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Rotational anisotropy second harmonic generation measurements conducted with incoming photon energies range of 1.1 - 1.8 eV revealed the presence of strong magnetic dipole (MD) transitions that we assign to the trivalent lanthanide ions. Extracting the spectra of the MD transition susceptibility tensor, we observe an asymmetric resonance at $\sim$ 1.5 eV, consistent with a Fano lineshape. Comparison of our data with a band structure obtained from density function theory revealed the hybridization of an unoccupied band deriving from unassigned orbitals in LaAlSi and CeAlSi, the unoccupied $^1D_2$ state of PrAlSi, and occupied $^4I_{\frac{9}{2}}$ state in NdAlSi. Moreover,polarimetry measurement was conducted at normal incidence in the paramagnetic phase of LnAlSi revealed a novel, nonlinear form of electromagnetically induced chirality (EIC) that derives from resonant MD transitions. This form of nonlinear magnetoelectricity is expressed as $P_i = \chi^{eem}_{ijk}E_jH_k$, which causes the emission of elliptically polarized SHG. \par In a separate study, we used the second and third harmonic nonlinear harmonic generation spectroscopy to study \ce{1T-TiSe2} below its charge density wave phase transition temperature at 200 K. The lack of a second harmonic signal below and above the transition temperature indicated that the low-temperature symmetry-breaking phase is achiral. Further study using rotational anisotropy nonlinear third harmonic generation revealed that \ce{1T-TiSe2} experiences a non-trivial phase transition at $\sim$ 180 K within the charge density phase that comprises two separate domain types that randomly rearrange upon thermal cycling. Taken together, our data support the onset of orbital ordering at 180 K without the emergence of an electronically chiral state.\\\par Finally, we describe THz emission spectroscopy to study the circular photogalvanic effect (CPGE ) and linear photogalvanic effect (LPGE) spectra of the structurally chiral Weyl semimetal PdGa. We reveal that CPGE and LPGE spectra produce signals of opposite signs for the two PdGa enantiomers, as predicted by theory. Measurement of the spectra deriving from the material's bulk reveals a peak in the photogalvanic spectra at 0.68 eV, which is due to optical transitions between the parallel bands near the Weyl nodes dispersing from $\Gamma$ to R and similar transitions between M and R. Surface sensitive measurement are consistent with helicoidally dispersing states of opposite helicity from the two different chirality samples. / Physics

Phase transitions in several quenched random systems are studied. We used the Migdal-Kadanoff renormalization group method and Monte Carlo simulations. The critical behavior of the quenched random systems exhibits a drastic change from that of the corresponding pure systems. We first studied the critical behavior of the directed polymer on the disordered hierarchical lattice. Using a Monte Carlo method, we obtained the fixed distribution of the random energy from which we calculated the critical exponent and the specific heat. We also studied random field Ising model on the hierarchical lattice. It is found that magnetization exponent is nonvanishing though small due to the fact that the fixed distribution of the couplings has a finite weight at zero. We also show this result analytically. Finally, we studied phase transitions in a fractal porous media. Our fractal model can be described as a two parameter Mandelbrot percolation process which generates a solid fractal with pores on all length scales. We study the connectivity of the pores and the solid as well. It is found that there is a critical dimension $D\sb{c}.$ If D $>$ $D\sb{c},$ there is no percolation phase transition, while for D $<$ $D\sb{c},$ there is a percolation transition and the correlation length exponent $\nu$ is D dependent. Furthermore, we studied thermal phase transitions of spin systems with spins placed in the pore space. In the thermodynamic limit, the specific heat is the same as that of the pure system. The renormalized couplings, however, exhibit two fixed distributions with one at the bulk phase transition $T\sb{c0}$ and the other at a temperature $T\sb{c}$ lower than $T\sb{c0}.$ The correlation length exponent at $T\sb{c}$ is considerably larger than that of the bulk phase transition. If the system is finite, our simulation shows that the specific heat has two peaks at $T\sb{c0}$ and $T\sb{c}.$

