Dissertationen zum Thema „Condensed systems“

Le sujet de cette these porte sur des calculs ab initio de proprietes d'etat fondamental et excite de systemes differents, dans le cadre de la dft et de la tddft. Du cote numerique, nous avons mis en oeuvre une methode originale pour l'evaluation de la polarisabilite dynamique a particules independantes, et generalise un code au spin dans le but d'etudier les proprietes magnetiques de systemes reels. Nous avons etudie des spectres de reflectivite anisotrope et de perte d'energie pour la surface (100) du silicium, propre ou oxydee. La comparaison entre les spectres mesures et simules, nous ont permis d'exclure la reconstruction p(2x1). En suite, nous avons mis en evidence le probleme de la description des excitations des systemes a couche ouverte presente un etude des proprietes optiques d'alliage magnetique interessants pour des applications en spintronique. Nous avons evalue les proprietes d'etat fondamental de ces alliages et la conductivite du fer ccc.

This thesis presents work done on the calculation of the effects of anharmonic nuclear motion on the properties of solid materials from first principles. Such anharmonic effects can be significant in many cases. A vibrational self-consistent field (VSCF) method is used as the basis for these calculations, which is then improved and applied to a variety of solid state systems. Firstly, work done to improve the efficiency of the VSCF method is presented. The standard VSCF method involves using density functional theory (DFT) to map the Born-Oppenheimer (BO) energy surface that the nuclei move in, a computationally expensive process. It is shown that the accurate forces available in plane-wave basis DFT can be used to help map the BO surface more accurately and reduce the computational cost. This improved VSCF+f method is tested on molecular and solid hydrogen, as well as lithium and zirconium, and is found to give a speed-up of up to 40%. The VSCF method is then applied to two different systems of physical interest. It is first applied to the case of the neutral vacancy in diamond, in order to resolve a known discrepancy between harmonic ab initio calculations and experiment -- the former predict a static Jahn-Teller distortion, whilst the latter leads to a dynamic Jahn-Teller effect. By including anharmonic corrections to the energy and nuclear wavefunction, we show that the inclusion of these effects results in agreement between first-principles calculations and experiment for the first time. Lastly, the VSCF method is applied to barium titanate, a prototypical ferroelectric material which undergoes a series of phase transitions from around 400 K downwards. The nature of these phase transitions is still unclear, and understanding them is an active area of research. We describe the physics of the phase transitions of barium titanate, including both anharmonicity and the effect of polarisation caused by long wavelength vibrations, to help understand the important physics from first principles.

This thesis is devoted to the ab initio calculation of ground state and excited state properties of different systems within the density functional theory and the time dependent density functional theory.From the numerical point of view we implemented an original method in a plane waves code devoted to calculate the independent particle response function.Moreover, we generalized the same code to the spin degree of freedom in order to study the magnetic properties of realistic condensed matter systems.We studied the reflectance anisotropy spectra and the energy loss spectraof the clean and oxidized surface, and we performed the analysis of the originof the main spectral features.Thanks to the comparison between experimental and theoretical REEL spectra,we could roule out the p(2x1) reconstruction for this surfcace.Moreover, we evidenced the problem of the correct description of the excitation spectra for open shell systems within the TDDFT framework, in thecase of the simple BeH molecule.In the second part of the thesis, we presented the study of the opticalproperties of magnetic systems such as FeS2, CoS2 or NiS2, interesting materialsfor possible technological applications in the growing field of spintronics.Within this context we calculated the ground state properties and the opticalcondictivity of BCC bulk iron, for which we found a nice agreement withavailable experimental data.

