Electronic Properties of Graphene Systems with Sublattice-Asymmetry

The interest in 2 dimensional materials has exploded in the last decade. Purposeful engineering of these materials has been a major field of research in this period, as specific properties from each material are wanted in different combinations. As a consequence of the fact that graphene has a collection of some of the most exotic properties, which together with the amazing ability of carbon to chemically bond to in many different ways, has resulted in graphene being one of the most studied of these materials.

In this thesis we deal with engineering of the electronic properties of graphene, where we have special interest in the formation of band gaps, which are essential for the use of graphene as field effect transistors, and the valleytronic applications of graphene. Valleytronics is a field similar to electronics where the valley, or pseudospin, degree of freedom is the carrier of information instead the electric charge.

Both gap opening and valley specific behaviour is seen when breaking the inversion symmetry of the graphene unit cell. By introducing sublattice dependent potentials in graphene based devices we investigate the interactions between geometry and different potential distributions. Using a tight binding description, we investigate boundaries between domains where the sublattice potentials are swapped in both graphene sheets and in graphene nanoribbons and see the formation of interface states that are potentially valley polarised.

These states appear for energies where the bulk of the material has no states. This effects are stable under disorder and appear even in the case of low concentrations of dopants with sublattice distributions similar to what is observed in experiments. We also show the importance of interactions with edge geometry when considering these sublattice-asymmetric potentials.

We consider scattering of electronic waves off circular localised sublattice-asymmetric potentials using the Dirac approximation and show strong valley dependence when pure mass dots are considered. The valley dependence is highly energy dependent and could be tuned using a back gate. We also use an atomistic tight binding model to confirm these results.

This is done in a dual probe setup with one probe far to the left of the mass dot simulating an incoming plane wave and the second probe placed behind the dot to pick up the scattered current. This atomistic calculation takes advantage of the Green’s functions patching methods. As the Green’s functions patching methods are etremely useful for calculations we also make an effort to make method accesible for materials other than graphene, by describing and testing an alternate implementation of the method, which takes advantage of the effciency of fast Fourier transforms.

This will be useful for research that consider devices with large separations and theoretical multi probe investigations.