Nanoacoustic Effects in Type-II Superconductors and Decoherence of Two-state Systems
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In this thesis we focus on two areas of research: nanoacoustic effects in superconductors, and decoherence of two-state systems due to radiation of acoustic phonons. In the first part of this thesis we propose two new nanoacoustic effects: induction of voltage by mechanical stress, and nucleation of a superconducting vortex by an acoustic standing wave. Both of these effects take place in type-II superconductors. In the second part we study relaxation processes via acoustic phonons of a particle in a double-well potential and of a flux qubit. Part 1: Mechanical stress causes motion of dislocations in solids. In a type-II superconductor a moving dislocation generates a pattern of current that exerts a force on the surrounding vortex lattice capable of depinning it. We show that the concentration and the speed of dislocations needed to produce depinning currents are within practical range. When external magnetic field and transport current are present, this effect generates voltage across the superconductor. In this manner, a type-II superconductor can serve as an electrical sensor of the mechanical stress. Nucleation of vortices in a superconductor below the first critical field can be assisted by transverse sound in the GHz frequency range. We work out from energy considerations that, in the presence of a sound wave, vortices enter and exit the superconductor at the frequency of the sound. The computed threshold parameters of the sound are shown to be within experimental reach. Part 2: We propose a method of computing phonon-induced relaxation of two-state systems that is based on symmetry arguments. This allows one to express the rates in terms of independently measurable parameters. For translationally and rotationally invariant systems the conservation of linear and angular momenta must be taken into account when formulating the interaction Hamiltonian. For a particle (e.g., electron or proton) in a rigid double-well potential embedded in a solid the rate is proportional to the seventh power of temperature. For a flux qubit the two-phonon relaxation is important only if the size of the qubit is much smaller than the phonon wavelength. Due to symmetry the two-phonon rate of both systems is proportional to the square of the bias. This allows for additional control of the relaxation rate.
Quantum dislocations in solid Helium-4
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In this thesis the following problems on properties of solid 4He are considered: i) the role of long-range interactions in suppression of dislocation roughening at T = 0; ii) the combined effect of 3He impurities and Peierls potential on shear modulus softening; iii) the dislocation superclimb and its connection to the phenomenon of “giant isochoric compressibility” ; iv) non-linear dislocation response to the applied stress and stress-induces dislocation roughening as a I-order phase transition in 1D at finite temperature. First we investigate the effect of long-range interactions on the state of edge dislocation at T = 0. Such interactions are induced by elastic forces of the solid. We found that quantum roughening transition of a dislocation at T = 0 is completely suppressed by arbitrarily small long-range interactions between kinks. A heuristic argument is presented and the result has been verified by numerical Monte-Carlo simulations using Worm Algorithm in J-current model. It was shown that the Peierls potential plays a crucial role in explaining the elastic properties of dislocations, namely shear modulus softening phenomenon. The crossover from T = 0 to finite temperatures leads to intrinsic softening of the shear modulus and is solely controlled by kink typical energy. It was demonstrated that the mechanism, involving only the binding of 3He impurities to the dislocations, requires an unrealistically high concentrations of defects (or impurities) in order to explain the shear modulus phenomenon and therefore an inclusion of Peierls potential in consideration is required. Superclimbing dislocations, that is the edge dislocations with the superfluidity along the core, were investigated. The theoretical prediction that superclimb is responsible for the phenomenon of “giant isochoric compressibility ” was confirmed by Monte-Carlo simulations. It was demonstrated that the isochoric compressibility is suppressed at low temperatures. The dependence of compressibility on the dislocation length was shown to be strongly dependent on long-range interaction. Non-linear behavior at high stresses was considered. The dislocation was observed to exhibit two types of behavior depending on the dislocation size: reversible and hysteretic. In the reversible regime responses of superclimbing dislocations exhibit sharp resonant peaks. We attribute this feature to the resonant creation of jog-antijog pairs. The peak in the compressibility results in the dip in the speed of sound which we believe was observed in “ UMASS-sandwich” mass-transport experiments. The hysteresis revealed an unusually strong sensitivity to the dislocation size signifying that the stress-induced roughening is a I-order phase transition in 1D at finite T.
