When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron–hole degeneracy and vanishing carrier mass near the point of charge neutrality1,2. Indeed, a distinctive half-integer quantum Hall effect has been predicted3,4,5 theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction—a consequence of the exceptional topology of the graphene band structure6,7. Recent advances in micromechanical extraction and fabrication techniques for graphite structures8,9,10,11,12 now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.
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We thank I. Aleiner, A. Millis, T. F. Heinz, A. Mitra, J. Small and A. Geim for discussions. This research was supported by the NSF Nanoscale Science and Engineering Center at Columbia University, New York State Office of Science (NYSTAR) and the Department of Energy (DOE).
Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.
This pdf formatted file contains detailed discussions of sample preparation method, cross-correlation of optical microscope and AFM images of single layer and few layer graphene samples, and electrical characterization of double layer graphene samples. (PDF 203 kb)
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Zhang, Y., Tan, YW., Stormer, H. et al. Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 438, 201–204 (2005). https://doi.org/10.1038/nature04235
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