Graphene and monoatomic boron nitride as members of the new class of two dimensional materials are discussed in this thesis. Since the discovery of graphene in 2004, various aspects of this one atom thick material have been studied with previously unexpected results. Out of many outstanding amazing properties of graphene, its elastic properties are remarkable as graphene can bear strain up to 20% of its actual size without breaking. This is the record value amongst all known materials. In this work experiments were conducted to study the mechanical behaviour of graphene under compression and tension. For this purpose graphene monolayers were prepared on top of polymer (PMMA) substrates. They were then successfully subjected to uniaxial deformation (tension- compression) using a micromechanical technique known as cantilever beam analysis. The mechanical response of graphene was monitored by Raman spectroscopy. A nonlinear behaviour of the graphene G and 2D Raman bands was observed under uniaxial deformation of the graphene monolayers. Furthermore the buckling strength of graphene monolayers embedded in the Polymer was determined. The critical buckling strain as the moment of the final failure of the graphene was found to be dependent on the size and the geometry of the graphene monolayer flakes. Classical Euler analysis show that graphene monolayers embedded in the polymer provide higher values of the critical buckling strain as compared to the suspended graphene monolayers. From these studies we find that the lateral support provided by the polymer substrate enhances the buckling strain more than 6 orders of magnitude as compared to the suspended graphene. This property of bearing stress more than any other material can be utilized in different applications including graphene polymer nanocomposites and strain engineering on graphene based devices. The second part of the thesis focuses on a two dimensional insulator, single layer boron nitride. These novel two dimensional crystals have been successfully isolated and thoroughly characterized. Large area boron nitride layers were prepared by mechanical exfoliation from bulk boron nitride onto an oxidized silicon wafer. For their detection, it is described that how varying the thickness of SiO2 and using optical filters improves the low optical contrast of ultrathin boron nitride layers. Raman spectroscopy studies are presented showing how this technique allows to identify the number of boron nitride layers. The Raman frequency shift and intensity of the characteristic Raman peak of boron nitride layers of different thickness was analyzed for this purpose. Monolayer boron nitride shows an upward shift as compared to the other thicknesses up to bulk boron nitride. The Raman intensity decreases as the number of boron nitride layers decreases. Complementary studies have been carried out using atomic force microscopy. With the achieved results it is now possible to successfully employ ultrathin boron nitride crystals for precise fabrication of artificial heterostrutures such as graphene-boron nitride heterostrutures.

A framework for constructing kinetic monte carlo (KMC) simulations of diffusive events on a lattice was developed. This code was then tested by running simulations of Fe adatom diffusion on graphene and graphene-boron nitride surfaces. The results from these simulations was then used to show that the modeled diffusion adheres to the laws of brownian motion and generates results similar to recent research findings.

In the past few years, led by graphene, a large variety of two dimensional (2D) materials have been discovered to exhibit astonishing properties. By assembling 2D materials with different designs, we are able to construct novel artificial van der Waals (vdW) heterostructures to explore new fundamental physics and potential applications for future technology. This thesis describes several novel vdW heterostructures and their fundamental properties. At the beginning, the basic properties of some 2D materials and assembled vdW heterostructures are introduced, together with the fabrication procedure and transport measurement setups. Then the graphene based capacitors on hBN (hexagonal Boron Nitride) substrate are studied, where quantum capacitance measurements are applied to determine the density of states and many body effects. Meanwhile, quantum capacitance measurement is also used to search for alternative substrates to hBN which allow graphene to exhibit micrometer-scale ballistic transport. We found that graphene placed on top of MoS2 and TaS2 show comparable mobilities up to 60,000cm2/Vs. After that, the graphene/hBN superlattices are studied. With a Hall bar structure based on the superlattices, we find that new Dirac minibands appear away from the main Dirac cone with pronounced peaks in the resistivity and are accompanied by reversal of the Hall effects. With the capacitive structure based on the superlattices, quantum capacitance measurement is used to directly probe the density states in the graphene/hBN superlattices, and we observe a clear replica spectrum, the Hofstadter-butterfly fan diagram, together with the suppression of quantum Hall Ferromagnetism. In the final part, we report on the existence of the valley current in the graphene/hBN superlattice structure. The topological current originating from graphene’s two valleys flows in opposite directions due to the broken inversion symmetry in the graphene/hBN superlattice, meaning an open band gap in graphene.

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Nanomaterials have attracted great interest due to the unique physical properties and great potential in the applications of nanoscale devices. Two dimensional atomic crystals, which are atomic thickness, especially graphene, have triggered the gold rush recently due to the fascinating high mobility at room temperature for future electronics. The crystal structure of nanomaterials will have great influence on their physical properties. Thus, this thesis is focused on developing the methods to control the crystal structure of nanomaterials, namely quantum dots as semiconductor, boron nitride (BN) as insulator, graphene as semimetal, with low cost for their applications in photonics, structural support and electronics. In this thesis, firstly, Mn doped ZnSe quantum dots have been synthesized using colloidal synthesis. The shape control of Mn doped ZnSe quantum dots has been achieved from branched to spherical by switching the injection temperature from kinetics to thermodynamics region. Injection rates have been found to have effect on controlling the crystal phase from zinc blende to wurtzite. The structural-property relationship has been investigated. It is found that the spherical wurtzite Mn doped ZnSe quantum dots have the highest quantum yield comparing with other shape or crystal phase of the dots. Then, the Mn doped ZnSe quantum dots were deposited onto the BN sheets, which were micron-sized and fabricated by chemical exfoliation, for high resolution imaging. It is the first demonstration of utilizing ultrathin carbon free 2D atomic crystal as support for high resolution imaging. Phase contrast images reveal moiré interference patterns between nanocrystals and BN substrate that are used to determine the relative orientation of the nanocrystals with respect to the BN sheets and interference lattice planes using a newly developed equation method. Double diffraction is observed and has been analyzed using a vector method. As only a few microns sized 2D atomic crystal, like BN, can be fabricated by the chemical exfoliation. Chemical vapour deposition (CVD) is as used as an alternative to fabricate large area graphene. The mechanism and growth dynamics of graphene domains have been investigated using Cu catalyzed atmospheric pressure CVD. Rectangular few layer graphene domains were synthesized for the first time. It only grows on the Cu grains with (111) orientation due to the interplay between atomic structure of Cu lattice and graphene domains. Hexagonal graphene domains can form on nearly all non-(111) Cu surfaces. The few layer hexagonal single crystal graphene domains were aligned in their crystallographic orientation over millimetre scale. In order to improve the alignment and reduce the layer of graphene domains, a novel method is invented to perform the CVD reaction above the melting point of copper (1090 ºC) and using molybdenum or tungsten to prevent the balling of the copper from dewetting. By controlling the amount of hydrogen during the growth, individual single crystal domains of monolayer over 200 µm are produced determined by electron diffraction mapping. Raman mapping shows the monolayer nature of graphene grown by this method. This graphene exhibits a linear dispersion relationship and no sign of doping. The large scale alignment of monolayer hexagonal graphene domains with epitaxial relationship on Cu is the key to get wafer-sized single crystal monolayer graphene films. This paves the way for industry scale production of 2D single crystal graphene.