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# Physics - Theses, Dissertations, and other Required Graduate Degree Essays

Receive updates for this collection## Chiral symmetry breaking in high-temperature superconductors and birefringent cold atoms, helicity modulus in layered bosons and phase diagram of superconductor-insulator transition

This work is a compilation of several research projects with them main theme being high-temperature superconductivity. We construct the field theory of underdoped cuprates beginning with a well-defined d-wave superconductor and adding the vortex degree of freedom using a singular gauge transformation. The symmetries of the theory both in the presence and absence of a quasi-particle mass are studied. Nodal quasi-particles are known to obey a relativistic Lorentz symmetry while their massless nature represent another symmetry which we will identify as a chiral SU(2) symmetry. It is shown that 2+1 quantum electrodynamics is the effective theory that describes underdoped cuprates in the zero- temperature pseudogap regime. We focus on the mechanism of dynamical mass generation in three dimensional quantum elec- trodynamics and theories with four-fermion interactions. This is a field that has been subject of extensive research in last two decades. However, our momentum-shell renormalization group ap- proach is new to the field and through that we are able to estimate the conditions for the mass generation mechanism and also work out the phase diagram of the theory for charge and inter- action strength. We discuss the applications of momentum-shell renormalization group to other four-fermionic theories in the absence of a gauge field. The justification for this is the fact that in the superconducting regime the system can be described by a massive gauge field theory coupled to relativistic quasi-particles which effectively represent a four-fermionic theory. Inspired by the field theory constructed for underdoped cuprates we discuss the superfluid re- sponse of the underdoped materials using an anisotropic bosonic model and compare it to experiment. The idea is to see how c-axis superfluid density measurements can help one set the parameters in our field theory for underdoped cuprates. The behaviours of the superfluid responses in both out- of-plane and in-plane measurements has been detailed as a function of temperature and density (doping) and it is shown that there is disagreement with the measured c-axis response using the iii conjectured bosonic Hamiltonian.

## Measurement of the neutrino asymmetry in the beta decay of laser-cooled, polarized 37k

The TRINAT collaboration began investigating fundamental symmetries searching for scalar contributions to the predominantly V - A structure of the weak interaction by measuring the /3 - v correlation parameter using the pure Fermi decay of magnetooptically trapped 38mK . This thesis describes the first physics measurement using polarized, laser-cooled 3 7 ~ , and represents the next generation of TRINAT experiments aimed at searching for right-handed currents predicted to restore parity at higher energy scales in some extensions to the Standard Model. Using a detector geometry similar to that of the scalar search, we have learned to implement optical pumping techniques to achieve very high (2 96%) nuclear polarizations of our radioactive atom sample. Furthermore, we have pioneered techniques to measure this observable - independent of the /3 decay observables - in situ on all the nuclei that are decaying. By observing the emitted /3+ and recoiling 37Ar in the back-to-back geometry, we have extracted a measurement of the neutrino asymmetry parameter: B, = -0.755 f 0.020 f 0.013, in agreement with the Standard Model (stat) (syst) prediction of -O.7692(15). This 3% measurement of the B, represents the first /3 decay physics measurement using a polarized, laser-cooled source. This is not yet competitive with other limits on right-handed current parameters; however, we have identified our dominant systematics and have learned how to minimize them so that the next time the experiment is performed, we expect to be able to reduce our uncertainty to the 0.5% level. Additionally, we have outlined how we may make use of a correlation unique to our setup to further enhance our sensitivity. We expect that future experiments will be able to have a significant impact in either finding new physics or helping to constrain the variety of models considered as viable extensions to the Standard Model.

