Browsing by Author "Panos, Konstantinos"

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Current distribution and Hall potential landscape within the quantum Hall effect in graphene and towards the breakdown in a (Al,Ga)As heterostructure
(2014) Panos, Konstantinos; von Klitzing, Klaus (Prof. Dr.)
Since its discovery in 1980 the quantum Hall effect (QHE) is becoming more and more important, currently because of the topological insulators and the aspired new definition of the kilogram by fixing the value of the Planck constant. The reachable measurement precision of the QHE is therefore of significant importance, since the precision of derived quantities is co-determined by the precision of the QHE. However, to be able to give answers to fundamental questions, like how well the quantum Hall resistance resembles h/e^2, an accurate microscopic picture has to be present. The formation of the so-called electrical compressible and incompressible landscape within the quantum Hall sample is thereby the key element. We have shown in this thesis that by such picture we can explain successfully the anomalous QHE in graphene, a monolayer of graphite. In addition we have developed a model for the breakdown of the QHE using the compressible/incompressible landscape picture. The graphene samples studied here are the usual "graphene on silicon dioxide" samples. We measured on this sample Hall potential profiles during QHE for different back gate voltages. The observed Hall potential profiles in n-type graphene is equivalent to the one in (Al,Ga)As-heterostructure samples. The position of the Hall potential drops and therefore also the position of the current path follows the position of incompressible stripes. To explain the measured evolution for p-type graphene, holes have to accumulate at the flake edges, in contrast to n-type graphene where electrons are depleted. We were able to show that with fixed negative charges at the graphene edges, we can explain the accumulation of holes as well as the depletion of electrons. The assumed fixed negative charge leads to two interesting consequences. First, there are pn-junctions parallel to the edges for n-type graphene. Second, the definition of a charge neutrality point becomes difficult. This is because of the charge carrier density profile across the sample, which does not allow for a situation without free charge carriers. The measurements on the breakdown of the QHE were done on (Al,Ga)As-heterostructure samples. From investigations on the transition into the breakdown of the QHE we could identify in the electrical transport measurements as well as in the Hall potential profiles two distinct magnetic field regions within a quantum Hall plateau. At the lower magnetic field side of the quantum Hall plateaus we found for the transition into the breakdown a continuously increasing longitudinal voltage drop with increasing voltage bias. In addition, one finds a continuous evolution with voltage bias in the respective Hall potential profiles. Currents flow for this quantum Hall regime, even after the breakdown, mainly at the edges of the two dimensional electron system (2DES). We call this type of breakdown the edge-dominated breakdown. In contrast, for the high magnetic field side of a quantum Hall plateau one finds abrupt transitions. Abrupt changes can be found in the longitudinal voltage drop as well as in the Hall potential profiles after increasing the bias voltage over a critical value. Since for this type of breakdown current flows predominantly in the bulk of the sample, we call this transition the bulk-dominated breakdown. With a closer look on the edge-dominated breakdown, one can recognize that with increasing bias, an increasing asymmetric distribution of the current between the two current carrying incompressible stripes evolves. With a self-consistent simulation done by Prof. Gerhardts, it could be shown that the asymmetric current distribution is a natural nonlinear response of the 2DES. In a simple model, a width change of the incompressible stripes due to voltage bias is responsible for the asymmetric voltage distribution. In the bulk-dominated breakdown we scanned larger areas of the devices. We could identify a constriction for the current at high voltage bias. At this constriction after exceeding a critical bias voltage an abrupt change of the Hall potential profile happens such that after the change the current flows mainly through the constriction. Self-consistent simulations of Prof. Gerhardts showed that, such as in the edge-dominated breakdown, for increasing bias a dominant incompressible segment evolves carrying most of the current.