4 QH state from the insulating regime, a direct 0-4 tran-

sition where the symbol 0 corresponds to the insulator

has been observed. It is worth pointing out that before

the 2DES enters the ν = 4 QH state, resistance oscilla-

tions due to Landau quantization in the insulating

regime have already been observed [15,19,21]. Therefore,

the experimental results of this study clearly demon-

strate that the crossover from localization from Landau

quantization actually covers a wide range of magnetic

field, in sharp contrast to Huckestein’s argument

[19-21].

As mentioned earlier, a GaN-based electron system can

be affected by nanoscaled dislocation and impurities. It is

therefore interesting to study such a system. Figure 4

shows magnetoresistance measurements on Sample B as

a function of magnetic field at different temperatures.

The data deviate slightly from the expected symmetric

behavior, i.e., R(B) = R(-B). The reason for this could be

due to slight misalignment of the voltage probes. Never-

theless, it can be seen that at Bc= 11 Tand -Bc= -11 T,

the measured resistances are approximately temperature

independent. The corresponding Landau level filling fac-

tor is about 50 in this case. Therefore, a direct 0-50 tran-

sition has been observed. Note that even at the highest

attainable field of approximately 15 T, there is no sign of

resistance oscillations due to the moderate mobility of

our GaN system. Therefore, the experimental results of

this study clearly demonstrate that the observed direct I-

QH transition is irrelevant to Landau quantization.

Therefore, the onset of Landau quantization does not

necessarily accompany the direct I-QH transition, incon-

sistent with Huckestein’s model [20].

Figure 5 shows magnetoresistance measurements on

Sample C as a function of magnetic field at various tem-

peratures. It can be seen that the 2DES undergoes a 0-8

transition characterized by an approximately tempera-

ture-independent point in rxxat the crossing field Bc.

Near the crossing field, rxxis very close to rxythough rxy-

shows a weak T dependence. For B <Bc, no resistance

oscillation is observed. At first glance, our experimental

results are consistent with Huckestein’s model. How-

ever, it is noted that Landau quantization should be

linked with quantum mobility, not classical Drude mobi-

lity [36]. Moreover, the observed oscillations for B >Bc

do not always correspond to formation of quantum Hall

states. As mentioned in our previous study [36], the

observed oscillations can be well approximated by con-

ventional Shubnikov-de Haas (SdH) formalism. It is

noted that the SdH formula is derived without consider-

ing quantum localization effects which give rise to for-

mation of quantum Hall state. Therefore, quantum

localization effects are not significant in the system

under this study. Actually, as shown in Figure 6, the

crossing point in sxyat around 7.9 Tmay correspond to

the extended states due to the onset of the strong locali-

zation effects. Therefore, in this study, the onset of

strong localization actually occurs at a magnetic field

approximately 4 Thigher than the crossing point.

It has been suggested that by converting the measured

resistivities into longitudinal and Hall conductivities, it is

possible to shed more light on the observed I-QH

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transition [5]. Figure 6 shows such results at various tem-

peratures. Interestingly, for B < 5 T,sxyis nominally T

independent. Such data are consistent with electron-elec-

tron interaction effects. Over the whole measurement

range, sxxdecreases with increasing T, consistent with

electron-electron interaction effects. Unlike sxy, sxxshows

a significant Tdependence.

By inspecting the conductivies, previously the authors

have studied the renormalized mobility [43] of a GaN-

based 2DES at high temperatures (Sample B) [44]. It is

Figure 2 A plane-view of TEM image of the wafer which was cut to fabricate sample A.

Liang et al. Nanoscale Research Letters 2011, 6:131

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therefore interesting to study such a mobility for both

Sample A and Sample C. It has been suggested the elec-

tron-electron interaction effects can renormalize the

mobility μ’ given by

( ’ )

xy

ne

+

B

B

=

’

,

2

2

1

(1)

( ’ )

xxee

d

ne

+

B

B

=+

’

.

