Magnetism of Dirac Fermions and nanostructured graphene

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The charge carriers in graphene act as massless, chiral Dirac fermions, and graphene thus exhibits intriguing electronic properties such as unconventional localization and novel manifestations of the quantum Hall effect. A divergence of the diamagnetic susceptibility in the limit of small magnetic fields and small carrier density was predicted. Nanostructured graphene should display magnetic properties that can be tailored by the geometry of edges and defects.In this project we aim at measuring the magnetization and the de Haas-van Alphen effect of single- and bi-layer graphene and of arrays of graphene nanostructures at low temperature and in magnetic fields. For this task we employ highly sensitive microcantilever magnetometers developed in our group, since commercial magnetometers are not sensitive enough. The magnetization M is a thermodynamic quantity which, at low temperature, directly monitors the evolution of the ground state energy of the charge carrier system. The measurement of M thus opens up a direct access to the spectral form of the density of states of graphene in a magnetic field. Energy gaps in the spectrum are measured directly.Employing microcantilever magnetometers we have measured the magnetization of large-area graphene either grown by chemical vapor deposition on different substrates or prepared by thermal decomposition of SiC. The predicted de Haas-van Alphen effect has however not yet been observed in a magnetization experiment on such samples by us and by the worldwide community. Our experimental results suggest that the electronic quality and homogeneity of graphene on the millimeter scale needs to be improved further. As a second route, the prerequisites for magnetometry with nanocantilevers on graphene samples with dimensions on the micrometer scale have been established. Such samples can be obtained by mechanical exfoliation of graphite and exhibit a high electronic quality.We propose to investigate the de Haas-van Alphen effect of exfoliated graphene on hexagonal boron nitride using nanocantilevers. At the same time, we will address recent advances in large-area graphene growth techniques using magnetometry with microcantilevers. Both techniques will be used to explore the magnetic properties of graphene nanostructures.