Elektronischer Transport in Graphen

In 2004 graphene, a monolayer of carbon atoms, has been isolated as the first real two-dimensional solid by the group of A. Geim at the University of Manchester. Graphene’s properties have been theoretically investigated since the 1950s. Until the successful preparation by Geim et al., graphene was suspected to be unstable under ambient conditions above 0 K (Mermin-Wagner theorem). Its two dimensionality and hexagonal lattice symmetry cause interesting novel properties and effects. At experimentally relevant energies, graphene has a linear band structure and charge carrier dynamics must be treated using Dirac’s equation. Therefore charge carriers in graphene are called “Dirac fermions”. Beside exotic effects like “Klein tunneling” an unconventional quantum Hall effect (QHE) can be observed with a Hall conductance quantized in units of 2e^2/h, 6e^2/h, 10e^2/h, 14e^2/h… . As a starting point for in-depth transport measurements the processing of graphene field effect transistors (GFETs) has been developed and optimized, based on the pioneering work by Novoselov et al.. The optimized process provides samples with carrier mobilities up to 16000 cm^2/Vs and a well defined Hall geometry. These samples are used to investigate external influences on the electronic properties of graphene. Among those influences molecular adsorbates are responsible for various effects of freshly prepared graphene samples e.g. an intrinsic p-doping, a mobility asymmetry of electrons and holes, the so called “minimal conductivity” and a field effect hysteresis at room temperature. In collaboration with the group of A. Yacoby (Harvard) density fluctuations in the vicinity of the Dirac point (“electron-hole puddles”) could be observed using a scanning single electron transistor (SSET). These fluctuations might be one reason for the “minimal conductivity” at vanishing average density. While molecular adsorbates are treated as long range Coulomb defects there are short range scatterers that localize Dirac fermions. They are created using electron beam irradiation and can be characterized by “weak localization”, “universal conductance fluctuations” and a metal-insulator transition. From the experiments regarding molecular adsorbates a process could be developed that allows the creation of graphene pn-junctions by chemical doping. These pn-junctions are investigated at high magnetic fields up to 12 T and low temperatures (QHE regime). Due to edge channel interaction at the p-n interface Hall resistances h/e^2, h/3e^2, h/15e^2 can be observed, which do not exist in pure graphene. In the final section the pn-junctions are further developed into ballistic pn-arrays which allow the analysis of tunnelling of charge carriers in graphene (“Klein tunneling”). For ballistic pn-arrays one observes a sqrt[4]-density dependence of the conductivity being characteristic for Dirac fermions