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...[ Read more ]

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 MoS₂, we designed a unique configuration of MoS₂ capacitance devices which is quite different from that of graphene, as thin layer MoS₂ capacitance suffers from impedance problems. Our unique configuration of MoS₂ capacitance devices allows us to access the intrinsic characteristics of MoS₂ in a wide excitation frequency (100 Hz-1 MHz) and temperatures (2 K-300 K). By capacitance and transport measurements in both monolayer and multilayer MoS₂ devices, we show direct evidences that the percolation-type metal-insulator-transition (MIT), driven by density inhomogeneity, occurs and results in the metal-to-insulator transition. The valence band of multilayer MoS₂ is accessible through measuring the device capacitance and the band gap width has been simultaneously determined. Charge traps are also detected and mainly locate at the band tails. Moreover, we successfully extracted the dielectric constant of thin MoS₂ displaying clearly thickness-dependent features.