A variety of methyl biphenyl-2-acrylate precursors, substituted in the 2’-, 3’- or 4’-positions, were synthesised using a Suzuki coupling reaction between 2-formylphenylboronic acid and the appropriate aryl halide, followed by Wittig olefination. These precursors were then pyrolysed to produce 3-cyano, 3-methyl and 3-chloro substituted phenanthrenes. The synthesis of 1-cyanophenanthrene was also successful. This route was also successful in producing naphthothiophenes and naphthofurans from appropriate heteroaryl-substituted precursors. This methodology was expanded into the synthesis of several four-ring systems. Due to the known toxicity of such compounds a nitrogen atom was included within the skeleton as this is known to reduce toxicity. This was done by using 4-chloroquinoline-3-carbaldehyde as a starting material for the Suzuki coupling reactions as this included both a nitrogen atom in the final structure and the aldehyde functionality required for the Wittig olefination. 10-Cyanobenzophenanthridine was synthesised in this way to demonstrate that it is possible to produce substituted four-ring systems. By coupling 4-chloroquinoline-3-carbaldehyde with thiophene- and furan-boronic acids followed by Wittig olefination and pyrolysis it was possible to produce two thienylphenathridines and two furanylphenanthridines. By reacting 2,5-dibromothiophene and two equivalents of 2-formylphenylboronic acid followed by a double Wittig olefination and pyrolysis it was possible to synthesise dinaphtho[1,2-b-2’,1’]thiophene. This is the first example of a double cyclisation of this type onto a single central ring. Four benzo[5]heterohelicenes were synthesised via a Suzuki coupling reaction of both dibenzothiopheneboronic acid and dibenzothiopheneboronic acid with both 1-bromonaphthalene-2-carbaldehyde and 4-chloroquinoline-3-carbaldehyde followed by Wittig olefination and pyrolysis. 1-Aza[5]helicene was also synthesised. It was possible to condense the 2-aryl and 2-heteroarylbenzaldehydes synthetic intermediates, with O-methylhydroxylamine hydrochloride to produce oxime ethers which were subjected to FVP at 700°C to give 5-azaphenanthrenes and their heterocyclic analogues.

Motivated by the large diversity of two dimensional condensed matter systems, various two dimensional models were studied using computer simulation. The structure and dynamics in a monolayer of dipolar soft spheres were studied using Molecular Dynamics simulation. This is a model for colloidal ferrofluids. Langevin Dynamics simulations have been employed to study the aggregate kinetics of the dipolar chains and rings starting from a ‘random’ configuration. Clusters were identified using an energy criterion, and classified as chains, rings or defect clusters. The mechanisms by which these clusters form are discussed. At high density, there is a high transient concentration of defects, indicating an interconnected network structure. This suggests that the phase transition proposed by Tlusty and Safran [Tlusty and Safran, Science 290, 1328 (2000)] could be recovered as a metastable phase transition if the system could be kinetically trapped in this transient state. The dynamics of antiferromagnetically coupled Heisenberg spins on a kagomé lattice has been studied using numerical simulation. This system is highly frustrated – the lattice places competing constraints on the spins. We investigate the effect of breaking bonds in the lattice, which relieves the frustration to a certain extent. The phase diagram of a two dimensional system of hard disk trimers has been explored by Monte Carlo simulation. This might serve as a coarse grained model for the aggregation of proteins in a biological membrane. Many proteins are roughly triangular in shape or form trimeric units. The model consists of three hard disks fused together in a triangular arrangement. One of the disks interacts with the corresponding disk on other trimers via a square-well potential, representing specific interactions between the protein molecules. In the fluid phase at low density the trimers form aggregates containing typically four to six trimers. In the solid phase, the trimers pack such that individual disks are on a triangular lattice. There are different possible packings of the trimers consistent with this packing of individual disks.

Two mathematical problems in disordered systems are studied: geodesics in first-passage percolation and conductivity of random resistor networks. In first-passage percolation, we consider a translation-invariant ergodic family {t(b): b bond of Z²} of nonnegative random variables, where t(b) represent bond passage times. Geodesics are paths in Z², infinite in both directions, each of whose finite segments is time-minimizing. We prove part of the conjecture that geodesics do not exist in any fixed half-plane and that they have to intersect all straight lines with rational slopes. In random resistor networks, we consider an independent and identically distributed family {C(b): b bond of a hierarchical lattice H} of nonnegative random variables, where C(b) represent bond conductivities. A hierarchical lattice H is a sequence {H(n): n = 0, 1, 2} of lattices generated in an iterative manner. We prove a central limit theorem for a sequence x(n) of effective conductivities, each of which is defined on lattices H(n), when a system is in a percolating regime. At a critical point, it is expected to have non-Gaussian behavior.

