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
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