## String theory, dual theories and D-branes

In the context of the Anti-de Sitter / Conformal Field Theory correspondence we consider the Berenstein-Maldacena-Nastase (BMN) sector of the large-N Super Yang-Mills theory and demonstrate explicitly the correspondence of four-impurity operators therein to known states in string theory on the pp-wave background obtained as a Penrose limit of Ads space. In the corresponding gauge theory we calculate matrix elements of the dilatation operator in the BMN operator basis. These matrix elements are found to coincide with those of the light-cone string Hamiltonian, which is computed using the string field theory vertex in the pp-wave background. Our results are in agreement with others' results obtained using gauge-theory three-point functions. We next solve perturbative superstring theory on the Nappi-Witten background, obtaining the bosonic and fermionic spectra, and find that supersymmetry can be preserved in the Penrose limit. Our results indicate that the high-energy sector of little string theory, being holographically dual to the string theory which we solve, retains a supersymmetric spectrum. We perform a semiclassical analysis of strings in the Nappi- Witten metric and find that the relationship between energy and momentum coincides with the known result for a flat background. In the context of Vacuum String Field Theory (VSFT), we put forth some ideas as to how a distinction might be made between 'background7 D-branes, which are encoded explicitly in the formulation of split-string field theory, and 'string-field' D-branes, which correspond to solitonic lump solutions. We use the geometrical surface-state formulation of VSFT to investigate tachyon fluctuations about certain lump solutions, called sliver states, and thereby calculate their tensions. We perform this analysis both with and without a background B-field, and are able to reproduce the standard string-theory results for the ratios of D-brane tensions. We investigate tachyon fluctuations about another state known as the butterfly. As would be expected for a D-brane, the equation of motion derived for the tachyon field corresponds to the requirement that the quadratic term in the string-field action vanish on-shell. We begin a calculation of the tension of the butterfly and conjecture that this too will coincide with the standard D-brane expression.

## Isotope effects on the fundamental band gap of lead sulfide

Lead sulfide (PbS) is one of the oldest known semiconductors, occurring naturally as the mineral galena. One of its interesting properties is a strong increase of the band gap energy with increasing temperature, opposite in sign to almost all other semiconductors. We report on the isotope shift of the band gap energy between natural PbS (containing mostly 32S) and PbS made with enriched 34S, measured using low temperature photoluminescence spectroscopy. The observed isotope shift is also opposite to the normal expectation of larger band gap for the heavier mass. In addition, we report on improved measurements of the temperature dependence of the band gap energy measured using absorption spectroscopy, to study the expected connection between the isotope shift of the band gap energy and its shift with temperature.

## Aluminum gallium nitride / gallium nitride high electron mobility transistor fabrication and characterization

In the last decade, All-,GaXN/GaN High Electron Mobility Transistors (HEMTs) have been intensively studied because their intrinsic electrical properties make them attractive for high power microwave device applications. Despite much progress, current slump continues to be a problem, limiting output power, reducing reliability, and complicating device modelling. In this work, a complete A~I-,G~,N/G~N HEMT fabrication procedure was developed, and electrical characteristics related to current slump, microwave modelling, and delay time analysis were explored. Low resistance ohmic contacts were achieved, enabling high channel current densities. Schottky contacts were developed with a new ion implant isolation architecture, enabling gate leakage currents 2 to 4 orders of magnitude lower than typical results from the literature. Through pulsed current-voltage measurements, the importance of bias stresses in the gate-source region was demonstrated for the first time. In contrast to the conventional "virtual gate" model, gate-source stresses were shown to be more important than gatedrain stresses when biased near threshold. Slow slump transients were studied by passivating transistor surfaces with ultrathin layers. These results excluded dielectric strain and electron injection reduction as viable passivation mechanisms. A novel model was proposed associating slow slump behaviour with trapping of many electrons at screw dislocation sites. The effect of slump on RF properties was examined through microwave measurements by extracting the parasitic source and drain resistances without special biasing. Besides significantly improving the accuracy of small-signal modelling, we were able to show the bias dependence of parasitic resistances which confirmed the effect of source-side bias stressing. The question of channel electron velocities in nitride transistors remains controversial. We determined an effective electron velocity of - 1.9 x 1 o7 cmls through two methods. We first extracted effective velocities through delay time analysis, and then through the small-signal model elements. To our knowledge, this was the first time an equivalent model extraction led to self-consistent electron velocity values for nitride transistors. Finally, our equivalent circuit model showed the correct interrelation between frequency response and access resistances. The cohesive picture of current slump, equivalent circuit model extraction, and delay time analysis gives a high degree of confidence in these results.