The highly parallel nature of the fundamental principles of quantum mechanics means that certain key resource-intensive tasks --- including searching, code decryption and medical, chemical and material simulations --- can be computed polynomially or even exponentially faster with a quantum computer. In spite of its remarkably fast development, the field of quantum computing is still young, and a large-scale prototype using any one of the candidate quantum bits (or 'qubits') under investigation has yet to be developed. Spin-based qubits in condensed matter systems are excellent candidates. Spins controlled using magnetic resonance have provided the first, most advanced, and highest fidelity experimental demonstrations of quantum algorithms to date. Despite having highly promising control characteristics, most physical ensembles investigated using magnetic resonance are unable to produce entanglement, a critical missing ingredient for a pure-state quantum computer. Quantum objects are said to be entangled if they cannot be described individually: they remain fundamentally linked regardless of their physical separation. Such highly non-classical states can be exploited for a host of quantum technologies including teleportation, metrology, and quantum computation. Here I describe how to experimentally create, control and characterise entangled quantum ensembles using magnetic resonance. I first explore the relationship between entanglement and quantum metrology and demonstrate a sensitivity enhancement over classical resources using molecular sensors controlled with liquid-state nuclear magnetic resonance. I then examine the computational potential of irreversible relaxation processes in combination with traditional reversible magnetic resonance control techniques. I show how irreversible processes can polarise both nuclear and electronic spins, which improves the quality of qubit initialisation. I discuss the process of quantum state tomography, where an arbitrary quantum state can be accurately measured and characterised, including components which go undetected using traditional magnetic resonance techniques. Lastly, I combine the above findings to initialise, create and characterise entanglement between an ensemble of electron and nuclear spin defects in silicon. I further this by generating pseudo-entanglement between an ensemble of nuclear spins mediated by a transient electron spin in a molecular system. These findings help pave the way towards a particular architecture for a scalable, spin-based quantum computer.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior
Nesta tese estudamos a influÃncia de potenciais de confinamento externos nas propriedades dinÃmicas de sistemas de matÃria condensada mole. Analisamos as propriedades difusivas de dois sistemas especÃficos utilizando simulaÃÃes computacionais (DinÃmica Molecular de Langevin e DinÃmica Browniana). No CapÃtulo 1, introduzimos o tÃpico sobre matÃria condensada mole. Mostramos vÃrios aspectos teÃricos e experimentais neste tipo de sistema. Fazemos uma breve introduÃÃo ao tÃpico de difusÃo, onde discutimos os principais aspectos do movimento Browniano. Introduzimos o problema de difusÃo em linha (SFD, do inglÃs "single-file diffusion") e o discutimos, teorica e experimentalmente, no contexto de sistemas de matÃria condensada mole. No CapÃtulo 2, introduzimos os mÃtodos computacionais utilizados nesta tese. Discutimos os mÃtodos de DinÃmica Molecular e suas variantes, o mÃtodo de DinÃmica de Langevin e DinÃmica Browniana. TambÃm introduzimos algoritmos de integraÃÃo utilizados nos capÃtulos posteriores. Nos Caps. 3, 4 e 5, analisamos dois sistemas distintos, (i) um sistema de partÃculas de Yukawa confinadas em um canal parabÃlico quasi-unidimensional (q1D) e (ii) um sistema de colÃides magnÃticos sob a influÃncia de um potencial parabÃlico e uma modulaÃÃo periÃdica externa ao longo da direÃÃo nÃo confinada. No primeiro sistema, estudamos a transiÃÃo do regime de difusÃo em linha (SFD) para o regime de difusÃo normal (2D). No segundo sistema, estudamos os efeitos de vÃrios parÃmetros que caracterizam o sistema (e.g., a magnitude do campo magnÃtico externo e a presenÃa da modulaÃÃo periÃdica externa) em suas propriedades dinÃmicas. Finalmente, apresentamos um sumÃrio dos principais resultados obtidos nesta tese e mostramos algumas questÃes em aberto como perspectivas para pesquisas futuras na Ãrea de difusÃo em sistemas de matÃria condensada mole.
In this thesis we study the influence of external confinement potentials on the dynamical properties of soft condensed matter systems. We analyze the diffusive properties of two specific systems by means of Langevin and Brownian Dynamics simulations. In Chapter 1, we introduce the subject of soft condensed matter. We show several theoretical and experimental aspects of these type of systems. We make a brief introduction to the topic of diffusion, where we discuss main aspects of Brownian motion. We introduce the single-file diffusion (SFD) problem and discuss it in the context of soft condensed matter systems, both theoretically and experimentally. In Chapter 2, we introduce the computational method used in this thesis. We discuss Molecular Dynamics (MD) and its variants, Langevin and Brownian Dynamics simulations. We also introduce numerical algorithms used in the following chapters. In Chapters 3, 4 and 5, we analyze two different systems, namely (i) a system of interacting Yukawa particles confined in a parabolic quasi-one-dimensional (q1D) channel and (ii) a system of magnetic colloidal particles under the influence of both a parabolic confinement potential and a periodic external modulation along the unconfined direction. In the former, we study the transition from the single-file diffusion (SFD) regime to the two-dimensional (2D) diffusion regime. In the latter, we study the influence of several parameters that characterizes the system, e.g., the strength of an external magnetic field and the periodic modulation along the unconfined direction, on its dynamical properties. Finally, we present the summary of the main findings reported in this thesis and we show some open questions as perspectives for future research in the field of diffusion in soft condensed matter systems.