<p>In this work, we tested the ability of an experimental system, involving the use of micropipettes as force transducers, to measure the coefficients of friction of several systems. Using a magnetic pipette puller, the micropipettes were produced by first heating and stretching the glass. The pipettes are then manipulated into an L-shape. This geometry allows one arm to act as the normal force transducer, and the other to act as the lateral force transducer for the purposes of friction measurements. We then analyzed the variation of the friction force of 15 micrometre polystyrene beads in contact with silicon and polystyrene in a fluid environment at increasing velocities. We also measured the variation in friction coefficient of poly(dimethyl siloxane) coated polystyrene beads in contact with a silicon surface. Our results were then compared to known values where possible, and the variation of the friction coefficient with increasing velocity was fit to a known phenomenological model. From our experiments, we have shown that our experimental technique can provide reproducible friction coefficient measurements, and these coefficients vary with velocity in a known manner. These results confirm the ability of micropipettes to act as both normal and lateral force transducers in friction experiments, and that they have the potential to be used in measuring friction coefficients of more complex materials.</p> / Master of Science (MSc)

<p> Current global energy usage is largely dependent on non-renewable resources such as fossil fuels. Research is expanding into alternative, renewable energy sources such as solar energy. Of specific focus is research into the use of metal chalcoginide semiconductor nanoparticles as a cost-efficient platform for future use in solar applications. These semiconductor nanoparticles have size-dependent electronic band gaps within the solar spectrum and can be deposited into thin films from colloidal solutions. To date, most electronic studies have focused on thin films with disordered morphologies, where the dominant inter-nanoparticle charge transport mechanism is hopping. Highly spatially ordered metal chalcoginide nanoparticle films may have the ability to form extended Bloch states, thereby resulting in more efficient charge transport. This work focuses on fabricating both highly spatially ordered and highly disordered PbSe nanoparticle thin films to compare their electronic properties and elucidate charge transport mechanisms.</p>

<p> This dissertation explores the effects of pressure and light on chalcogenide based materials. In ZnSe, ZnTe, and CdSe the surprising precipitation of the constituent anion under hydrostatic pressure and moderate laser exposure in high quality bulk and MBE film samples is explored in detail. In ZnSe the anomalous broadening in the TO(&Gamma;) phonon region is explored by careful low laser power pressure cycling experiments. The experimental results are supported with density functional theory calculations of the phonon band structure. Finally, the photo-induced crystallization onset of amorphous selenium films is explored as a function of temperature and substrate structure. The morphology of the photocrystallized spots is also explored using Raman mapping, optical microscopy, and atomic force microscopy.</p>

Doctor of Philosophy / Department of Physics / Amit Chakrabarti / We carry out Brownian Dynamics Simulations to study the self-assembly of ligated gold nanoparticles for various ligand chain lengths. First, we develop a phenomenological model for an effective nanoparticle-nanoparticle pair potential by treating the ligands as flexible polymer chains. Besides van der Waals interactions, we incorporate both the free energy of mixing and elastic contributions from compression of the ligands in our effective pair potentials. The separation of the nanoparticles at the potential minimum compares well with experimental results of gold nanoparticle superlattice constants for various ligand lengths. Next, we use the calculated pair potentials as input to Brownian dynamics simulations for studying the formation of nanoparticle assembly in three dimensions. For dodecanethiol ligated nanoparticles in toluene, our model gives a relatively shallower well depth and the clusters formed after a temperature quench are compact in morphology. Simulation results for the kinetics of cluster growth in this case are compared with phase separations in binary mixtures. For decanethiol ligated nanoparticles, the model well depth is found to be deeper, and simulations show hybrid, fractal-like morphology for the clusters. Cluster morphology in this case shows a compact structure at short length scales and a fractal structure at large length scales. Growth kinetics for this deeper potential depth is compared with the diffusion-limited cluster-cluster aggregation (DLCA) model. We also did simulation studies of nanoparticle supercluster (NPSC) nucleation from a temperature quenched system. Induction periods are observed with times that yield a reasonable supercluster interfacial tension via classical nucleation theory (CNT). However, only the largest pre-nucleating clusters are dense and the cluster size can occasionally range greater than the critical size in the pre-nucleation regime until a cluster with low enough energy occurs, then nucleation ensues. Late in the nucleation process the clusters display a crystalline structure that is a random mix of fcc and hcp lattices and indistinguishable from a randomized icosahedra structure. Next, we present results from detailed three-dimensional Brownian dynamics simulations of the self-assembly process in quenched short-range attractive colloids. Clusters obtained in the simulations range from dense faceted crystals to fractal aggregates which show ramified morphology on large length scales but close-packed crystalline morphology on short length scales. For low volume fractions of the colloids, the morphology and crystal structure of a nucleating cluster are studied at various times after the quench. As the volume fraction of the colloids is increased, growth of clusters is controlled by cluster diffusion and cluster-cluster interactions. For shallower quenches and low volume fractions, clusters are compact and the growth-law exponent agrees well with Binder–Stauffer predictions and with recent experimental results. As the volume fraction is increased, clusters do not completely coalesce when they meet each other and the kinetics crosses over to diffusion-limited cluster-cluster aggregation (DLCA) limit. For deeper quenches, clusters are fractals even at low volume fractions and the growth kinetics asymptotically reaches the irreversible DLCA case.

