Electronic Transport in Graphene Nanoribbons and Topological Insulators

Graphene is an atomically thin sheet of carbon atoms arranged in a honeycomb lattice. Low-energy electronic excitations in graphene behave like massless Dirac fermions, and are expected to exhibit exotic phenomena such as relativistic Klein tunneling.

While the band structure of graphene sheets is gapless, experiments have observed gap-like behavior in graphene nanoribbons, strips of graphene tens of nanometers wide. In one part of this thesis, I will present annealing experiments and electronic transport measurements on nanoribbons of varying lengths and a standardized 30 nm width. The data support a model in which quantum dots form in series along the ribbon due to charged impurities, giving rise to the observed gap-like behavior.

Recent theoretical investigations of the effect of spin-orbit coupling in graphene have led to the discovery of a class of materials known as topological insulators. A topological insulator is a three-dimensional material which has a band gap for charge carriers in the bulk, but has gapless surface states protected from disorder by time-reversal symmetry. A number of novel physical effects are expected in these materials, such as the formation of Majorana fermions in a topological insulator via the superconducting proximity effect.

In the second part of this thesis, I will describe an ongoing experiment whose first goals are to produce thin films of bismuth selenide, a material predicted to be a topological insulator, and to tune the Fermi level throughout the bulk band gap with an electrostatic gate. Films as thin as 4 nm can be produced, and show a peak in resistance as the Fermi level is moved by a gate, perhaps corresponding to the Fermi level crossing the "Dirac point" of the surface states.