In this thesis we have thermodynamically characterized finite time processes performed on a colloidal particle, kept in contact with thermal reservoir(s). Thermodynamic processes are implemented on the colloidal particle by systematically changing the confining potential in a time dependent way, according to an external driving protocol or by controlling the environmental conditions over a finite duration. First, we study two externally driven systems: one in which the driving is deterministic, and another where the driving is stochastic. These models have appeared in the literature as the building blocks of microscopic machines such as Brownian heat engines and are hence of interest to analyze. In particular, it is of interest to understand the distribution of work done by the colloidal particle as well as the distribution of heat dissipated. These distributions are known in all generality only in a very few cases. In the work we present here, we determine exactly the asymptotic forms of the work distributions (for a finite time duration of the process), which is shown to have non-Gaussian fluctuations. We also find a method to obtain the exact moment generating function of the work distribution, using which we can explicitly calculate aspects of a recently discovered relation for non-equilibrium systems, namely the thermodynamic uncertainty relation. To our knowledge, our model provides the only non-trivial example of a system where the uncertainty relation can be investigated exactly for all times. We have studied the system in various temporal regimes, and have found interesting features such as a time of minimum uncertainty, which may be relevant for the functioning of microscopic machines. Finally, we discuss, an experimentally realized colloidal heat engine model which consists of a single colloidal particle as the working substance. Exact finite time statistics can be obtained for this model using the methods we discuss in the thesis. We present our preliminary results illustrating this.

It is well known that in conventional three dimensional (3D) Hermitian two band models, the intersections between the energy bands are generically given by points. The typical example are Weyl semimetals, where these singular points can be effectively described as Weyl fermions in the low energy regime. By explicitly imposing discrete symmetries or fine-tuning, the intersection can form higher- dimensional nodal structures, e.g. nodal lines. By instead considering dissipative contributions to such a system, the degeneracies will generically take the form of closed 1D curves, consisting of exceptional points, i.e. points where the Hamiltonian becomes defective. By constructing the Hamiltonian in a particular way, the 1D exceptional curves can host non-trivial topology, i.e. they can form links or knots in the Brillouin zone. In stark contrast to line nodes occurring in Hermitian systems, which inevitably rely on discrete symmetries or fine tuning, the exceptional knots are generically stable towards any small perturbation. In further contrast to point singularities and unknotted circles, the topology of knots cannot be characterized by usual integer valued invariants. Instead, the complexity of the knottedness is captured by polynomial type invariants, making the physical classification and interpretation of these system challenging. To this end, the study of knotted nodal band structures naturally brings two different aspects of topology together – mathematical knot theory on the one hand, and the physical theory of topological phases on the other hand. This licentiate thesis focuses on providing the necessary theoretical background to understand the two accompanying publications entitled Knotted non-Hermitian metals, written by Johan Carlström, together with the author of this thesis, Jan Carl Budich and Emil J. Bergholtz, published in Physical Review B on April 24 2019, and Hyperbolic nodal band structures and knot invariants, written by the author of this thesis, together with Lukas Rødland, Gregory Arone, Jan Carl Budich and Emil J. Bergholtz, published in SciPost Physics August 8 2019. An introduction to gapless topological phases in the Hermitian regime, focusing on Weyl semimetals, their classification and surface states, is provided. Then, the light is brought to non-Hermitian operators and the differences from their conventional Hermitian counterpart, such as the two different set of eigenvectors bi-orthogonal to each other, exceptional eigenvalue degeneracies and some of their consequences, are explained. Afterwards, these operators are applied to dissipative physical system, and some of the striking differences from the conventional Hermitian systems are highlighted, the main focus being the possibly non-trivial topology of the 1D exceptional eigenvalue degeneracies. In order to be somewhat self contained, a brief conceptual introduction to the utilized concepts of knot theory is given, and lastly, further research directions and possible experimental realization of the considered systems are discussed.

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In this study, the chemical bonding in hard and elastic amorphous carbon nitride (a-CNx) films is investigated with x-ray photoelectron spectroscopy (XPS) and 15N, 13C, and 1H nuclear magnetic resonance (NMR) spectroscopy. The films were deposited by DC Magnetron sputtering in a pure nitrogen discharge on Si(001) substrates at 300--400??C. Nanoindentation measurements reveal an elastic modulus of ∼50 GPa and a hardness of ∼5 GPa, thus confirming our films are highly elastic but resist plastic deformation.;Our 13C NMR study demonstrates the absence of sp 3-bonded carbon in this material. Collectively, our N(1s) XPS, 13C NMR, and 15N NMR data suggest a film-bonding model that has an aromatic carbon structure with sp2-hybridized nitrogen incorporated in heterocyclic rings. We demonstrate that the nitrogen bonding is predominantly in configurations similar to those in pyridine and pyrrole. In addition, the data indicate that the a-CNx films prepared for this study have low hydrogen content, but are hydrophilic. Specifically, results from 15N and 13C cross polarization (CP) and 1H magic angle spinning (MAS) NMR experiments suggest that nitrogen sites are susceptible to protonation from water absorbed during sample preparation for the NMR experiments. The sensitivity of the surface of a-CNx to water absorption may impact tribological applications for this material.;In accord with our XPS and NMR spectroscopic studies on a-CN x films, we propose a film-structure model consisting of buckled graphitic planes that are cross-linked together by sp2 hybridized carbons. The curvature and cross-linking is attributed to a type of compound defect, which is formed by placing a pentagon next to single-atom vacancy in a graphite layer. Our proposed film structure is called the pentagon-with-vacancy-defect (5VD) model. Using Hartree-Fock calculations, we show that the 5VD, film-structure model is compatible with our XPS, NMR, and nanoindentation measurements and with previous transmission electron microscopy (TEM) and computational work.

