Localized electrons in graphene nanostructures

Graphene consists of a single layer of carbon atoms arranged in a honeycomb lattice. Its special mechanical, thermal, optical and electronic properties make it a promising material for a wide range of applications. Graphene exhibits an unusual linear electronic band structure leading to a variety of effects, such as Klein tunneling, which make it an intriguing material to study novel physics. It is crucial to understand the implications of these effects to design graphene devices for basic research and applications. Graphene devices with an in-plane dimension in the nanometer scale are called “graphene nanodevices”. Theoretical and experimental research was conducted for graphene nanostructures to explore possible applications, to confirm predicted properties and to answer fundamental physical questions. Despite a tremendous research effort, many unsolved puzzles still remain for electronic transport in graphene nanostructures: • in a majority of experiments, it was found that charge carriers tend to localize inside graphene nanostructures. The exact mechanism for this behavior is so far not understood and severely limits the performance of devices. • a variety of effects were observed for quantum dots in other material systems but so far not for graphene dots. One example is spin blockade. The observation of spin blockade would enable to use graphene quantum dots for quantum information processing. • it is unclear if and at which length scale bulk effects such as Klein tunneling start to disappear. This thesis presents a number of electronic transport experiments designed to gain insight into some of these open questions. Investigated devices were patterned in geometries of small stripes called “nanoribbons” and small islands called “quantum dots”. All presented measurements were performed at cryogenic temperatures in order to resolve processes with small energy scales. In a first experiment, a process to fabricate graphene nanoribbons on a hexagonal boron nitride substrate was developed. Similar to described in literature, a clear improvement of device properties was found for wide graphene devices. However, nanoribbons did not exhibit similarly improved device characteristics. This indicates that the edges are the main origin of the observed localization of charge carriers. In a second experiment, a quantum dot geometry was investigated: it was found that for some gate configurations, the quantum dot behaved as expected for a single dot. In this regime, additional side gates were used to demonstrate that the device was clearly in a configuration where three dots in series exist. This apparent contradiction was explained by higher order cotunneling of electrons through the outer two quantum dots located in the constrictions and explains why certain effects of single dot physics are so far hard to observe in graphene quantum dots. Short graphene constrictions on a hexagonal boron nitride substrate were investigated in a third experiment: a special geometry allowed to establish that the area on which charge is localized can be significantly larger than the constriction itself. It was concluded that charge carriers mostly localize along the edge and that their wave function extends into the graphene leads of the device. The fourth experiment investigated ribbons with added “wings”. It was shown that these wings significantly influence transport. The findings obtained from this experiment again indicate that electron transport happens preferentially along the edge with additional coupling of edges over the bulk and strong coherent coupling between different sites of localized charge taking place at the same time. The fifth and sixth experiments exploited the intrinsic properties of graphene to perform measurements that are challenging in other material systems. In both experiments, a graphene nanoribbon was separated by a thin insulating layer from a second graphene sheet on top. In the fifth experiment, the ribbon was used to locally probe the quantum capacitance of the graphene sheet. In the sixth experiment, the second layer was also patterned into a ribbon geometry. The strong capacitive coupling enabled the observation of double dot physics. It also allowed to investigate “mesoscopic Coulomb drag”, which was theoretically predicted four years ago. Finally, the different findings from this thesis are put together and compared with literature in order to obtain a more accurate picture of electronic transport in graphene nanodevices. The fifth and the sixth experiments demonstrated how future experiments in graphene can be designed such that novel physics can be investigated despite the current limitations of graphene nanodevices.