Experimental evidence for direct insulatorquantum Hall transition in multilayer graphene
 Chiashain Chuang^{1, 2},
 LiHung Lin^{3},
 Nobuyuki Aoki^{2}Email author,
 Takahiro Ouchi^{2},
 Akram M Mahjoub^{2},
 TakPong Woo^{1},
 Jonathan P Bird^{2, 4},
 Yuichi Ochiai^{2},
 ShunTsung Lo^{5} and
 ChiTe Liang^{1, 5}Email author
DOI: 10.1186/1556276X8214
© Chuang et al.; licensee Springer. 2013
Received: 5 April 2013
Accepted: 24 April 2013
Published: 6 May 2013
Abstract
We have performed magnetotransport measurements on a multilayer graphene flake. At the crossing magnetic field B_{c}, an approximately temperatureindependent point in the measured longitudinal resistivity ρ_{ xx }, which is ascribed to the direct insulatorquantum Hall (IQH) transition, is observed. By analyzing the amplitudes of the magnetoresistivity oscillations, we are able to measure the quantum mobility μ_{q} of our device. It is found that at the direct IQH transition, μ_{q}B_{c} ≈ 0.37 which is considerably smaller than 1. In contrast, at B_{c}, ρ_{ xx } is close to the Hall resistivity ρ_{ xy }, i.e., the classical mobility μB_{c} is ≈ 1. Therefore, our results suggest that different mobilities need to be introduced for the direct IQH transition observed in multilayered graphene. Combined with existing experimental results obtained in various material systems, our data obtained on graphene suggest that the direct IQH transition is a universal effect in 2D.
Keywords
Insulatorquantum Hall transition Graphene flake Multilayer grapheneBackground
Graphene, which is an ideal twodimensional system [1], has attracted a great deal of worldwide interest. Interesting effects such as Berry's phase [2, 3] and fractional quantum Hall effect [4–6] have been observed in mechanically exfoliated graphene flakes [1]. In addition to its extraordinary electrical properties, graphene possesses great mechanical [7], optical [8], and thermal [9] characteristics.
The insulatorquantum Hall (IQH) transition [10–13] is a fascinating physical phenomenon in the field of twodimensional (2D) physics. In particular, a direct transition from an insulator to a high Landaulevel filling factor ν > 2 QH state which is normally dubbed as the direct IQH transition continues to attract interest [14]. The direct IQH transition has been observed in various systems such as SiGe hole gas [14], GaAs multiple quantum well devices [15], GaAs twodimensional electron gases (2DEGs) containing InAs quantum dots [16–18], a deltadoped GaAs quantum well with additional modulation doping [19, 20], GaNbased 2DEGs grown on sapphire [21] and on Si [22], InAsbased 2DEGs [23], and even some conventional GaAsbased 2DEGs [24], suggesting that it is a universal effect. Although some quantum phase transitions, such as plateauplateau transitions [25] and metaltoinsulator transitions [26–29], have been observed in singlelayer graphene and insulating behavior has been observed in disordered graphene such as hydrogenated graphene [30–33], graphene exposed to ozone [34], reduced graphene oxide [35], and fluorinated graphene [36, 37], the direct IQH transition has not been observed in a graphenebased system. It is worth mentioning that the Anderson localization effect, an important signature of strong localization which may be affected by a magnetic field applied perpendicular to the graphene plane, was observed in a doublelayer graphene heterostructure [38], but not in singlelayer pristine graphene. Moreover, the disorder of single graphene is normally lower than those of multilayer graphene devices. Since one needs sufficient disorder in order to see the IQH transition [11], multilayer graphene seems to be a suitable choice for studying such a transition in a pristine graphenebased system. Besides, the top and bottom layers may isolate the environmental impurities [39–42], making multilayer graphene a stable and suitable system for observing the IQH transition.
