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In this thesis, we contribute to the understanding of electronic and optical properties of 2-dimensional materials, with a strong focus on graphene-based nanostructures \cite{graphene_book}. The thesis is structured into eight chapters, starting with an introduction and ending with a conclusion. In chapter 2, we present the methods used throughout this thesis. We start by introducing the tight-binding model to understand the single-particle properties of graphene, bilayer graphene, and graphene quantum dots. We then introduce configuration interaction, the Hubbard model, the Bethe-Salpeter equation, and Hartree-Fock as tools for tackling the interacting problem and correlated electron systems. We also discuss numerical methods, including techniques for addressing the numerical complications that arise when working with the many-body problem such as the calculation of Coulomb matrix elements. In chapter 3, we present a new approach to the energy spectra of $p_z$ electrons in small hexagonal graphene quantum dots. This approach is analytical, and allows us to predict the dependence of the energy gap on size and edge type. In chapter 4, we describe a proposal of a quantum simulator of an extended bipartite highly tunable Hubbard model with broken sublattice symmetry inspired by graphene. We predict the electronic and magnetic properties of a small simulator. The proposed simulator, allows us to study the ground state of the Hubbard Hamiltonian for a broad range of regimes accessible due to the high tunability of the simulator. In chapter 5, we study the electronic properties of quasi 2-dimensional quantum dots made of topological insulators using HgTe. We show that in a square HgTe quantum dot one set of material parameters defines the topologically nontrivial case, in which topologically protected edge states are found, and another set of parameters defines a topologically trivial regime corresponding to a trivial insulator without edge states. In chapter 6, we examine excitons in AB-stacked gated bilayer graphene (BLG) quantum dots (QDs). We confine both electrons and holes using gates and demonstrate that excitons can exist in the BLG QD. We predict absorption to occur in the terahertz regime and find that low-energy excitons are dark. In chapter 7, we determine the many-body states of massive Dirac Fermions confined in a bilayer graphene lateral gated quantum dot. Tuning the strength of Coulomb interactions versus the single-particle level spacing we predict the existence of spontaneously spin and valley symmetry-broken states of interacting massive Dirac Fermions.

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2D materials like graphene and MoS_2 are atomically thin, extremely strong and flexible, making them attractive for integration into strain engineered devices. Strain on these materials can change physical properties, as well as induce exotic physics, not typically seen in solid-state systems. Here, we probe the novel physics arising from distorted lattices of 2D materials, strained by nanopillars indentation and microelectromechanical systems (MEMS), using Raman and photoluminescence (PL) spectroscopy. From nanopillars strained multilayer MoS_2, we observe exciton and charge carrier funneling due to strain, inducing dissociation of excitons in to free electron-hole pairs in the indirect material. Using MEMS devices, we were able to dynamically strain monolayer and multilayer graphene. Multilayer graphene under MEMS strain showed signatures of loss in Bernal stacking due to shear of the individual layers, indicating that MEMS can be used to tune the layer commensuration with tensile strain. We further explore simulation of pseudo-magnetic fields (PMFs) generated in monolayer graphene strained by MEMS, using machine learning, to accelerate and optimize the strength and uniformity of the PMF in new graphene geometries. Nanopillars provide non-uniform, centrally biaxial strain to multilayer MoS_2 transferred on top. Raman E^1_2g and PL redshift across the pillar confirms 1-2% strain in the material. We also observe a softening in the A_1g Raman mode and an enhancement in the overall PL with an increase in radiative trions, under strain. The changes in these charge-dependent features indicates funneling of charge carriers and neutral excitons to the apex of the pillar, as strain locally deforms the band structure of the conduction and valence bands. DFT calculations of the band structure in bilayer MoS_2 under biaxial strain shows the conduction band is lowered, further increasing the indirectness of multilayer MoS_2. This should cause the PL intensity to decrease, whereas we observe an increase in MoS_2 PL intensity under strain. We theorize that this is due to a dissociation of excitons into free electron-hole pairs. The increase in charge carrier densities due to strain leads to a renormalization of the local band structure and increased dielectric screening, supporting free electron-hole recombination at the K-point without momentum restrictions. In turn, electron-hole recombination occurs around the K-point inducing a high intensity PL, which opens attractive opportunities for utilization in optoelectronic devices. MEMS chevron actuators can dynamically strain 2D materials, which we demonstrate through uniaxial strain in CVD and exfoliated graphene. We use a novel microstructure assisted transfer technique which can deterministically place materials on non-planar surfaces like MEMS devices. Building on previously reported 1.3% in monolayer MoS2 from our group, we report tunable 0.3% strain in CVD monolayer graphene and 1.2% strain in multilayer exfoliated graphene using MEMS chevron actuators, detected by Raman spectroscopy. The asymmetric-to-symmetric strain evolution of the 2D phonon line shape in multilayer graphene is evidence of changes in interlayer interactions, caused by shearing between layers. This demonstrates that MEMS can be used to tune the commensuration in few layer 2D materials, which is a promising avenue towards Moiré engineering. Using machine learning, we also simulate optimal monolayer graphene geometries for generating strong, uniform pseudo-magnetic fields by MEMS strain. The coupled use of finite-element methods, variational auto-encoder, and auxiliary neural network accelerates the search for PMFs in strained graphene, while optimizing the graphene shape for fabrication through electron-beam lithography. Our experimental and simulated work creates a road-map for rapid advancement in zero-field quantum Hall effect devices using graphene-integrated MEMS actuators.

