Transport properties and local imaging of graphene quantum dots

Abstract

In this thesis, we present transport and scanning-gate microscopy experiments on graphene nanostructures at cryogenic temperatures. Moreover, an analytic expression for the quantum states of a circular graphene quantum dot in a perpendicular magnetic field is derived. Graphene is a semi-metal showing the electric field effect and thus is an interesting material for the mesoscopic semiconductor community. In graphene quantum dots, we observed clear indications of transport through confinementinduced excited states. These showed up in resonant sequential tunneling and in inelastic co-tunneling in the Coulomb-blockaded regime using tunneling spectroscopy. To deepen our understanding of the confining potential, we looked at the magnetic-field dependence and identified a transition from confinement-induced to magnetic-field induced behavior. Motivated by these experimental results, we could derive an analytic mathematical expression which qualitatively describes both the confinement-induced and the magnetic-field induced effects as well as the transition between both. As a side-effect, a strategy for determining experimentally the electron-hole crossover in graphene quantum dots was developed. A second graphene quantum dot was studied with our dilution refrigerator scanning-gate microscope. We could clearly resolve Coulomb resonances of the quantum dot. More than 35 Coulomb resonances were recorded in some measurements where a spacing of around 20 nm of adjacent Coulomb resonances could clearly be resolved. This proved the exceptional quality of both the sample and the scanning sensor. Our measurements also gave direct proof of the existence of localized states in graphene nanostructures: We could image and locate a single localized puddle in each constriction connecting the quantum dot to source and drain. Furthermore, our technique enabled us to deduce a radius of around 10 to 13 nm for such a localized state. Despite the good spatial resolution, we could not resolve quantum confinement effects in the quantum dot or in one of the localized puddles. Finally, we analyzed experimentally how a change in the electrostatic environment can influence the outcome of a scanning-gate measurement. We identified