In this paper, we report magnetotransport measurements on a multilayer graphene flake. We observe an approximately temperatureindependent point in the measured longitudinal resistivity ρ_{ xx } which can be ascribed to experimental evidence for the direct IQH transition. At the crossing field B_{c} in which ρ_{ xx } is approximately Tindependent, ρ_{ xx } is close to ρ_{ xy }. In contrast, the product of the quantum mobility determined from the oscillations in ρ_{ xx } and B_{c} is ≈ 0.37 which is considerably smaller than 1. Thus, our experimental results suggest that different mobilities need to be introduced when considering the direct IQH transition in graphenebased devices.
Methods
A multilayer graphene flake, mechanically exfoliated from natural graphite, was deposited onto a 300nmthick SiO_{2}/Si substrate. Optical microscopy was used to locate the graphene flakes, and the thickness of multilayer graphene is 3.5 nm, checked by atomic force microscopy. Therefore, the layer number of our graphene device is around ten according to the 3.4 Å graphene interlayer distance [1, 43]. Ti/Au contacts were deposited on the multilayer graphene flake by electronbeam lithography and liftoff process. The multilayer graphene flake was made into a Hall bar pattern with a lengthtowidth ratio of 2.5 by oxygen plasma etching process [44]. Similar to the work done using disordered graphene, our graphene flakes did not undergo a postexfoliation annealing treatment [45, 46]. The magnetoresistivity of the graphene device was measured using standard AC lockin technique at 19 Hz with a constant current I = 20 nA in a He^{3} cryostat equipped with a superconducting magnet.
Results and discussion
It has been shown that the elementary neutral excitations in graphene in a high magnetic field are different from those of a standard 2D system [51]. In this case, the particular Landaulevel quantization in graphene yields linear magnetoplasmon modes. Moreover, instability of magnetoplasmons can be observed in layered graphene structures [52]. Therefore, in order to fully understand the observed IQH transition in our multilayer graphene sample, magnetoplasmon modes as well as collective phenomena may need to be considered. The spin effect should not be important in our system [53]. At present, it is unclear whether intra and/or intergraphene layer interactions play an important role in our system. Nevertheless, the fact that the lowfield Hall resistivity is nominally Tindependent suggests that Coulomb interactions do not seem to be dominant in our system.
Conclusion
In conclusion, we have presented magnetoresistivity measurements on a multilayered graphene flake. An approximately temperatureindependent point in ρ_{ xx } is ascribed to the direct IQH transition. Near the crossing field B_{c}, ρ_{ xx } is close to ρ_{ xy }, indicating that at B_{c}, the classical mobility is close to 1/B_{c} such that B_{c} is close to 1. On the other hand, μ_{q}B_{c}≈ 0.37 which is much smaller than 1. Therefore, different mobilities must be considered for the direct IQH transition. Together with existing experimental results obtained on various material systems, our new results obtained in a graphenebased system strongly suggest that the direct IQH transition is a universal effect in 2D.
Abbreviations
 2D:

Twodimensional
 2DEGs:

Twodimensional electron gases
 IQH:

Insulatorquantum Hall
 SdH:

Shubnikovde Haas.
Declarations
Acknowledgments
This work was funded by the National Science Council (NSC), Taiwan (grant no: NSC 992911I002126 and NSC 1012811M002096). CC gratefully acknowledges the financial support from Interchange Association, Japan (IAJ) and the NSC, Taiwan for providing a Japan/Taiwan Summer Program student grant.