Thesis (Ph. D.) -- University of Maryland, College Park, 2008.
Thesis research directed by: Dept. of Physics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

CAMARÃO, Diego de Lucena. Diffusive properties of soft condensed matter systems under external confinement. 2014. 142 f. Tese (Doutorado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2014.
Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-04-09T20:25:36Z No. of bitstreams: 1 2014_tese_dlcamarao.pdf: 4771668 bytes, checksum: 12d4989237a73eeafcc143c607fa30dd (MD5)
Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-04-10T20:52:49Z (GMT) No. of bitstreams: 1 2014_tese_dlcamarao.pdf: 4771668 bytes, checksum: 12d4989237a73eeafcc143c607fa30dd (MD5)
Made available in DSpace on 2015-04-10T20:52:49Z (GMT). No. of bitstreams: 1 2014_tese_dlcamarao.pdf: 4771668 bytes, checksum: 12d4989237a73eeafcc143c607fa30dd (MD5) Previous issue date: 2014
In this thesis we study the influence of external confinement potentials on the dynamical properties of soft condensed matter systems. We analyze the diffusive properties of two specific systems by means of Langevin and Brownian Dynamics simulations. In Chapter 1, we introduce the subject of soft condensed matter. We show several theoretical and experimental aspects of these type of systems. We make a brief introduction to the topic of diffusion, where we discuss main aspects of Brownian motion. We introduce the single-file diffusion (SFD) problem and discuss it in the context of soft condensed matter systems, both theoretically and experimentally. In Chapter 2, we introduce the computational method used in this thesis. We discuss Molecular Dynamics (MD) and its variants, Langevin and Brownian Dynamics simulations. We also introduce numerical algorithms used in the following chapters. In Chapters 3, 4 and 5, we analyze two different systems, namely (i) a system of interacting Yukawa particles confined in a parabolic quasi-one-dimensional (q1D) channel and (ii) a system of magnetic colloidal particles under the influence of both a parabolic confinement potential and a periodic external modulation along the unconfined direction. In the former, we study the transition from the single-file diffusion (SFD) regime to the two-dimensional (2D) diffusion regime. In the latter, we study the influence of several parameters that characterizes the system, e.g., the strength of an external magnetic field and the periodic modulation along the unconfined direction, on its dynamical properties. Finally, we present the summary of the main findings reported in this thesis and we show some open questions as perspectives for future research in the field of diffusion in soft condensed matter systems.
Nesta tese estudamos a influência de potenciais de confinamento externos nas propriedades dinâmicas de sistemas de matéria condensada mole. Analisamos as propriedades difusivas de dois sistemas específicos utilizando simulações computacionais (Dinâmica Molecular de Langevin e Dinâmica Browniana). No Capítulo 1, introduzimos o tópico sobre matéria condensada mole. Mostramos vários aspectos teóricos e experimentais neste tipo de sistema. Fazemos uma breve introdução ao tópico de difusão, onde discutimos os principais aspectos do movimento Browniano. Introduzimos o problema de difusão em linha (SFD, do inglês "single-file diffusion") e o discutimos, teorica e experimentalmente, no contexto de sistemas de matéria condensada mole. No Capítulo 2, introduzimos os métodos computacionais utilizados nesta tese. Discutimos os métodos de Dinâmica Molecular e suas variantes, o método de Dinâmica de Langevin e Dinâmica Browniana. Também introduzimos algoritmos de integração utilizados nos capítulos posteriores. Nos Caps. 3, 4 e 5, analisamos dois sistemas distintos, (i) um sistema de partículas de Yukawa confinadas em um canal parabólico quasi-unidimensional (q1D) e (ii) um sistema de colóides magnéticos sob a influência de um potencial parabólico e uma modulação periódica externa ao longo da direção não confinada. No primeiro sistema, estudamos a transição do regime de difusão em linha (SFD) para o regime de difusão normal (2D). No segundo sistema, estudamos os efeitos de vários parâmetros que caracterizam o sistema (e.g., a magnitude do campo magnético externo e a presença da modulação periódica externa) em suas propriedades dinâmicas. Finalmente, apresentamos um sumário dos principais resultados obtidos nesta tese e mostramos algumas questões em aberto como perspectivas para pesquisas futuras na área de difusão em sistemas de matéria condensada mole.

