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On the direct insulator-quantum Hall transition in two-dimensional electron systems in the vicinity of nanoscaled scatterers
Nanoscale Research Letters volume 6, Article number: 131 (2011)
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.
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 . 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 I-QH 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 , and a possible 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 , 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 positively charged Si atoms to introduce long-range random potential in the 2DES . 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 . It has been shown that by deliberately introducing nanoscaled InAs quantum dots  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  has argued that such a direct transition is not a quantum phase 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 . 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.
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 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 . 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 localization theory with real experimental systems . 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 . 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 samples A, B, and C are compared.
Figure 2 shows a TEM image of the wafer for fabricating 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 estimated to be 20 nm in diameter and 4 nm in height. Experiments were performed in a top-loading He3 cryostat 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 measurements on Sample A as a function of B at various temperatures. It can be seen that at a crossing field B c = 0.9 T, ρxx is approximately T-independent. For B <B c, ρ xx decreases with increasing temperature, characteristics of an insulating regime . For B > B c, ρ xx increases 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 transition 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 oscillations due to Landau quantization in the insulating regime have already been observed [15, 19, 21]. Therefore, the experimental results of this study clearly demonstrate 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. Nevertheless, it can be seen that at B c = 11 T and -B c = -11 T, the measured resistances are approximately temperature independent. The corresponding Landau level filling factor is about 50 in this case. Therefore, a direct 0-50 transition 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, inconsistent with Huckestein's model .
Figure 5 shows magnetoresistance measurements on Sample C as a function of magnetic field at various temperatures. It can be seen that the 2DES undergoes a 0-8 transition characterized by an approximately temperature-independent point in ρ xx at the crossing field B c. Near the crossing field, ρ xx is very close to ρ xy though ρ xx shows a weak T dependence. For B < B c, no resistance oscillation is observed. At first glance, our experimental results are consistent with Huckestein's model. However, it is noted that Landau quantization should be linked with quantum mobility, not classical Drude mobility . Moreover, the observed oscillations for B > B c do not always correspond to formation of quantum Hall states. As mentioned in our previous study , the observed oscillations can be well approximated by conventional Shubnikov-de Haas (SdH) formalism. It is noted that the SdH formula is derived without considering quantum localization effects which give rise to formation 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 σ xx at around 7.9 T may correspond to the extended states due to the onset of the strong localization effects. Therefore, in this study, the onset of strong localization actually occurs at a magnetic field approximately 4 T higher 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 transition . Figure 6 shows such results at various temperatures. Interestingly, for B < 5 T, σ xy is nominally T independent. Such data are consistent with electron-electron interaction effects. Over the whole measurement range, σ xx decreases with increasing T, consistent with electron-electron interaction effects. Unlike σ xy , σ xx shows a significant T dependence.
By inspecting the conductivies, previously the authors have studied the renormalized mobility  of a GaN-based 2DES at high temperatures (Sample B) . It is therefore interesting to study such a mobility for both Sample A and Sample C. It has been suggested the electron-electron interaction effects can renormalize the mobility μ' given by
Figure 7 and the inset to Figure 7 show σxy and σxx , together with fits to Equations 1 and 2 over limited ranges for Sample C, respectively. From the fits, it is possible 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 possible that different mobilities should be taken into account to understand the direct I-QH transition [37, 43, 45].
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 quantization as no resistance oscillations are observed even up to a magnetic field 4 T higher than the crossing 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 transition. All these three pieces of experimental evidence show that a 2DES in the vicinity of nanoscaled scatterers 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 Huckestein's model  must be made.
two-dimensional electron systems.