Authors’ Affiliations
References
 Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Grigorieva IV, Firsov AA: Electric field effect in atomically thin carbon films. Science 2004, 306: 666. 10.1126/science.1102896View Article
 Zhang Y, Tan YW, Stormer HL, Kim P: Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 2005, 438: 201. 10.1038/nature04235View Article
 Novoselov KS, Geim AK, Morozov SV, Jiang D, Katsnelson MI, Grigorieva IV, Dubonos SV, Firsov AA: Twodimensional gas of massless Dirac fermions in graphene. Nature 2005, 438: 197. 10.1038/nature04233View Article
 Bolotin KI, Ghahari F, Shulman MD, Stormer HL, Kim P: Observation of the fractional quantum Hall effect in graphene. Nature 2009, 462: 196. 10.1038/nature08582View Article
 Du X, Skachko I, Duerr F, Luican A, Andrei EY: Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene. Nature 2009, 462: 192. 10.1038/nature08522View Article
 Feldman BE, Krauss B, Smet JH, Yacoby A: Unconventional sequence of fractional quantum Hall states in suspended graphene. Science 2012, 337: 1196. 10.1126/science.1224784View Article
 Lee C, Wei X, Kysar JW, Hone J: Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 2008, 321: 385. 10.1126/science.1157996View Article
 Nair PR, Blake P, Grigorenko AN, Novoselov KS, Booth TJ, Stauber T, Peres NMR, Geim AK: Fine structure constant defines visual transparency of graphene. Science 2008, 320: 1308. 10.1126/science.1156965View Article
 Balandin AA, Ghosh S, Bao W, Calizo I, Teweldebrhan D, Miao F, Lau CN: Superior thermal conductivity of singlelayer graphene. Nano Lett 2008, 8: 902. 10.1021/nl0731872View Article
 Kivelson S, Lee DH, Zhang SC: Global phase diagram in the quantum Hall effect. Phys Rev B 1992, 46: 2223. 10.1103/PhysRevB.46.2223View Article
 Jiang HW, Johnson CE, Wang KL, Hannahs ST: Observation of magneticfieldinduced delocalization: transition from Anderson insulator to quantum Hall conductor. Phys Rev Lett 1993, 71: 1439. 10.1103/PhysRevLett.71.1439View Article
 Wang T, Clark KP, Spencer GF, Mack AM, Kirk WP: Magneticfieldinduced metalinsulator transition in two dimensions. Phys Rev Lett 1994, 72: 709. 10.1103/PhysRevLett.72.709View Article
 Hughes RJF, Nicholls JT, Frost JEF, Linfield EH, Pepper M, Ford CJB, Ritchie DA, Jones GAC, Kogan E, Kaveh M: Magneticfieldinduced insulatorquantum Hallinsulator transition in a disordered twodimensional electron gas. J Phys Condens Matter 1994, 6: 4763. 10.1088/09538984/6/25/014View Article
 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.78.2200View Article
 Lee CH, Chang YH, Suen YW, Lin HH: Magneticfieldinduced delocalization in centerdoped GaAs/Al_{ x }Ga_{1}_{x}As multiple quantum wells. Phys Rev B 1998, 58: 10629. 10.1103/PhysRevB.58.10629View Article
 Huang TY, Juang JR, Huang CF, Kim GH, Huang CP, Liang CT, Chang YH, Chen YF, Lee Y, Ritchie DA: On the lowfield insulatorquantum Hall conductor transitions. Physica E 2004, 22: 240. 10.1016/j.physe.2003.11.258View Article
 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.View Article
 Liang CT, Lin LH, Chen KY, Lo ST, Wang YT, Lou DS, Kim GH, Chang YH, Ochiai Y, Aoki N, Chen JC, Lin Y, Huang CF, Lin SD, Ritchie DA: On the direct insulatorquantum Hall transition in twodimensional electron systems in the vicinity of nanoscaled scatterers. Nanoscale Res Lett 2011, 6: 131. 10.1186/1556276X6131View Article
 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 twodimensional electron system. J Phys Condens Matter 2008, 20: 295223. 10.1088/09538984/20/29/295223View Article
 Lo ST, Chen KY, Lin TL, Lin LH, Luo DS, Ochiai Y, Aoki N, Wang YT, Peng ZF, Lin Y, Chen JC, Lin SD, Huang CF, Liang CT: Probing the onset of strong localization and electron–electron interactions with the presence of a direct insulator–quantum Hall transition. Solid State Commun 2010, 150: 1902. 10.1016/j.ssc.2010.07.040View Article
 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 twodimensional electron system. J Korea Phys Soc 2006, 49: 1130.