I derive and apply quantum propagator techniques to atomic and condensed matter systems. I observe many interesting features by following the evolution of a wavepacket. In atomic systems, I revisit the Stern-Gerlach effect and study the spin dynamics inside an inhomogeneous magnetic field. The results I obtained are not exactly the same as the textbook description of the effect which is usually a manifestation of a perfect space and spin entanglement. This discovery can provide insight on more reliable quantum computation device designs. In condensed matter systems, the doping concentration inhomogeneity leads to the Rashba spin-orbit interaction. This makes it possible to control the spin without the external magnetic field. By propagating the wave packet in systems exhibiting Rashba spin-orbit interactions, I discover several features such as spin separation, spin accumulation, persistent spin-helix, and ripple formation.

Physical systems composed of a large number of reciprocally interacting constituents provide the natural context for the rise of emergent phenomena. Despite the intrinsic difficulty in providing a mathematical definition of what is meant for ‘emergence’ (see [Baas, in Langton, Alife III, Santa Fe Studies in the Sciences of Complexity, Proc. Volume XVII, Addison-Wesley, (1994)]), the intuitive notion of emergent property is that of a collection of interact- ing objects showing a novel collective behavior, qualitatively different from and not immediately attributable to the behaviors of the individual components. Non-linear interactions among elements of the system, or interactions between the system and the environment, or merely the large number of constituents are usually the motivations addressed to be responsible for emergent behavior. It is important to remark that emergent properties can only be inferred from a comprehension of the collective properties of the microscopic constituents [Kivelson et al, npj Quant. Mater. 1, 16024 (2016)]. In this regard, computer simulations provide a unique tool to support experimental observation, develop abstract models and investigate systems’ properties at a microscopic level. In general, condensed matter, particularly soft matter but also the complex systems studied in Physics, are necessarily described via simplified models, which include the key features of the corresponding real systems. On the one hand, this certainly represents a powerful approach when it finds its roots in the concept of universality, connected with critical phenomena, but this also turns into a limiting factor for the realistic description of the considered phenomena. On the other hand, it makes the properties of such abstract simulated systems calculable and investigable via computer simulations. As a consequence, the simulations assume a key role in complementing the comparison between experiments and theory [Frenkel and Smit, Understanding Molecular Simulations, Academic Press (2002); Allen and Tildesley, Computer simulation of liquids, Oxford University Press (2017)]. In this sense, simulations are often regarded as being computer experiments, in which materials properties and novel phases of matter can be investigated. The present PhD thesis is a collection of the main results coming from four different research lines which I have been involved into in the last 3 years. The topics could appear to be rather diverse but they are all connected by the presence of emergent phenomena which were studied via computer simulations (Molecular Dynamics and Monte Carlo methods, mainly). Three of these four research lines are related to collaborations with as many experimental groups. The first group I started collaborating with is led by dr. R. Grisenti, at the University of Frankfurt (https://www.atom. uni-frankfurt.de/hhng-grisenti/index.html). As reported in Chapter 1 and in a recent paper which I contributed to as first co-author [Schottelius, Mambretti et al., Nat. Mat. (2020)], we studied the crystal growth of supercooled Ar–Kr liquid mixtures by means of a micro–jet experiment, Molecular Dynamics simulation and thermodynamic analysis. The second ongoing collaboration is with the group of prof. P. Milani, which is the leader of the CIMaINa laboratories (http://cimaina.unimi.it/) at the Università degli Studi di Milano. We developed