This thesis presents ultrafast laser pump-probe differential transmission experiments on epitaxial CrO2 (110). The experiments were conducted at the wavelengths of 600 nm, 800 nm and 1200 nm, corresponding to the transition energies of 2 eV, 1.5 eV and 1 eV respectively. The wavelength dependent results, comparing with linear optical absorption, revealed the electronic structure of the material. The experimental results also showed polarization dependence of the probe beams. This is attributed to the electronic orbital anisotropy.;Temperature dependence was observed in the pump-probe experiments. The ultrafast transmission data show similar temperature dependence as ultrafast MOKE (Magneto-Optical Kerr Effect) data. A critical change of transient transmission was observed at the Curie temperature of 386 K. Spin decay processes are discussed based on these temperature dependent time resolved data.;Ultrafast MOKE experiments are also presented. Oscillations of the time resolved MOKE signal corresponding to the ferromagnetic resonance were observed. The magnetic anisotropies of the CrO2 thin film were studied by analyzing these oscillations. A computer program was developed for data analysis.;A general discussion of the relation between magnetic properties and the electronic properties of the material is delivered.

Carbon nanosheets are a novel two-dimensional nanostructure made up of 2-20 graphene atomic planes oriented with their in-plane axis perpendicular to the growth substrate. Previous efforts in developing nanosheet technology have focused on the characterization of the system and their development as an electron source due to the high atomic enhancement factor (beta) and low turn on field. Further investigation of nanosheets as high surface area electrodes revealed poor wetting by polymeric material and extreme hydrophobic behavior.;Because nanosheet technology has promise as a high surface area electrode material, this thesis research has focused on three areas of interest: the enhancement of nanosheets through chemical modification, the incorporation of the nanosheets into a polymeric composite and the delivery of a proof of concept measurement. We have successfully introduced defects into the graphene lattice of the nanosheet system via an acid treatment. Inspection of these defects by x-ray absorption near-edge spectroscopy (XANES) shows the introduction of two features in the spectra assigned to C=O pi* and C-O sigma* transitions. Thermal desorption spectroscopy (TDS) was used to identify the oxygen containing groups created during the functionalization as carboxylic and hydroxyl functional groups. These groups were identified through the combination of carboxylic, hydroxyl, anhydride and lactone peaks in the CO2, CO and H 2O TDS spectra. Deconvolution of the TDS spectra using 1st and 2nd order Polanyi-Wigner equations enables the calculation of desorption energy values for individual features and for the estimation of the number of atoms desorbing from the surface during a particular event. Identification of the exact nature of the functional groups was attempted through high resolution x-ray photoelectron spectroscopy (XPS) of the C(1s) and O(1s) peaks. Though the pairing of sub-peaks with specific functionalities of the system was not possible due to the complexities of the spectra, the trends observed in the data support the data gathered via the XANES and TDS experiments.;Also, a procedure for the classification of defect density and exact functionality was outlined. Deconvolution of the TDS spectra using 1 st and 2nd order Polanyi-Wigner equations enabled the calculation of desorption energy values for individual features and for the estimation of the number of atoms desorbing from the surface during a particular event. This information along with the changing sub-peak areas from dedicated and calibrated XPS system would allow for not only a more accurate estimation of defect density, but also for the identification of sub-peaks in the C(1s) and O(1s) spectra.;Finally, photoluminescence measurements of poly[2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylene vinylene] (MEH-PPV) and MEH-PPV/nanosheet systems showed a quenching of three orders of magnitude for the MEH-PPV/nanosheet system suggesting that nanosheets are a viable option for excition separation in organic photovoltaics.