 Kannan ES, Kim GH, Lin JY, Chen JH, Chen KY, Zhang ZY, Liang CT, Lin LH, Youn DH, Kang KY, Chen NC: Experimental evidence for weak insulatorquantum Hall transitions in GaN/AlGaN twodimensional electron systems. J Korean Phys Soc 2007, 50: 1643. 10.3938/jkps.50.1643View Article
 Gao KH, Yu G, Zhou YM, Wei LM, Lin T, Shang LY, Sun L, Yang R, Zhou WZ, Dai N, Chu JH, Austing DG, Gu Y, Zhang YG: Insulatorquantum Hall conductor transition in high electron density gated InGaAs/InAlAs quantum wells. J Appl Phys 2010, 108: 063701. 10.1063/1.3486081View Article
 Lo ST, Wang YT, Bohra G, Comfort E, Lin TY, Kang MG, Strasser G, Bird JP, Huang CF, Lin LH, Chen JC, Liang CT: Insulator, semiclassical oscillations and quantum Hall liquids at low magnetic fields. J Phys Condens Matter 2012, 24: 405601. 10.1088/09538984/24/40/405601View Article
 Giesbers AJM, Zeitler U, Ponomarenko LA, Yang R, Novoselov KS: Scaling of the quantum Hall plateauplateau transition in graphene. Phys Rev B 2009, 80: 241411.View Article
 Amado M, Diez E, Rossela F, Bellani V, LópezRomero D, Maude DK: Magnetotransport of graphene and quantum phase transitions in the quantum Hall regime. J Phys Condens Matter 2012, 24: 305302. 10.1088/09538984/24/30/305302View Article
 Amado M, Diez E, LópezRomero D, Rossella F, Caridad JM, Dionigi F, Bellani V, Maude DK: Plateau–insulator transition in graphene. New J Phys 2010, 12: 053004. 10.1088/13672630/12/5/053004View Article
 Zhu W, Yuan HY, Shi QW, Hou JG, Wang XR: Topological transition of graphene from a quantum Hall metal to a quantum Hall insulator at ν = 0. New J Phys 2011, 13: 113008. 10.1088/13672630/13/11/113008View Article
 Checkelsky JG, Li L, Ong NP: Zeroenergy state in graphene in a high magnetic field. Phys Rev Lett 2008, 100: 206801.View Article
 Elias DC, Nair RR, Mohiuddin TMG, Morozov SV, Blake P, Halsall MP, Ferrari AC, Boukhvalov DW, Katsnelson MI, Geim AK, Novoselov KS: Control of graphene's properties by reversible hydrogenation: evidence for graphane. Science 2009, 323: 610. 10.1126/science.1167130View Article
 Chuang C, Puddy RK, Lin HD, Lo ST, Chen TM, Smith CG, Linag CT: Experimental evidence for EfrosShklovskii variable range hopping in hydrogenated graphene. Solid State Commun 2012, 152: 905. 10.1016/j.ssc.2012.02.002View Article
 Chuang C, Puddy RK, Connolly MR, Lo ST, Lin HD, Chen TM, Smith CG, Liang CT: Evidence for formation of multiquantum dots in hydrogenated graphene. Nano Res 2012, 7: 459. Lett LettView Article
 Lo ST, Chuang C, Puddy RK, Chen TM, Smith CG, Liang CT: Nonohmic behavior of carrier transport in highly disordered graphene. Nanotechnology 2013, 24: 165201. 10.1088/09574484/24/16/165201View Article
 Moser J, Tao H, Roche S, Alzina F, Torres CMS, Bachtold A: Magnetotransport in disordered graphene exposed to ozone: from weak to strong localization. Phys Rev B 2010, 81: 205445.View Article
 Wang SW, Lin HE, Lin HD, Chen KY, Tu KH, Chen CW, Chen JY, Liu CH, Liang CT, Chen YF: Transport behavior and negative magnetoresistance in chemically reduced graphene oxide nanofilms. Nanotechnology 2011, 22: 335701. 10.1088/09574484/22/33/335701View Article
 Hong X, Cheng SH, Herding C, Zhu J: Colossal negative magnetoresistance in dilute fluorinated graphene. Phys Rev B 2011, 83: 085410.View Article
