The role of disorder in modifying electronic properties of graphene and molybdenum disulphide

The discovery of graphene in 2004 by simple micromechanical exfoliation technique has opened up a new physical world of two-dimensional (2D) materials. Graphene is a true 2D material comprised of a single layer of carbon atoms in a honeycomb structure. Extraordinary physical phenomena, such as massless Dirac Fermions, half-integer quantum Hall effect, and linear density of states (DOS), are uncovered in graphene. Inspired by the discovery of graphene, other 2D layered materials are successfully revealed, including topological insulators like Bi2Se3 and Bi2Te3 and layered transition-metal dichalcogenides (TMDs) like MoS2, MoSe2, WS2, and WSe2. Among them, MoS2 is one of the most popular 2D materials for its unusual properties, such as superconductivity at large carrier density region, controllable valley polarization and metal-insulator transition (MIT). In this thesis, I mainly study the role of disorder in modifying electronic properties of graphene and MoS2 through capacitance measurements, an indispensable complementary technique to transport measurements. We have investigated the electronic properties of graphene containing charge impurities, Anderson disorder and resonant impurities, which show distinct different characteristics. Some interesting physical phenomena, such as electron-electron (e-e) interactions, fluctuation of local DOS, resonant states, and negative quantum capacitance/compressibility are observed in graphene. Our results prove that capacitance measurements are able to detect impurity states and their related properties in 2D structures, in which strong localization effects or other scattering mechanisms of electrons may involve and thus seriously affect the conventional transport measurement data from the sample. We also accessed MoS2 properties through capacitance measurements. For capacitance measurements of MoS2b