<p> In this thesis, we investigate theoretically a new model of charge regulation of a single charged planar surface immersed in an aqueous electrolyte solution. Assuming that the adsorbed ions are mobile in the charged plane, we formulate a field theory of charge regulation where the numbers of adsorbed ions can be determined consistently by equating the chemical potentials of the adsorbed ions to that of the ions in the bulk. We analyze the mean-field treatment of the model for electrolyte of arbitrary valences, and then beyond, where correlation effects are systematically taken into account in a loop expansion. In particular, we compute exactly various one-loop quantities, including electrostatic potentials, ion distributions, and chemical potentials, not only for symmetric (1; 1) electrolyte but also for asymmetric (2; 1) electrolyte, and make use of these quantities to address charge regulation at the one-loop level. We find that correlation effects give rise to various phase transitions in the adsorption of ions, and present phase diagrams for (1; 1) and (2; 1) electrolytes, whose distinct behaviors suggest that charge regulation, at the one-loop level, is no longer universal but depends crucially on the valency of the ions.</p>

<p> Quantum information science has made significant progress over the last several decades, but the eventual form a quantum computer will take has yet to be determined. Several physical systems have been shown to operate as quantum bits, or qubits, but each faces a central challenge: the qubit must be sufficiently isolated from its environment to maintain quantum coherence while simultaneously having sufficient coupling to the environment to allow quantum mechanical interactions for manipulation and measurement. An approach to achieve these conflicting requirements is to create qubits that are insensitive to small perturbing interactions within their environment by using topological properties of the physical system in which the qubits are formed. This dissertation presents studies on low-dimensional semiconductor heterostructures of InAs, GaSb and AlSb fabricated by molecular beam epitaxy with focus on relevant properties for their utilization in forming a topologically protected (TP) qubit. </p><p> The theoretical basis regarding the semiconductor characteristics suitable for realizing TP qubits stipulates the need for strong spin-orbit coupled semiconductors with high carrier mobility. A comparative study of InAs/AlSb heterostructures wherein structure parameters were systematically varied led to a greater understanding of the limits to mobility in InAs quantum wells. Magnetotransport measurements using a dual-gated device geometry and a comparison of experiment to models of carrier mobility as a function of carrier density were used to identify dominant scattering mechanisms in these heterostructures. </p><p> The development of dual-gated devices and high quality InAs channels with AlSb barriers led to a demonstration of the gate control of spin-orbit coupling in a high mobility InAs/AlSb quantum well in which the gate-tuned electron mobility exceeded 700,000 cm²/V&middot;s. Analysis of low temperature magnetoresistance oscillations indicated the zero field spin-splitting could be tuned via the Rashba effect while keeping the two-dimensional electron gas charge density constant. </p><p> Findings from the work on InAs quantum wells were applied to investigations on InAs/GaSb bilayers, a system predicted to be a two-dimensional topological insulator (TI). The temperature and magnetic field dependence of the resistance in dual-gated InAs/GaSb heterostructures gate-tuned to the predicted TI regime were found consistent with conduction through a disordered two-fluid system. The impact of disorder on the formation of topologically protected edge states and an insulating bulk was considered. Potential fluctuations in the band structure for realistic levels of disorder in state-of-the-art heterostructures were calculated using a gated heterostructure model. Potential fluctuations were estimated to be sufficiently large such that conduction in the predicted TI regime was likely dominated by tunneling between localized electron and hole charge fluctuations, corresponding to a symplectic metallic phase rather than a topological insulator. The implications are that future efforts must address defects and disorder in this system if the TI regime is to be achieved. </p>