## Confinement and the superfluid density in theories of the underdoped cuprates, and strongly commensurate dirty bosons in the large-N limit

In this thesis, we study various issues arising from the QED theory of underdoped, high temperature superconductors in 2+1 dimensions. The theory breaks up roughly into two sectors: fermionic and bosonic. With regard to the fermionic sector, we consider confinement of the emergent gauge field which we take to be compact. In the absence of fermions, the interaction between monopoles is Coulombic and the well known result is that the pure gauge theory is permanently confining. With the addition of fermions, the interaction becomes logarithmic, and an analogy with the usual Kosterlitz-Thouless transition suggests a deconfinement transition for the fermions. We show, however, that, when screening is taken into account, the deconfined phase is destabilized and fermions remain permanently confined. The bosonic sector models Cooper pair phase fluctuations, whose effect on the depletion of the superfluid density we examine in two separate studies. In the first of these, we study the quantum XY model, and show that the quasi-two dimensionality, low critical temperatures and large d-wave gap characteristic of underdoped cuprates severely constrain the form of the superfluid density. Under these assumptions, we find that phase fluctuations alone are insufficient to account for recent observations of deviations from Uemura scaling, and that the quasiparticle contribution is a necessity. We use our results to satisfactorily fit the recent data. In the second study, we model the cuprates by a layered system of interacting bosons and examine the collective excitations in this system. Depending on the anisotropy and the interaction strength, we find find four different regimes of temperature dependence of the superfluid density. We argue that interactions in the underdoped cuprates are effectively short-ranged and weak. Finally, we study the related issue of disordered, interacting bosons in the large-N limit and 2 strong commensuration. Perturbatively at weak disorder and numerically at strong, we show that th screening of the random potential due to interactions is insufficient to delocalize the single-particl states so that no superfluid transition occurs from the Mott insulator.

## Reconstructing DNA replication kinetics from small DNA fragments

In higher organisms, DNA replicates simultaneously from many origins. Recent in vitro experiments have yielded large amounts of data on the state of replication of DNA fragments. From measurements of the time dependence of the average size of replicated and non-replicated domains, one can estimate the rate of initiation of DNA replication origins. One problem with such estimates is that, in the experiments, the DNA is broken up into small fragments, whose finite size can bias the measured averages. Here, I present a systematic way of accounting for this bias. In particular, I derive theoretical relationships between the original domain-length distributions and fragment-domain length distributions. I also derive unbiased average-domain-length estimators, which can yield accurate results even in cases where the replicated (or nonreplicated) domains are larger than the average DNA fragment. Then I apply these estimators to previously obtained experimental data to extract replication kinetics parameters.

## Probing the mechanical properties of short molecules with optical tweezers

Structural proteins play vital roles in many human tissues, roles to which their mechanical properties are of direct relevance. Optical tweezers give us the remarkable ability to quantitatively probe these properties at the single-molecule level, potentially revealing a wealth of information on how such proteins fulfil their physiological functions. I have worked toward applying this technique, in which micron-sized beads chemically linked to the protein are manipulated by focussed laser beams, to structural proteins, particularly elastin. I developed methods to eliminate or account for several experimental complications presented by the fact that these proteins are short compared to other molecules studied with optical tweezers. I proceeded to design and test multiple strategies for linking elastin to beads, discovering that its unusual biochemical properties raise significant additional challenges. Some of these I overcame, and an assay I developed for linking effectiveness may be of use in overcoming others

## An experimental model for MRI-detected measurements of oxygen uptake in the lungs

Oxygen, which is paramagnetic, influences the nuclear relaxation rate of Helium-3, and can be the limiting factor when hyperpolarized (HP) gases are used as inhaled contrast agents in MR lung imaging. The decay rate of a HP 3He NMR signal, acquired during a single breath-hold, will thus change as oxygen is exchanged with the bloodstream. We model this effect in vitro using a time-varying magnetic field gradient to mimic oxygen uptake in the lung. The goal of the study is to investigate the expected accuracy and precision with which oxygen concentrations and uptake rates can be extracted from lung imaging experiments performed in vivo. Particular emphasis is placed on the effects of varying signal-to-noise ratio and acquisition time. These experiments are expected to inform developments in the field of hyperpolarized gas MRI, and may lead to new tools for the treatment and detection of lung diseases and disorders.

## Metallic scattering lifetime measurements with terahertz time-domain spectroscopy

The momentum scattering lifetime is a fundamental parameter of metallic conduction that can be measured with terahertz time-domain spectroscopy. This technique has an important strength over optical reflectance spectroscopy: it is capable of measuring both the phase and the amplitude of the probing radiation. This allows simultaneous, independent measurements of the scattering lifetime and resistivity. Broadly, it is the precision of the phase measurement that determines the precision of scattering lifetime measurements. This thesis describes milliradian-level phase measurement refinements in the experimental technique and measures the conductivity anisotropy in the correlated electron system CaRuO3. These phase measurement refinements translate to femtosecond-level refinements in scattering lifetime measurements of thin metallic films.