COMPUTATIONAL INSIGHTS INTO THE OXYGEN EVOLVING COMPLEX OF PHOTOSYSTEM ΙΙ
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The Oxygen Evolving Complex (OEC) of Photosystem II (PSII) is a unique Mn4O5Ca2+ cluster that catalyzes the photoactivated water splitting reaction. The OEC is a model system for bio-inspired artificial systems to use solar energy to pull electrons from water to produce fuel. The OEC goes through a cycle of 5 S states storing 4 holes, via electron transfer to P680+, the primary electron donor in PSII to generate a high valence S4 state that oxidizes water. The key questions are what controls the order of oxidation and deprotonation of the OEC complex and how does the PSII protein modulate the cluster behavior. Here, we present a classical electrostatics Monte Carlo (MC) technique, with input from density functional theory (DFT) and molecular dynamics (MD) to study the thermodynamics of the S0 to S3 states in a cluster embedded in the whole PSII. The model is tested against model complexes and yields a very good agreement with the experiment. In the simulation, the electrochemical potential (Eh) is varied to oxidize the OEC. The MC sampling allows the Âµ-oxo-bridges, terminal waters and amino acid residues to change their protonation states and/or their rotamer position to respond to the Mn oxidation. In addition, chloride is allowed to move during the cycle. The order of Mn oxidation found here is Mn2, Mn3, Mn4 and finally Mn1 as the system goes from the S0 to S3 states. In the S-1 state O1 and O4 are protonated as are the terminal waters on Mn4 and the Ca2+. O4 and O1 are deprotonated when S0 and S1 are formed respectively. The formation of S2 includes proton transfer from W2 to the nearby D61, reducing the release of protons to the media, consistent with experimental measurements. Protons are also lost from H337 and E329. The proton-release pattern is compared fixing the protonation states for H337, D61, terminal waters and with chloride-depleted PSII. The calculated midpoint potential of each Mn and their dependence on pH is discussed.
Electrodynamics of Nearly Ferroelectric Superconductors in the local London and non-local Pippard limits
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In this work, electrodynamics of a Nearly Ferroelectric Superconduct- ing (NFE-SC) material in local London limit and nonlocal Pippard limit is reported. NFE-SC materials exhibit superconductivity and are in a nearly- ferroelectric state. One example of such materials is 'n' or 'p' doped $SrTiO_3$ . The structure of a single vortex in an NFE-SC thin film is explored. Taking $n-SrTiO_3$ as our sample of choice, the frequency dependent magnetic field and current within the sample are calculated. The expulsion of the vortex from the sample at resonances is observed. The interaction between two vortices due to the presence of high background dielectric is explored. The effect of finite thickness on the vortex structure is explored for an NFE-SC film. With increase in film thickness, the resonances become sharper and as a result the system undergoes oscillatory transition between ferroelectric, superconducting and Meissner-like states. Nonlocal effects in the NFE-SC thin film are explored in the Pippard limit. Specular Reflection and Random scattering are studied. Analytical as well as numerical methods are used to investigate the nature of the material and solve for the current and magnetic field within the sample. The current is found to be non-zero within the sample. The material properties can be manipulated to enhance or expel the current from within the sample with the change in frequency. The material shows complex transitions between Type-I, Type-II superconducting as well as Dielectric states. Numerical codes developed for the solution of the integro-differential equations are given.
Solid State Nuclear Magnetic Resonance Investigations of Advanced Energy Materials
Year of Dissertation:
In order to better understand the physical electrochemical changes that take place in lithium ion batteries and asymmetric hybrid supercapacitors solid state nuclear magnetic resonance (NMR) spectroscopy has been useful to probe and identify changes on the atomic and molecular level. NMR is used to characterize the local environment and investigate the dynamical properties of materials used in electrochemical storage devices (ESD). NMR investigations was used to better understand the chemical composition of the solid electrolyte interphase which form on the negative and positive electrodes of lithium batteries as well as identify the breakdown products that occur in the operation of the asymmetric hybrid supercapacitors. The use of nano-structured particles in the development of new materials causes changes in the electrical, structural and other material properties. NMR was used to investigate the affects of fluorinated and non fluorinated single wall nanotubes (SWNT). In this thesis three experiments were performed using solid state NMR samples to better characterize them. The electrochemical reactions of a lithium ion battery determine its operational profile. Numerous means have been employed to enhance battery cycle life and operating temperature range. One primary means is the choice and makeup of the electrolyte. This study focuses on the characteristics of the solid electrolyte interphase (SEI) that is formed on the electrodes surface during the charge discharge cycle. The electrolyte in this study was altered with several additives in order to determine the influence of the additives on SEI formation as well as the intercalation and de-intercalation of lithium ions in the electrodes. 7Li NMR studies where used to characterize the SEI and its composition. Solid state NMR studies of the carbon enriched acetonitrile electrolyte in a nonaqueous asymmetric hybrid supercapacitor were performed. Magic angle spinning (MAS) coupled with cross polarization NMR techniques were used to determine what effects 200 ppm of intentionally added water would have on the decomposition of the acetonitrile. The resultant NMR spectra yielded several prominent peaks which were assigned to acetamide, glycolonitrile, formaldehyde and other lithium carbon derivatives. The aforementioned decomposition products are a believed to be a result of the acetonitrile being hydrolyzed as well as its interaction with the lithium salt. The decomposition products are deposited on electrode surface leading to operation changes in the life of the supercapacitors. The information gained from the NMR studies may be beneficial understanding the supercapacitor operation and aid in future design. Carbon nanotubes are used to enhance structural stability and performance. In this experiment NMR is used to determine if the addition of nanotubes to two types of polymer matrix changes the structural stiffness and motional dynamics. The polymers studied by direct 1H NMR observations are Polybutadiene (PB) and Polyisobutylene (PIB). PB and PIB with single walled carbon nanotubes (SWNT) as well as functionalized with fluorine (F) produce significantly stronger composites as compared to composites without SWNT.