von Klitzing K, Dorda G, Pepper M: New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance. Phys Rev Lett 1980, 45: 494. 10.1103/PhysRevLett.45.494
Kivelson S, Lee DH, Zhang SC: Global phase diagram in the quantum Hall effect. Phys Rev B 1992, 46: 2223. 10.1103/PhysRevB.46.2223
Jiang HW, Johnson CE, Wang KL, Hannah ST: Observation of magnetic-field-induced delocalization: Transition from Anderson insulator to quantum Hall conductor. Phys Rev Lett 1993, 71: 1439. 10.1103/PhysRevLett.71.1439
Wang T, Clark KP, Spencer GF, Mack AM, Kirk WP: Magnetic-field-induced metal-insulator transition in two dimensions. Phys Rev Lett 1994, 72: 709. 10.1103/PhysRevLett.72.709
Hughes RJF, Nicholls JT, Frost JEF, Linfield EH, Pepper M, Ford CJB, Ritchie DA, Jones GAC, Kogan E, Kaveh M: Magnetic-field-induced insulator-quantum Hall-insulator transition in a disordered two-dimensional electron gas. J Phys Condens Matter 1994, 6: 4763. 10.1088/0953-8984/6/25/014
Laughlin RB: Levitation of Extended-State Bands in a Strong Magnetic Field. Phys Rev Lett 1984, 52: 2304. 10.1103/PhysRevLett.52.2304
Khmelnitskii D: Quantum hall effect and additional oscillations of conductivity in weak magnetic fields. Phys Lett 1984, 106A: 182.
Liu DZ, Xie XC, Niu Q: Weak Field Phase Diagram for an Integer Quantum Hall Liquid. Phys Rev Lett 1996, 76: 975. 10.1103/PhysRevLett.76.975
Sheng DN, Weng ZY: Disappearance of Integer Quantum Hall Effect. Phys Rev Lett 1997, 78: 318. 10.1103/PhysRevLett.78.318
Sheng DN, Weng ZY: Phase diagram of the integer quantum Hall effect. Phys Rev B 2000, 62: 15363. 10.1103/PhysRevB.62.15363
Kravchenko SV, Kravchenko GV, Furneaux JE, Pudalov VM, D'Iorio M: Possible metal-insulator transition at B = 0 in two dimensions. Phys Rev B 1994, 50: 8039. 10.1103/PhysRevB.50.8039
Dobrosavljevic V, Abrahams E, Miranda E, Chakravarty S: Scaling Theory of Two-Dimensional Metal-Insulator Transitions. Phys Rev Lett 1997, 79: 455. 10.1103/PhysRevLett.79.455
Chang WH, Lin CH, Fu YJ, Lin TC, Lin H, Cheng SJ, Lin SD, Lee CP: Impacts of Coulomb Interactions on the magnetic response of excitonic complexes in single semiconductor nanostructures. Nanoscale Res Lett 2010, 5: 680. 10.1007/s11671-010-9531-3
Kim GH, Nicholls JT, Khondaker SI, Farrer I, Ritchie DA: Tuning the insulator-quantum Hall liquid transitions in a two-dimensional electron gas using self-assembled InAs. Phys Rev B 2000, 61: 10910. 10.1103/PhysRevB.61.10910
Kim GH, Liang CT, Huang CF, Nicholls JT, Ritchie DA, Kim PS, Oh CH, Juang JR, Chang YH: From localization to Landau quantization in a two-dimensional GaAs electron system containing self-assembled InAs quantum dots. Phys Rev B 2004, 69: 073311. 10.1103/PhysRevB.69.073311
Song SH, Shahar D, Tsui DC, Xie YH, Monroe D: New Universality at the Magnetic Field Driven Insulator to Integer Quantum Hall Effect Transitions. Phys Rev Lett 1997, 78: 2200. 10.1103/PhysRevLett.78.2200
Lee CH, Chang YH, Suen YW, Lin HH: Magnetic-field-induced delocalization in center-doped GaAs/Al x Ga 1-x As multiple quantum wells. Phys Rev B 1998, 58: 10629. 10.1103/PhysRevB.58.10629
Huang CF, Chang YH, Lee CH, Chuo HT, Yeh HD, Liang CT, Lin HH, Cheng HH, Hwang GJ: Insulator-quantum Hall conductor transitions at low magnetic field. Phys Rev B 2002, 65: 045303. 10.1103/PhysRevB.65.045303
Huang TY, Juang JR, Huang CF, Kim GH, Huang CP, Liang CT, Chang YH, Chen YF, Lee Y, Ritchie DA: On the low-field insulator-quantum Hall conductor transition. Physica E 2004, 22: 240. 10.1016/j.physe.2003.11.258
Huckestein B: Quantum Hall Effect at Low Magnetic Fields. Phys Rev Lett 2000, 84: 3141. 10.1103/PhysRevLett.84.3141
Huang TY, Liang CT, Kim GH, Huang CF, Huang CP, Lin JY, Goan HS, Ritchie DA: From insulator to quantum Hall liquid at low magnetic fields. Phys Rev B 2008, 78: 113305. 10.1103/PhysRevB.78.113305
Huang TY, Huang CF, Kim GH, Huang CP, Liang CT, Ritchie DA: An Experimental Study on the Hall Insulators. Chin J Phys 2009, 47: 401.