1

2

Δ

(2)

Figure 7 and the inset to Figure 7 show sxyand sxx,

together with fits to Equations 1 and 2 over limited

ranges for Sample C, respectively. From the fits, it is pos-

sible to determine the respective renormalized mobilites

as a function of temperature as shown in Figure 8a for

Sample C and in Figure 8b for Sample A. The

renormalized mobility calculated using Equation 1 is only

slightly larger than that using Equation 2. It may be pos-

sible that different mobilities should be taken into

account to understand the direct I-QH transition

[37,43,45].

Conclusions

In conclusion, the authors have presented studies on

three completely different electron systems. In these

three samples, the nanoscaled scatterers, in close

proximity of the 2DES, provide necessary disorder for

observing the direct I-QH transition. In these studies,

it has been shown that the crossover from localization

to Landau quantization actually covers a wide range of

magnetic field. Moreover, the observed direct I-QH

transition is not necessarily linked with Landau quanti-

zation as no resistance oscillations are observed even

up to a magnetic field 4 T higher than the crossing

Figure 3 rxx(B) at various temperatures ranging from 0.25 to

2.85 K (Sample A).

Figure 4 rxx(B) at various temperatures ranging from 0.28 to

20 K (Sample B).

Figure 5 rxx(B) at various temperatures ranging from 0.3 to 4

K (Sample C). rxx at T = 0.3 K and T = 4 K are shown.

Figure 6 Converted sxx(B) and sxy(B) at various temperatures

ranging from 0.3 to 4 K (Sample C).

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field. Most importantly, the onset of strong localization

which gives rise to the formation of quantum Hall

state does not correspond to the direct I-QH transi-

tion. All these three pieces of experimental evidence

show that a 2DES in the vicinity of nanoscaled scat-

terers is an ideal playground for studying the direct

I-QH transition. Furthermore, in order to obtain a

thorough understanding of the underlying physics of

the direct I-QH transition, modifications of Huckes-

tein’s model [20] must be made.

Abbreviations

I-QH: insulator-quantum Hall; SdH: Shubnikov-de Haas; 2DESs: two-

dimensional electron systems.

Acknowledgements

This research was supported by the WCU (World Class University) program

through the National Research Foundation of Korea (NRF) funded by the

Ministry of Education, Science and Technology (Grant No. R32-2008-000-

10204-0). C.T.L. acknowledges financial support from the NSC (Grant no: NSC

99-2119-M-002-018-MY3). The authors would like to thank Yi-Chun Su and

Jau-Yang Wu for providing help in the experiments.

Author details

1Department of Physics, National Taiwan University, Taipei 106, Taiwan

2Department of Applied Physics, National Chiayi University, Chiayi 600,

Taiwan3Department of Physics, National Tsinghwa University, Hsinchu 300,

Taiwan4Department of Electronic and Electrical Engineering and SAINT,

Sungkyunkwan University, Suwon 440-746, Korea5Graduate School of

Advanced Integration Science, Chiba University, Chiba 263-8522, Japan

6National Measurement Laboratory, Centre for Measurement Standards,

Industrial Technology Research Institute, Hsinchu 300, Taiwan7Department

of Electronics Engineering, National Chiao Tung University, Hsinchu 300,

Taiwan8Cavendish Laboratory, J.J. Thomson Avenue, Cambridge CB3 0HE,

UK

Authors’ contributions

CTL, GHK and YHC coordinated the measurements on Sample A. CTL

coordinated the measurements on Sample B. KYC performed the

measurements on Sample B. JCC and YL coordinated the measurements on

Sample C undertaken in Taiwan. YO and NA coordinated early

measurements on Sample C in Japan. CTL, STL and CFH drafted the

manuscript. LHL, YTW and DLS performed measurements on Sample C. SDL

and DAR grew the MBE wafers. All authors read and approved the final

manuscript.

Competing interests

The authors declare that they have no competing interests.

Received: 14 August 2010 Accepted: 11 February 2011

Published: 11 February 2011

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doi:10.1186/1556-276X-6-131

Cite this article as: Liang et al.: On the direct insulator-quantum Hall

transition in two-dimensional electron systems in the vicinity of

nanoscaled scatterers. Nanoscale Research Letters 2011 6:131.

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