 Withers F, Russo S, Dubois M, Craciun MF: Tuning the electronic transport properties of graphene through functionalisation with fluorine. Nanoscale Res Lett 2011, 6: 526. 10.1186/1556276X6526View Article
 Ponomarenko LA, Geim AK, Zhukov AA, Jalil R, Morozov SV, Novoselov KS, Grigorieva IV, Hill EH, Cheianov VV, Falko VI, Watanabe K, Taniguchi T, Gorbachev RV: Tunable metal–insulator transition in doublelayer graphene heterostructures. Nat Phys 2011, 7: 958. 10.1038/nphys2114View Article
 Hass J, de Heer WA, Conrad EH: The growth and morphology of epitaxial multilayer graphene. J Phys Condens Matter 2008, 20: 323202. 10.1088/09538984/20/32/323202View Article
 Sui Y, Appenzeller J: Screening and interlayer coupling in multilayer graphene fieldeffect transistors. Nano Lett 2009, 9: 2973. 10.1021/nl901396gView Article
 Kim K, Park HJ, Woo BC, Kim KJ, Kim GT, Yun WS: Electric property evolution of structurally defected multilayer graphene. Nano Lett 2008, 8: 3092. 10.1021/nl8010337View Article
 Hass J, Varchon F, MillánOtoya JE, Sprinkle M, Sharma N, de Heer WA, Berger C, First PN, Magaud L, Conrad EH: Why multilayer graphene on 4 H SiC(0001) behaves like a single sheet of graphene. Phy Rev Lett 2008, 100: 125504.View Article
 Dresselhaus MS, Dresselhaus G: Intercalation compounds of graphite. Adv Phys 2002, 51: 1. 10.1080/00018730110113644View Article
 Ponomarenko LA, Schedin F, Katsnelson MI, Yang R, Hill EW, Novoselov KS, Geim AK: Chaotic Dirac billiard in graphene quantum dots. Science 2008, 320: 356. 10.1126/science.1154663View Article
 Bohra G, Somphonsane R, Aoki N, Ochiai Y, Ferry DK, Bird JP: Robust mesoscopic fluctuations in disordered graphene. Appl Phys Lett 2012, 101: 093110. 10.1063/1.4748167View Article
 Bohra G, Somphonsane R, Aoki N, Ochiai Y, Akis R, Ferry DK, Bird JP: Nonergodicity and microscopic symmetry breaking of the conductance fluctuations in disordered mesoscopic graphene. Phys Rev B 2012, 86: 161405(R).View Article
 Sharapov SG, Gusynin VP, Beck H: Magnetic oscillations in planar systems with the Diraclike spectrum of quasiparticle excitations. Phys Rev B 2004, 69: 075104.View Article
 Berger C, Song Z, Li X, Wu X, Brown N, Naud C, Mayou D, Li T, Hass J, Marchenkov AN, Conrad EH, First PN, de Heer WA: Electronic confinement and coherence in patterned epitaxial graphene. Science 2006, 312: 1191. 10.1126/science.1125925View Article
 Coleridge PT, Stoner R, Fletcher R: Lowfield transport coefficients in GaAs/Ga_{1x} Al_{x}As heterostructures. Phys Rev B 1989, 39: 1120. 10.1103/PhysRevB.39.1120View Article
 Huckestein B: Quantum Hall effect at low magnetic fields. Phys Rev Lett 2000, 84: 3141. 10.1103/PhysRevLett.84.3141View Article
 Roldán R, Fuchs JN, Goerbig MO: Collective modes of doped graphene and a standard twodimensional electron gas in a strong magnetic field: linear magnetoplasmons versus magnetoexcitons. Phys Rev B 2009, 80: 085408.View Article
 Berman OL, Gumbs G, Lozovik YE: Magnetoplasmons in layered graphene structures. Phys Rev B 2008, 78: 085401.View Article
 Cho KS, Liang CT, Chen YF, Tang YQ, Shen B: Spindependent photocurrent induced by Rashbatype spin splitting in Al_{0.25}Ga_{0.75}N/GaN heterostructures. Phys Rev B 2007, 75: 085327.View Article
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