Entropy of Jammed Granular Matter
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Granular matter can be considered a non-equilibrium system, such that equilibrium statistics is insufficient to describe the dynamics. A phase transition occurs when granular materials are compressed such that a nonzero stress develops in response to a strain deformation. This transition, referred to as the jamming transition, occurs at a critical volume fraction, depending on friction and preparation protocol. Analysis of the jamming transition produces a phase diagram of jammed granular matter for identical spheres, characterized by the critical volume fraction, and the average coordination number. The boundaries of the phase diagram are related to well-defined upper and lower limits in the density of disordered packings; random close packing (RCP) and random loose packing (RLP). Frictional systems, such as granular matter, exhibit an inherent path dependency resulting in the loss of energy conservation, an important facet of equilibrium statistics. It has been suggested Edwards that the volume-force (V-F) ensemble, wherein volume replaces energy as the conservative quantity, may provide a sufficient framework to create a statistical ensemble for jammed granular matter. Treating a jammed system via the V-F ensemble introduces an analogue to temperature in equilibrium systems. This analogue, "compactivity", measures how compact a system could be and governs fluctuation in the volume statistics. Randomness in statistical systems is typically characterized by entropy, the equation of state derived from the number of microstates available to the system. In equilibrium statistical mechanics, entropy provides the link between these microstates and the macroscopic thermodynamic properties of the system. Therefore, calculating the entropy within the V-F ensemble can relate the available microscopic volume for each grain to the macroscopic system properties. The entropy is shown to be minimal at RCP and maximal at the minimum RLP limit, via several methods utilizing simulations and theoretical models. Within this framework RCP is achieved in the limit of minimal compactivity and RLP is achieved in the limit of maximal compactivity. The boundaries of a phase diagram for jammed matter could thereby be defined by the limits of zero and infinite compactivities, characterizing the RCP and RLP limits of granular matter.
Horava Gravity: Symmetries and Generalized Particle Dynamics
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In the search for a theory of Quantum Gravity a new proposal was recently made by P. Horava. The main feature of this new proposed theory is that it is power-counting renormalizable by construction, and could prove to be truly renormalizable, although more work is needed in this direction. The renormalizability of the theory is a central issue. Indeed, General Relativity does not have this property, implying that to construct its quantum version we need to "complete" the theory in the UV. Horava suggested a possible way to provide a UV completion of GR by giving up full spacetime reparametrization symmetry, which is one of the fundamental assumptions of GR, and adding appropriate higher order terms in the action. In this Thesis we review Horava's theory and analyze some of the issues related to the breaking of the spacetime structure. Specifically, we derive the general static spherically symmetric solutions for Horava's theory with a nonvanishing radial "shift" field gtr. Such "hedgehog" configurations are not considered in GR, since gtr can be mapped to zero with an appropriate reparametrization, but they are physically distinct solutions in Horava gravity where the reparametrization is not allowed by the reduced symmetry. These new solutions exhibit specific properties from the particle dynamics point of view and possess an extra gauge symmetry. We also study the deformed kinematics of point particles allowed by the reduced reparametrization symmetry. The main result is that particles can have generalized dispersion relations that include higher even powers of the momentum. We analyze the implications of this and provide some examples that may be converted into possible experimental tests for the deviations of this new theory of gravity from standard GR.
