Magnetism of Dirac Fermions and nanostructured graphene

石墨烯中的载流子作为无质量的手性狄拉克费米子，因此石墨烯表现出有趣的电子特性，如非常规的局域化和量子霍尔效应的新表现。预测了在小磁场和小载流子密度极限下的抗磁化率发散。纳米结构的石墨烯应该显示出可以根据边缘和缺陷的几何形状定制的磁性。在这个项目中，我们的目标是在低温和磁场下测量单层和双层石墨烯以及石墨烯纳米结构阵列的磁化强度和de Haas-van Alphen效应。对于这项任务，我们采用了我们小组开发的高灵敏度微悬臂式磁力计，因为商用磁力计不够灵敏。磁化强度M是一个热力学量，它在低温下直接监测载流子体系基态能量的演变。因此，对M的测量开辟了一个直接获取磁场中石墨烯状态密度的光谱形式的途径。光谱中的能隙是直接测量的。利用微悬臂式磁力计，我们测量了在不同衬底上通过化学气相沉积生长或通过SiC热分解制备的大面积石墨烯的磁化强度。然而，我们和国际社会尚未在对这些样品的磁化实验中观察到预测的de Haas-van Alphen效应。我们的实验结果表明，石墨烯在毫米尺度上的电子质量和均匀性需要进一步提高。作为第二种途径，已经建立了在微米尺度的石墨烯样品上使用纳米反杠杆进行磁强计的先决条件。这种样品可以通过石墨的机械剥落得到，并表现出高电子质量。我们建议使用纳米反杠杆来研究剥离石墨烯对六方氮化硼的de Haas-van Alphen效应。同时，我们将讨论使用微悬臂磁强计的大面积石墨烯生长技术的最新进展。这两种技术都将用于探索石墨烯纳米结构的磁性。

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.