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Drying and evaporation from nanoscale conduits are two ubiquitous phenomena found in nature. As these two nanoscale liquid-vapor phase change phenomena are significantly “accelerated” compared with the corresponding ones at micro- and macro-scales, various industrial applications, including oil recovery, electronic cooling, membrane desalination, and energy harvesting, have been developed. Despite their important implications, the fundamental mechanisms for these two accelerated phase-change processes have not been completely understood. For drying, it is widely accepted that liquid corner flow and film flow could significantly enhance mass transport in microscale conduits other than the sole contribution by vapor diffusion. However, it is unclear if the same principles apply to smaller scales and if the vapor diffusivity will change at the nanoscale. For evaporation, the evaporation kinetics at the nanoscale interface, rather than liquid/vapor transport toward/from the interface, determine the ultimate transport limit, which can be significantly higher than the classical prediction derived under quasi-equilibrium evaporation conditions. Still, the contributions to such enhanced kinetically limited evaporation remain unclear. This thesis aims to answer these unsolved questions by conducting systematic experimental studies on drying and evaporation from single nanochannels and nanopores. We used state-of-art fabrication to create close-end 2D nanochannels with heights from 29 to 122 nm and measure water drying in such channels using an optical microscope. Combining with the channel confinement study and relative humidity study, we decoupled the individual contributions from vapor and liquid transport to the drying and extracted the water vapor diffusivity in nanochannels. We also developed a hybrid nanochannel-nanopore design to achieve and measure kinetically limited evaporation flux from silicon nitride nanopores and graphene nanopores with pore diameters ranging from 24 to 347 nm. Our results show that the evaporation flux increases with the decreasing diameter for both types of nanopores. Furthermore, graphene nanopores overall exhibit higher evaporation fluxes than silicon nitride nanopores with similar diameters. We attribute the diameter-dependent evaporation flux to the diameter-dependent hydronium ion concentration in silicon nitride nanopores and the edge-facilitated evaporation in graphene nanopores, respectively. We expect this work to advance our understanding of nanoscale fast drying and evaporation and provide design guidance for novel nanoporous membrane evaporators.

Graphene nanoribbons, graphene based optical sensors, and grating based plasmonics are explored experimentally. Graphene nanoribbons exhibit highly insulating states that may allow for graphene based digital applications. We investigate the sensitivity of these states to local charged impurities in ultra high vacuum. We look into the possibility of isolating two-dimensional films of H-BN and BSCCO, and test for any interesting phenomena. We also assess graphene*s applicability for optical sensing by implementing a new style of spectral detector. Utilizing surface plasmon excitations nearby a graphene field-effect transistor we are able to produce a detector with wavelength sensitivity and selectivity in the visible range. Finally, we study another plasmonic phenomenon, and observe the resonant enhancement of diffraction into a symmetry-prohibited order in silver gratings.