This dissertation presents various investigations into the structure-property correlations in highly anisotropic FePt and FePd thin films and nanostructures. These binary alloy thin films may exhibit long-range chemical ordering (e.g. L10), which induces a strong uniaxial magnetic anisotropy whose orientation is dependent on the ordering direction in the thin film. The chemical ordering, and hence the magnetic anisotropy, in these thin films can be controlled and tailored through sputter deposition and ion implantation conditions followed by subsequent processing. Two novel fabrication methods, x-ray rapid thermal annealing (XRTA) and heavy ion implantation, successfully demonstrate the ability to obtain highly anisotropic nanometer-sized L10 ordered regions in thin films. XRTA has the advantage of using high brilliance x-ray undulator radiation to simultaneously induce and probe microstructural changes in real time and is shown to favorably modify the chemical order in partially-ordered FePt thin films without affecting the average ordered grain size. Heavy ion implantation has the advantage of fabricating nonequilibrium nanocomposite thin films, which in the case of Fe+ implanted Pt thin films requires lower activation energies to nucleate and grow the L10 phase thus implying lower processing temperatures. The magnetic anisotropy in these binary alloy thin films is not only tailored through the chemical ordering, but can be further influenced by an adequate choice of the capping layer. Magnetically polarizable capping layers (e.g. Pd) decrease the perpendicular magnetic anisotropy (PMA) of FePd thin films, while non-polarizable capping layers (e.g. MgO) have no effect on the PMA. Different magnetization profiles of the films obtained from x-ray resonant magnetic scattering measurements explain this change observed in the magnetic anisotropy. The magnetic domain structure in these highly anisotropic thin films is also important and influenced by the magnetic anisotropy. An analytical model shows good quantitative agreement with experiment for FePd thin films above a critical thickness, thus showing the direct correlations between chemical order, magnetic anisotropy, and magnetic domain structure in these films.

Field emission and breakdown characteristics of high voltage, large area electrodes determine the performance of many vacuum-based electron sources. A corroborative project with the Thomas Jefferson National Accelerator Facility involves studying the behavior of such electrodes after nitrogen ion implantation. A Plasma Source Ion Implantation (PSII) facility is designed and constructed at William and Mary, and used to treat stainless steel electrodes. PSII is a novel implantation technique developed at the University of Wisconsin-Madison. A workpiece is submerged in a quiescent plasma of the species to be implanted. A series of high, negative voltages (30--100 kV) is applied to the workpiece to accelerate the ions in the plasma, implanting them to depths of several hundred Angstroms. to characterize the response of the modified electrodes to high field gradients, fields as high as 20 MV/m are applied between parallel electrodes in a VG ESCALab MKII surface analysis system. XPS, AES, and SEM are used to characterize the surface of the cathodes. The pre-breakdown current from implanted electrodes is compared to that of thin film coated, polished, electron beam treated, and untreated electrodes. Current models to explain anomalous field emission are reviewed and considered as explanation of observed effects.

The study of the properties of magnetic materials is of primary importance in the development of newtechnologies. In this project, we aim to investigate the symmetries of some of the relevant properties ofa cobalt and platinum alloy that emerge from the symmetry of the crystal structure of the alloy. Morespecifically, our goal is to calculate the magnetocrystalline anisotropy energy (MAE) for various orientations of the magnetization. The MAE is computed through the implementation of density functionaltheory (DFT) via the open-source package OpenMX.The project consists of three main parts: Study on the convergence of the total energy of the systemas a function of some relevant parameters, computation of the energy, the spin magnetic moment andthe orbital magnetic moment as a function of the orientation of the magnetization, and a calculation ofthe magnetocrystalline anisotropy energy of the studied alloy.The studied system is an ordered compound of cobalt and platinum, with a tetragonal crystal structure.The easy axis of magnetization was found to be along the c-axis of the crystal, and defined accordinglytowards the z-axis in cartesian coordinates. The compound exhibits angular symmetry for the energy,the spin and orbital magnetic moments and the MAE, with a minimum energy along the easy axis ofmagnetization and a maximum at spherical angles θ=90◦ and ϕ=45◦. Looking at the plots for the MAE,this maximum can be interpreted as an energy barrier that must be surpassed in order to invert thedirection of the magnetization. Using an expression of the MAE in spherical angles, theoretical valuesfor the anisotropy constants K1, K2 and K3 are determined. / Computational Study of the Magnetocrystalline Anisotropy Energy of Ordered CoPt

This thesis aims to study the nonlinear electrical transport response of monolayer and bilayer graphene systems under the influence of different lattice deformations (strain). Broken inversion and rotation symmetries can generate a second-order transverse current response called the nonlinear Hall effect in the presence of time-reversal symmetry. The nonlinear Hall currents are proportional to the Berry curvature dipole (BCD), a quantity proportional to an intrinsic topological quantity known as the Berry curvature. We investigate homo-strain and hetero-strain in bilayer graphene, in which the two carbon layers are deformed symmetrically and asymmetrically respectively. Our numerical results show that bilayer graphene systems give a larger BCD, up to an order of magnitude using homo-strain and up to two orders of magnitude using heterostrain, when compared to monolayer graphene for the same strain due to larger Berry curvature and density of states. Furthermore, we obtain a large BCD in bilayer graphene under hetero-strain, which breaks both the inversion and three-fold rotational symmetries. Based on an effective k · p analysis, it is necessary to consider higher-order corrections, that are linear in momentum qj and strain uij, in the velocity renormalization of the Dirac fermions to obtain a finite Berry curvature induced by hetero-strain. Larger BCD and the implication of hetero-strain make bilayer graphene a better candidate for practical applications such as detecting terahertz radiation. The result of this thesis motivates the investigation of hetero-strain in twisted bilayer graphene, a hot topic in condensed matter physics. In particular, the impact of strain-induced velocity renormalization is not explored systematically in the literature, which can be a subject of future study.