SYNTHESIS AND CHARACTERIZATION OF POLYCRYSTALLINE SEMICONDUCTOR CsSnI3 THIN-FILMS
Year of Dissertation:
This thesis deals with a virtually unexplored semiconductor material CsSnI3 from material synthesis, structural, optical, and electrical characterization to the fabrication and validation of CsSnI3 thin-film solar cells. We started with synthesizing CsSnI3 thin films based on CsI and SnCl2 (or SnI2) by using an apparatus which consists of e-beam and thermal evaporators. The quality of polycrystalline CsSnI3 thin-films were studied by scanning electron microscopy (SEM), transmission electron microscopy (TEM), and X-ray diffraction (XRD). Experimental data on XRD and electron diffraction patterns taking from the synthesized thin-films match very well to the theoretically calculated ones based the first principles calculations, confirming that the synthesized CsSnI3 thin-films have an orthorhombic crystal structure. With the well-defined crystal structure, we theoretically studied the electronic band structure of CsSnI3. Extensive optical characterizations of CsSnI3 thin-films were then carried out revealing many extraordinary properties such as 1) direct band gap energy of 1.32 eV at 300 K with its abnormal temperature dependence, 2) extremely high photoluminescence quantum yield, 3) large exciton binding energy, and 4) strong two-phonon assisted excitonic absorption near band edge. These properties are interpreted in terms of the unique electronic and structural properties of CsSnI3. The value of 1.3 eV for the energy band gap of CsSnI3 suggests a unique application of CsSnI3 thin-films on solar cells. This is because this value is right in the small range of the optimal band gaps for the Shockley-Queisser maximum efficiency limit of a single-junction solar cell. A prototype Schottky solar cell was designed, fabricated, and validated. The measured power conversion efficiency (PCE) is 0.9 % which is presently limited by the series and shunt resistance. The improvement strategy on PCE is given at the end of my thesis. In order to make the CsSnI3 thin-film solar cells cost effective, various low cost materials synthesis methods for CsSnI3 are also described in this thesis. CsSnI3 thin-films can be now inexpensively deposited on to glass or other low-cost substrates. I believe that the CsSnI3 based materials are ideally suited for many applications such as lasers, light-emitting diodes, integrated photonic devices such as infrared electro-optic modulator, solar cells, and even more specialized applications such as spectral solar concentrators.
Novel materials and techniques for renewable energy and biosensing applications
Year of Dissertation:
Ultrasmall (1 nm and 2.8 nm) colloidal silicon nanoparticles behave as electrocatalysts for the electrooxidation of the renewable energy sources such as ethanol, methanol and glucose. Particle-immobilized electrodes show an onset of electrocatalysis occurring at potentials between -0.4 V and 0.05 V vs. Ag/AgCl at neutral pH. Both the onset potential and the strength of electrocatalysis are dependent on particle size. Tafel measurements show that electrooxidation of the fuels is a first order reaction with the transfer of one electron. The electrocatalytic activity of the particles to the fuels undergoes at least a 50-fold increase under alkaline condition compared to under acidic condition. A significant increase in the electrocatalytic current is obtained when the electrocatalysis is performed in darkness. Prototype single-compartment and double-compartment hybrid fuel cells have been constructed and tested, using the particles as the anode electrocatalyst, in order to demonstrate the potential of the particles in fuel cell applications. Voltage-controlled amplification of the output current of an enzymatic transistor has been demonstrated. By applying external voltage between the gating and the working electrode on which the enzyme glucose oxidase was immobilized, the biocatalytic output current was increased significantly, allowing the detection limit of glucose to be lowered from the milli-molar to the zepto-molar level. The current amplification was reversibly controlled by the applied voltage. Applying this technique to the ethanol-alcohol dehydrogenase system showed similar results. The enzyme's bio-specificity was preserved in the presence of the field. The detector, with its output current controlled by the voltage applied at a third electrode, behaves as a field-effect transistor, whose current-generating mechanism is the conversion of analytes to products using an enzyme as catalyst. In addition, voltage-controlled reaction kinetics of biological catalysis is achieved using the microperoxidase-11 and hydrogen peroxide system. The interfacial electron transfer of the system was manipulated by applying the voltage to the electrode. The manipulated electron transfer causes kinetic parameters of the catalysis to acquire nonlinear dependences on the voltage. The nonlinearity indicates the feasibility of effectively controlling the efficiency of a bio-catalytic reaction or a conversion process using the voltage
Generalization of the three-term recurrence formula and its applications
Year of Dissertation:
In an earlier paper we showed development of a bilocal baryon-meson field from two quark-antiquark fields. In the local approximation the hadron field was shown to exhibit supersymmetry which was then extended to hadronic mother trajectories and to inclusion of multiquark states. The Hamiltonian in the case of vanishing quark masses was shown to have a very good agreement with experiments. The theory for vanishing mass was solved using confluent hypergeometric functions. In order to solve the spin-free Hamiltonian with light quark masses we are led to develop a totally new kind of special function theory in mathematics that generalize all existing theories of confluent hypergeometric types. We call it the `Grand Confluent Hypergeometric Function.' Our new solution produces previously unknown extra "hidden" quantum numbers relevant for description of supersymmetry and for generating new mass formulas. Furthermore, we show for the first time how to solve mathematical equations having three term recursion relations and go on producing the exact solutions of some of the well-known special function theories that include Mathieu, Heun, Lame and the Grand Confluent Hypergeometric Function. We hope these new functions and their solutions will produce remarkable new range of applications not only in supersymmetric field theories as is shown here, but in the areas of all different classes of mathematical physics, applied mathematics and in engineering applications.