The isolation of single layer graphene in 2004 by Geim and Novoselov introduced a method that researchers could extend to other van der Waals materials. Interesting and new properties arise when we reduce a crystal to two dimensions where they are often different from their bulk counterpart. Due to the van der Waals bonding between layers, these single sheets of crystal can be combined and stacked with diferent sheets to create novel materials. With the goal to study the interesting physics associated to these stacks, the focus of this work is on the fabrication and characterization of van der Waals heterostructures. In this work, we first present a brief history of 2D materials, the fabrication of heterostructures, and the various tools used to characterize these materials. We then give a description of the custom-built instrument that was used to assemble various 2D heterostructures followed by the findings associated with the optimization of the cleanliness of the stack's interface and surface. Finally, we discuss the results related to the twisting of adjacent layers of stacked MoS2 and its relation to the interlayer coupling between said layers.

The ability to isolate single atomic layers of van der Waals materials has led to renewed interest in the electronic and optical properties of these materials as they can be fundamentally different at the monolayer limit. Moreover, these 2D crystals can be assembled together layer by layer, with controllable sequence and orientation, to form artificial materials that exhibit new features that are not found in monolayers nor bulk. Twisted bilayer graphene is one such prototype system formed by two monolayer graphene layers placed on top of each other with a twist angle between their lattices, whose electronic band structure depends on the twist angle. This thesis presents the efforts to explore the electronic and optical properties of twisted bilayer graphene by Raman spectroscopy and scanning tunneling microscopy measurements. We first synthesize twisted bilayer graphene with various twist angles via chemical vapor deposition. Using a combination of scanning tunneling microscopy and Raman spectroscopy, the twist angles are determined. The strength of the Raman G peak is sensitive to the electronic band structure of twisted bilayer graphene and therefore we use this peak to monitor changes upon doping. Our results demonstrate the ability to modify the electronic and optical properties of twisted bilayer graphene with doping. We also fabricate twisted bilayer graphene by controllable stacking of two graphene monolayers with a dry transfer technique. For twist angles smaller than one degree, many body interactions play an important role. It requires eight electrons per moire unit cell to fill up each band instead of four electrons in the case of a larger twist angle. For twist angles smaller than 0.4 degree, a network of domain walls separating AB and BA stacking regions forms, which are predicted to host topologically protected helical states. Using scanning tunneling microscopy and spectroscopy, these states are confirmed to appear on the domain walls when inversion symmetry is broken with an external electric field. We observe a double-line profile of these states on the domain walls, only occurring when the AB and BA regions are gaped. These states give rise to channels that could transport charge in a dissipationless manner making twisted bilayer graphene a promising platform to realize controllable topological networks for future applications.

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Perovskite oxides have provided a wide variety of exotic functionalities based on their unique physical and chemical properties. By combining different perovskite oxides, interesting physical phenomena have been observed at the interfaces of perovskite heterostructures. The most interesting among these phenomena is the formation of two dimensional electron gas at the interface of two perovskite materials SrTiO3 and LaAlO3 which led to a number of fascinating physical properties such as metal-insulator transition, super-conductivity, large negative magnetoresistance and so on. This has raised the interest in exploiting the interface of various hybrids structures built on the perovskite oxide backbone. On the other hand, the two dimensional (2D) van der Waals materials such as graphene, MoS2, boron nitride etc. represent a new paradigm in the 2D electron-ics. The functionalities of these individual materials have been combined to obtain new enriched functionalities by stacking different materials together forming van der Waals heterostructures. In this work, we present a detailed study of the interface in hybrid structures made of vander Waals materials (graphene and MoS2) and their hybrids with a perovskite material namely, SrTiO3 which is known as the building block of complex oxide heterostructures. In graphene-MoS2 vertical heterostructure, we have carried out a detailed set of investigations on the modulation of the Schottky barrier at the graphene-MoS2 interface with varying external electric field. By using different stacking sequences and device structures, we obtained high mobility at large current on-off ratio at room temperature along with a tunable Schottky barrier which can be varied as high as ∼ 0.4 eV by applying electric field. We also explored the interface of graphene and SrTiO3 as well as MoS2 and SrTiO3 by electrical transport and low frequency 1/f noise measurements. We observed a hysteretic feature in the transfer characteristics of dual gated graphene and MoS2 field effect transistors on SrTiO3. The dual gated geometry enabled us to measure the effective capacitance of SrTiO3 interface which showed an enhancement indicating the possible existence of negative capacitance developed by the surface dipoles at the interface of SrTiO3 and the graphene or MoS2 channel. Our 1/f noise study and the analysis of higher order statistics of noise also support the possibility of electric field-driven reorient able surface dipoles at the interface.

<p dir="ltr">This thesis deals with optical cavity-coupled two-dimensional (2D) materials. First, we describe a new theoretical approach to model the properties of cavity-coupled plasmons in 2D conductors. Next, we propose an optical cavity architecture for enhanced light-matter interaction with potential for performance and functionality beyond that of traditional approaches and describe an initial investigation of one example of such a system. Finally, we provide a thorough description of the fabrication techniques used to produce the previously mentioned optical cavities.</p><p dir="ltr">The advent of 2D materials has opened exciting possibilities for controlling light-matter interactions at the nanoscale. The first major contribution of this work is the investigation of coupling between patterned 2D Van der Waals materials and Fabry-Perot cavities, focusing on how system parameters like pattern shape and material properties influence these interactions. Using a quasistatic eigenmode expansion approach, we develop a theoretical framework to predict and manipulate optical behavior in these systems. Our work opens new pathways for engineering light-matter interactions within patterned 2D material platforms, paving the way for the engineering of novel optical phenomena.</p><p dir="ltr">The second major contribution of this work is the development of a versatile platform for light-matter coupling experiments in Van der Waals materials. It is well-known that light-matter interaction can be used to realize unprecedented functionality in the coupled materials. However, few---if any---approaches to date utilize this phenomenon to its fullest extent. We have provided a platform that can be used to realize light-matter coupling efficiencies beyond what is possible in conventional systems, can be easily integrated with 2D materials, and provides new opportunities to engineer the photonic environment of the coupled material. In particular, we focus on silicon dielectric bowtie cavities (DBCs) coupled to few-layer flakes of $\rm WSe_2$. This approach leverages topology-optimized cavity architectures to achieve simultaneous spatial and spectral confinement, yielding Purcell factors exceeding 2500, mode volumes as small as $\sim10^{-3}(\lambda/2n)^3$, and quality factors up to $\sim200$---performance metrics limited only by material losses. The lithographically defined DBCs enable deterministic emission hotspot placement and tunability across a broad wavelength range with minimal performance impact. Photoluminescence imaging and spectroscopy reveal comparable $\rm WSe_2$ exciton emission enhancement to plasmonic structures. This platform surpasses the limitations of conventional cavity architectures by enabling unprecedented coupling efficiencies and unique functionality while maintaining sufficient mechanical robustness for 2D material transfer.</p><p dir="ltr">The final chapter outlines the fabrication process for the cavities described in the previous chapter. The fabrication involves advanced nanolithography techniques to define patterns with high resolution, addressing challenges such as proximity effects and process blur. Techniques such as proximity effect correction (PEC) are used to enhance pattern accuracy, while careful optimization of exposure and development parameters ensures minimal distortion. The process utilizes high-anisotropy reactive ion etching to transfer the patterns onto the substrate, where precise optimization of the etching parameters has been performed to achieve high resolution and selectivity. The final optimized process yields structures with a minimum feature size of approximately 20 nm and minimum radius of curvature of approximately 10 nm, allowing for the repeatable fabrication of complex inverse-designed cavities.</p>