Experimental evidence for direct insulator-quantum Hall transition in multi-layer graphene
© Chuang et al.; licensee Springer. 2013
Received: 5 April 2013
Accepted: 24 April 2013
Published: 6 May 2013
We have performed magnetotransport measurements on a multi-layer graphene flake. At the crossing magnetic field Bc, an approximately temperature-independent point in the measured longitudinal resistivity ρ xx , which is ascribed to the direct insulator-quantum Hall (I-QH) transition, is observed. By analyzing the amplitudes of the magnetoresistivity oscillations, we are able to measure the quantum mobility μq of our device. It is found that at the direct I-QH transition, μqBc ≈ 0.37 which is considerably smaller than 1. In contrast, at Bc, ρ xx is close to the Hall resistivity ρ xy , i.e., the classical mobility μBc is ≈ 1. Therefore, our results suggest that different mobilities need to be introduced for the direct I-QH transition observed in multi-layered graphene. Combined with existing experimental results obtained in various material systems, our data obtained on graphene suggest that the direct I-QH transition is a universal effect in 2D.
KeywordsInsulator-quantum Hall transition Graphene flake Multi-layer graphene
Graphene, which is an ideal two-dimensional system , 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 . In addition to its extraordinary electrical properties, graphene possesses great mechanical , optical , and thermal  characteristics.
The insulator-quantum Hall (I-QH) transition [10–13] is a fascinating physical phenomenon in the field of two-dimensional (2D) physics. In particular, a direct transition from an insulator to a high Landau-level filling factor ν > 2 QH state which is normally dubbed as the direct I-QH transition continues to attract interest . The direct I-QH transition has been observed in various systems such as SiGe hole gas , GaAs multiple quantum well devices , GaAs two-dimensional electron gases (2DEGs) containing InAs quantum dots [16–18], a delta-doped GaAs quantum well with additional modulation doping [19, 20], GaN-based 2DEGs grown on sapphire  and on Si , InAs-based 2DEGs , and even some conventional GaAs-based 2DEGs , suggesting that it is a universal effect. Although some quantum phase transitions, such as plateau-plateau transitions  and metal-to-insulator transitions [26–29], have been observed in single-layer graphene and insulating behavior has been observed in disordered graphene such as hydrogenated graphene [30–33], graphene exposed to ozone , reduced graphene oxide , and fluorinated graphene [36, 37], the direct I-QH transition has not been observed in a graphene-based 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 double-layer graphene heterostructure , but not in single-layer pristine graphene. Moreover, the disorder of single graphene is normally lower than those of multi-layer graphene devices. Since one needs sufficient disorder in order to see the I-QH transition , multi-layer graphene seems to be a suitable choice for studying such a transition in a pristine graphene-based system. Besides, the top and bottom layers may isolate the environmental impurities [39–42], making multi-layer graphene a stable and suitable system for observing the I-QH transition.
In this paper, we report magnetotransport measurements on a multi-layer graphene flake. We observe an approximately temperature-independent point in the measured longitudinal resistivity ρ xx which can be ascribed to experimental evidence for the direct I-QH transition. At the crossing field Bc in which ρ xx is approximately T-independent, ρ xx is close to ρ xy . In contrast, the product of the quantum mobility determined from the oscillations in ρ xx and Bc 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 I-QH transition in graphene-based devices.
A multi-layer graphene flake, mechanically exfoliated from natural graphite, was deposited onto a 300-nm-thick SiO2/Si substrate. Optical microscopy was used to locate the graphene flakes, and the thickness of multi-layer 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 inter-layer distance [1, 43]. Ti/Au contacts were deposited on the multi-layer graphene flake by electron-beam lithography and lift-off process. The multi-layer graphene flake was made into a Hall bar pattern with a length-to-width ratio of 2.5 by oxygen plasma etching process . Similar to the work done using disordered graphene, our graphene flakes did not undergo a post-exfoliation annealing treatment [45, 46]. The magnetoresistivity of the graphene device was measured using standard AC lock-in technique at 19 Hz with a constant current I = 20 nA in a He3 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 . In this case, the particular Landau-level quantization in graphene yields linear magnetoplasmon modes. Moreover, instability of magnetoplasmons can be observed in layered graphene structures . Therefore, in order to fully understand the observed I-QH transition in our multi-layer graphene sample, magnetoplasmon modes as well as collective phenomena may need to be considered. The spin effect should not be important in our system . At present, it is unclear whether intra- and/or inter-graphene layer interactions play an important role in our system. Nevertheless, the fact that the low-field Hall resistivity is nominally T-independent suggests that Coulomb interactions do not seem to be dominant in our system.
In conclusion, we have presented magnetoresistivity measurements on a multi-layered graphene flake. An approximately temperature-independent point in ρ xx is ascribed to the direct I-QH transition. Near the crossing field Bc, ρ xx is close to ρ xy , indicating that at Bc, the classical mobility is close to 1/Bc such that Bc is close to 1. On the other hand, μqBc≈ 0.37 which is much smaller than 1. Therefore, different mobilities must be considered for the direct I-QH transition. Together with existing experimental results obtained on various material systems, our new results obtained in a graphene-based system strongly suggest that the direct I-QH transition is a universal effect in 2D.
Two-dimensional electron gases
This work was funded by the National Science Council (NSC), Taiwan (grant no: NSC 99-2911-I-002-126 and NSC 101-2811-M-002-096). CC gratefully acknowledges the financial support from Interchange Association, Japan (IAJ) and the NSC, Taiwan for providing a Japan/Taiwan Summer Program student grant.
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