On the direct insulator-quantum Hall transition in two-dimensional electron systems in the vicinity of nanoscaled scatterers

Liang et al. Nanoscale Research Letters 2011, 6:131 http://www.nanoscalereslett.com/content/6/1/131 NANO EXPRESS Open 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 integer 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 insulator-quantum Hall (I-QH) transition is an approximately temperature (T)-independent point in the measured longitudinal resistivity of a 2DES [3-5]. The IQH transition continues to attract a great deal of interest 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 possible metal-insulator transition in 2D [11,12]. It is worth pointing out that in order to observe an IQH transition separating the zero-field insulator from the QH liquid, one needs to deliberately introduce * Correspondence: 1 Department of Physics, National Taiwan University, Taipei 106, Taiwan Full list of author information is available at the end of the article 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-nmthick heavily doped GaAs layer so as to allow the positively 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-nmthick 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 quantum dots [13] in the vicinity of a modulation-doped GaAs/AlGaAs heterostructure, a strongly disordered 2DES which shows an I-QH transition can be experimentally 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 © 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. Liang et al. Nanoscale Research Letters 2011, 6:131 http://www.nanoscalereslett.com/content/6/1/131 transition, but a narrow crossover in B due to weak localization to Landau quantization. In this study, the authors compare three different electron 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 substrate [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 Page 2 of 7 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. Liang et al. Nanoscale Research Letters 2011, 6:131 http://www.nanoscalereslett.com/content/6/1/131 of great potential applications. Sample C is a deltadoped 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 Al xGa 1x As/GaAs heterostructure [39-41] have shown that 2DESs influenced by short-range disorder provides an excellent opportunity to connect the Anderson localization theory with real experimental systems [41]. Moreover, 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 transiti (...truncated)