Huang TY, Liang CT, Kim GH, Huang CF, Huang CP, Ritchie DA: Probing two-dimensional metallic-like and localization effects at low magnetic fields. Physica E 2010, 42: 1142. 10.1016/j.physe.2009.11.049
Nakamura S, Senoh M, Iwasa N, Hagahama S, Yamada Y, Mukai Y: Superbright Green InGaN Single-Quantum-Well-Structure Light-Emitting Diodes. Jpn J Appl Phys 2 1995, 34: L1332. 10.1143/JJAP.34.L1332
Wu Y, Keller B, Keller S, Kapolnek D, Kozodoy P, DenBaars S, Mishra U: Very high breakdown voltage and large transconductance realized on GaN heterojunction field effect transistors. Appl Phys Lett 1996, 69: 1438. 10.1063/1.117607
Bulman GE, Doverspike K, Sheppard ST, Weeks TW, Kong HS, Dieringer HM, Edmond JA, Brown JD, Swindell JT, Schetzina JF: Pulsed operation lasing in a cleaved-facet InGaN/GaN MQW SCH laser grown on 6H-SiC. Electron Lett 1997, 33: 1556. 10.1049/el:19971025
Mack MP, Abare A, Aizcorbe M, Kozodoy P, Keller S, Mishra UK, Coldren L, Denbaars S: Characteristics of indium-gallium-nitride multiple-quantum-well blue laser diodes grown by MOCVD. MRS Internet J Nitride Semicond Res 1997, 2: 41.
Hang DR, Liang CT, Juang JR, Huang TY, Hung WK, Chen YF, Kim GH, Lee JH, Lee JH: Electrically detected and microwave-modulated Shubnikov-de Haas ocsillcations in an Al 0.4 Ga 0.6 N/GaN heterostructure. J Appl Phys 2003, 93: 2055. 10.1063/1.1539286
Juang JR, Huang TY, Chen TM, Lin MG, Lee Y, Liang CT, Hang DR, Chen YF, Chyi JI: Transport in a gated Al 0.18 Ga 0.82 N/GaN electron system. J Appl Phys 2003, 94: 3181. 10.1063/1.1594818
Cho KS, Huang TY, Huang CP, Chiu YH, Liang CT, Chen YF, Lo I: Exchange-enhanced g-factors in an Al 0.25 Ga 0.75 N/GaN two-dimensional electron system. J Appl Phys 96: 7370. 10.1063/1.1815390
Chen JH, Lin JY, Tsai JK, Park H, Kim GH, Youn D, Cho HI, Lee EJ, Lee JH, Liang CT, Chen YF: Experimental evidence for Drude-Boltzmann-like transport in a two-dimensional electron gas in an AlGaN/GaN heterostructure. J Korean Phys Soc 2006, 48: 1539.
Lin JY, Chen JH, Kim GH, Park H, Youn DH, Jeon CM, Baik JM, Lee JL, Liang CT, Chen YF: Magnetotransport measurements on an AlGaN/GaN two-dimensional electron system. J Korean Phys Soc 2006, 49: 1130.
