Summary:
Grahpene is a material that is strictly two-dimensional in nature and composed
solely of carbon atoms. Since the first observation of an isolated graphene
monolayer in 2004 it became clear that graphene possesses unique electronic,
optical and mechanical properties leading to a tremendous outburst of
scientific activity in numerous areas, like solid state physics, chemistry and
engineering. New substrate materials now make it possible to fabricate high
mobility, gated graphene samples that allow the observation of ballistic
transport phenomena. Very recently (Nov. 2015) graphene samples patterned with
antidot super-lattices (ADSLs) were fabricated that for the first time showed
commensurably effects between the super-lattice and the cyclotron motion of the
electrons in a magnetic field.
We study ballistic magneto-transport in graphene ADSLs in a quasi-classical
approach. By the addition of appropriate adjustments, we develop a theoretical
model that extends models that were successfully used to describe the electron
dynamics in the modulated two-dimensional electron gases of semiconductor
lateral surface superlattices. Our model is very rich in nonlinear phenomena
which we thoroughly explain using various techniques from nonlinear dynamics.
Examples of these phenomena are the commensurability peaks due to nonlinear
resonances and hierarchies of partial transport barriers in phase space, or the
negative Hall-resistance due the negative cross-correlation tails of the
channeling orbits.
We compare our model simulations to experimental data and find overall very
good agreement both qualitatively and quantitatively. However, some
characteristic discrepancies, especially in the small magnetic field regime,
shed new light onto the scattering of the carriers by disorder and
imperfections in the specific experiment. Based on the results of this
comparison, we implement a first extension to our model incorporating the
non-homogeneity of the antidot diameters in the experiment, and propose
additional extensions which will be tested in future studies. In addition we
suggest an extension of our study towards parameter regimes, not yet studied in
experiments, with anomalous non-isotropic cyclotron motion promising new, more
complex incommensurability effects.
Keywords:
Graphene, Antidots, Ballistic, Transport, Magnetic-field
