A study of the transport properties of a substance requires the determination of a set of transport coefficients by experiment. From these coefficients, the elements of the electrical conductivity tensor, thermoelectric tensor, et cetera can be determined. In this experiment, measurements and analyses of galvanomagnetic effects in a single crystal of arsenic were performed. The measurements were made at liquid-helium temperatures in magnetic fields ranging to 25 kilogauss. The gross isothermal, electrical conductivities have been analyzed to determine various parameters characterizing the energy bands in arsenic.

Quasiparticle interference (QPI) is a powerful technique within Scanning Tunneling Microscopy (STM) that is used to probe the electronic bandstructure of materials. This thesis presents two examples using QPI to measure the bandstructure in materials with exotic electronic states that can be tuned via outside parameters (temperature and strain). In Part I of the thesis, we discuss the temperature dependence of Fermi Arcs in 1T’-MoTe2, and then in Part II, the strain dependent nematic state in NaFeAs. The recent discovery of Weyl semimetals has introduced a new family of materials with topologically protected electronic properties and potential applications due to their anomalous transport effects. Even more useful is a Weyl semimetal that can be turned “on” and “off,” switching between a topological and trivial state. One possible material is MoTe2, which undergoes a phase transition at 240K. This thesis consists of experiments using Scanning Tunneling Microscopy (STM) and Spectroscopy (STS) at different temperatures to visualize changes in the electronic bandstructure of MoTe2 across the topological phase transition. We show that a signature of topologically protected Fermi Arcs is present at low temperatures but disappears at room temperature, in the trivial phase. We include an in-depth discussion of how to account for thermal effects when comparing these two types of measurements. In Part II, we discuss strain induced nematicity in NaFeAs, an iron pnictide. Nematic fluctuations and spin correlations play an important role in the phase diagram of the iron pnictides, a family of unconventional superconductors. Illuminating the mechanism behind this symmetry breaking is key to understanding the superconducting state. Previous work has shown that nematicity in the iron pnictides responds strongly to applied strain [1, 2]. In this thesis, I present results from a new experimental technique, elasto-scanning tunneling microscopy (E-STM), which combines in situ strain and atomic resolution STM/STS. For the first time, we are able to observe the effects of strain on nematicity at the local level. We perform E-STM measurements in both the spin density wave phase and the tetragonal phase of NaFeAs and measure a distinct response in each. We successfully use strain to manipulate domain boundaries in the spin density wave state and we find the intensity of nematic fluctuations is coupled to strain in NaFeAs in the tetragonal phase.

In this dissertation I present advances in the studies of artificial lattices with honeycomb topology, called artificial graphene (AG), in nano-patterned GaAs quantum wells (QWs). AG lattices with very small lattice constants as low as 40 nm are achieved for the first time in GaAs. The high quality AG lattices are created by optimized electron-beam (E-beam) lithography followed by inductively coupled plasma reactive-ion etching (ICP-RIE) process. E-beam lithography is used to define a honeycomb lattice etch mask on the surface of the GaAs QW sample and the optimized anisotropic ICP-RIE process is developed to transfer the pattern into the sample and create the AG lattices. Such high-resolution AG lattices with small lattice constants are essential to form AG miniband structures and create well-developed Dirac cones. Characterization of electron states in the nanofabricated artificial lattices is by optical experiments. Optical emission (photoluminescence) yields a determination of the Fermi energy of the electrons. A significant reduction of the Fermi energy is due to the nano-patterning process. Resonant inelastic light scattering (RILS) spectra reveal novel transitions related to the electron band structures of the AG lattices. These transitions exhibit a remarkable agreement with the predicted joint density of states (JDOS) based on the band structure calculation for the honeycomb topology. I calculate the electron band structures of AG lattices in nano-patterned GaAs QWs using a periodic muffin-tin potential model. The evaluations predict linear energy-momentum dispersion and Dirac cones, where the massless Dirac fermions (MDFs) appear, occur in the band structures. Requirements of the parameters of the AG potential to achieve isolated and well-developed Dirac cones are discussed. Density of states (DOS) and JDOS from AG band structures are calculated, which provide a basis to interpret quantitatively observed transitions of electrons involving AG bands. RILS of intersubband transitions reveal intriguing satellite peaks that are not present in the as-grown QWs. These additional peaks are interpreted as combined intersubband transitions with simultaneous change of QW subband and AG band index. The calculated JDOS for the electron transitions within the AG lattice model provide a remarkably accurate description of the combined intersubband excitations. Novel low-lying excitation peaks in RILS spectra, interpreted as direct transitions between AG bands without change in QW subband, provide a more direct insight on the AG band structures. We discovered that RILS transitions around the Dirac cones are resonantly enhanced by varying the incident photon energies. The spectral lineshape of these transitions provides insights into the formation of Dirac cones that are characteristic of the honeycomb symmetry of the AG lattices. The results confirm the formation of AG miniband structures and well-developed Dirac cones. The realization of AG lattices in a nanofabricated high mobility semiconductor offers the advantage of tunability through methods suitable for device scalability and integration. The last part of this thesis describes the growth of nanocrystalline single layer and bilayer graphene on sapphire substrates by molecular beam epitaxy (MBE) with a solid carbon source. Raman spectroscopy reveals that fabrication of single layer, bilayer or multilayer graphene crucially depends on MBE growth conditions. Etch pits revealed by atomic force microscopy indicate a removal mechanism of carbon by reduction of sapphire. Tuning the interplay between carbon deposition and its removal, by varying the incident carbon flux and substrate temperature, should enable the growth of high quality graphene layers on large area sapphire substrates.

The (001) surface of silicon has been the topic of our study in this thesis. The clean surface, an-adatom or submonolayer adsorption on the surface, the monolayer adsorption and its stability conditions as well as growth simulation on the surface were investigated using the state of the art techniques. We have used ab initio density functional calculations based on norm-conserving pseudopotentials to investigate the Mg adsorption on the Si(001) surface for 1/4, 1/2 and 1 monolayer (ML) coverages. For both 1/4 and 1/2 ML coverages it has been found that the most favorable site for the Mg adsorption is the cave site between two dimer rows consistent with recent experiments. For the 1 ML coverage (2 Mg atoms per 2X1 unit cell) we have found that the most preferable configuration is when both Mg atoms on 2X1 reconstruction occupy the two shallow sites. We have found that the minimum energy configurations for 1/4 ML coverage is a 2X2 reconstruction while for the 1/2 and 1 ML coverages they are 2X1. Same method was also used to investigate the surface stress and energetics of the clean-, Sb-adsorbed-, and Sb-interdiffused-Si(001) surface. It is found that interdiffusion of Sb into deeper layers of Si(001) leads to a more isotropic surface stress but corresponds to a higher total energy configuration. As a result of competition between stress relief and energy gain, the surface with all the Sb atoms adsorbed on top of Si(001) surface layer is predicted to have a less ordered geometry and roughness in z-direction. We have repeated the similar calculations on the Ge(001) surface for comparison. Finally using empirical molecular dynamics method, we have investigated the crystalline growth of silicon on Si(001) as a function of substrate temperature and incident particle energy. Our results show that the increase of substrate temperature enhances the crystallinity in the film grown on the Si(001) surface, on the other hand, the crystalline growth can be enhanced at low temperature by using higher incidence energy.