Hang DR, Chou MMC, Hsieh MH, Heuken M: Influence of an Advanced Buffer Layer on the Optical Properties of an InGaN/GaN MQW Grown on a (111) Silicon Substrate. J Korean Phys Soc 2007, 50: 797. 10.3938/jkps.50.797
Chen KY, Liang CT, Chen NC, Chang PH, Chang CA: Weak Localization and electron-electron interaction effects in Al0.15Ga0.85N/GaN High Electron Mobility Transistor Structure. Chin J Phys 2007, 45: 616.
Schremer AT, Smart JA, Wang Y, Ambacher O, MacDonald NC, Shealy JR: High electron mobility AlGaN/GaN heterostructure on (111) Si. Appl Phys Lett 2000, 76: 736. 10.1063/1.125878
Chen KY, Chang YH, Liang CT, Aoki N, Ochiai Y, Huang CF, Lin LH, Cheng KA, Cheng HH, Lin HH, Wu JY, Lin SD: Probing Landau quantization with the presence of insulator-quantum Hall transition in a GaAs two-dimensional electron system. J Phys Condens Matter 2008, 20: 295223. 10.1088/0953-8984/20/29/295223
Chen KY, Liang CT, Aoki N, Ochiai Y, Cheng KA, Lin LH, Huang CF, Li Y-R, Tseng YS, Yang CK, Lin PT, Wu JY, Lin SD: Probing insulator-quantum Hall transitions by current heating. J Korean Phys Soc 2009, 55: 64. 10.3938/jkps.55.64
Kannan ES, Kim G-Ho, Lin JY, Chen JH, Chen KY, Zhang ZY, Liang CT, Lin LH, Youn DH, Kang KY, Chen NC: Experimental Evidence for Weak Insulator-Quantum Hall Transitions in GaN/AlGaN Two-Dimensional Electron Systems. J Korean Phys Soc 2007, 50: 1643. 10.3938/jkps.50.1643
Li W, Csathy GA, Tsui DC, Pfeiffer LN, West KW: Direct observation of alloy scattering of two-dimensional electrons in Al x Ga 1-x As. Appl Phys Lett 2003, 83: 2832. 10.1063/1.1611650
Li W, Csáthy GA, Tsui DC, Pfeiffer LN, West KW: Scaling and Universality of Integer Quantum Hall Plateau-to-Plateau Transitions. Phys Rev Lett 2005, 94: 206807. 10.1103/PhysRevLett.94.206807
Li W, Vicente CL, Xia JS, Pan W, Tsui DC, Pfeiffer LN, West KW: Scaling in Plateau-to-Plateau Transition: A Direct Connection of Quantum Hall Systems with the Anderson Localization Model. Phys Rev Lett 2009, 102: 216801. 10.1103/PhysRevLett.102.216801
Shahar D, Tsui DC, Shayegan M, Shimshoni E, Sondhi SL: A Different View of the Quantum Hall Plateau-to-Plateau Transitions. Phys Rev Lett 1997, 79: 479. 10.1103/PhysRevLett.79.479
Minkov GM, Germanenko AV, Rut OE, Sherstobitov AA, Larionova VA, Bakarov AK, Zvonkov BN: Diffusion and ballistic contributions of the interaction correction to the conductivity of a two-dimensional electron gas. Phys Rev B 2006, 74: 045314. 10.1103/PhysRevB.74.045314
Liang CT, Lin LH, Huang JZ, Zhang ZY, Sun ZH, Chen KY, Chen NC, Chang PH, Chang CA: Electron-electron interactions in Al 0.15 Ga 0.85 N/GaN high electron mobility transistor structures grown on Si substrates. Appl Phys Lett 2007, 90: 022107. 10.1063/1.2430778
Murzin SS: On the phase boundaries of the integer quantum Hall effect. Part II. JETP Lett 2010, 91: 155. 10.1134/S0021364010030112
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.
The authors declare that they have no competing interests.
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.
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Liang, C., Lin, L., Kuang Yoa, C. et al. On the direct insulator-quantum Hall transition in two-dimensional electron systems in the vicinity of nanoscaled scatterers. Nanoscale Res Lett 6, 131 (2011). https://doi.org/10.1186/1556-276X-6-131
- Quantum Phase Transition
- Strong Localization
- Quantum Hall State
- Landau Quantization