an abstract stochastic model of resistive switching devices that they are characterizing for neuromorphic applications (see Chapter 3). More recently, I started a collaboration with the group led by prof. T. Bellini at the Università degli Studi di Milano (https://sites.google.com/site/unimisoft/), in order to investigate the spinodal decomposition of mixtures of DNA nanostars via light scattering experiments and Monte Carlo simulations, as described in Chapter 4. I will now provide a brief overview of the contents of each Chapter, where each Chapter corresponds to a different research line. Crystal growth from a supercooled melt is of fundamental theoretical and practical importance in many fields, ranging from materials science to the production of phase–change memories. To date, the temperature dependence of the growth rates of many materials, including pure metals, metallic alloys, colloids and many others are still under intense scrutiny (see e.g. Tang et al., Nat. Mat. (2013) and Sun et al., Nat. Mat. (2018)). The majority of systems display a maximum growth rate at a temperature located between the melting point and the glass transition [Orava et al., J. Chem. Phys. (2014)]. Several materials are characterized by a range of many orders of magnitude between this maximum value and the crystal growth rates measured in other regimes. We still lack a deep comprehension of the mechanism underlying this phenomenology, which emerges from experiments and simulations both. Classical models of crystal growth from a melt hypothesize either a diffusion-limited process, or a collision–limited one, but for a lot of materials them both fail to fit the available data. This situation claims for further investigation about the key elements that tune the crystal growth rates from supercooled liquids, extending the current theoretical framework. Jointly with the experimental group of dr. Grisenti (which performed measurements at the EU-XFEL facility https://www.xfel.eu/), we studied the crystallization of supercooled mixtures of argon and krypton via Molecular Dynamics. Our results showed that their crystal growth rates (obtained from the analysis of simulated configurations exploiting Steinhardt angular order parameters) can be reconciled with existing crystal growth models only by explicitly accounting for the non–ideality of the mixtures. Our theoretical and computational contribution aided in highlighting the importance of thermodynamic aspects in describing the crystal growth kinetics, yielding a substantial step towards a more sophisticated theory of crystal growth. A second project concerns the study of soft matter systems in one dimension (1D), detailed in Chapter 2. Soft matter systems are made of particles which can overlap by paying a finite energy cost and they are renowned for being able to display complex emerging phenomena. Some of them, for example, are characterized by the presence of clustering phases [Prestipino, Phys. Rev. E (2014)]. Recently, a surprising quantum phase transition has been revealed in a 1D system composed of bosons interacting via a pairwise soft potential in the continuum. It was shown that the spatial coordinates undergoing two-particle clustering could be mapped into quantum spin variables of a 1D transverse Ising model [Rossotti et al., Phys. Rev. Lett. (2017)]. Extending the description and the results provided in a very recent paper I contributed to as first author [Mambretti et al., Phys. Rev. E (2020)], in the second Chapter we investigate the manifestation of an analogous critical phenomenon in 1D classical fluids of soft particles in the continuum. In particular, we studied the low–temperature behavior of three different classical models of 1D soft matter, whose inter–particle interactions allow for cluster- ing. The two–particle cluster phase is largely explored, by simulating the systems at the commensurate density via Monte Carlo and Simulated Annealing methods. The same string variables exploited in the aforementioned quantum case highlight that, at the right commensurate density, the peculiar pairing of neighboring soft particles can be nontrivially mapped onto a 1D discrete classical Ising model. We also observe a related phenomenon, i.e. the presence of an anomalous peak in the low–temperature specific heat, thus indicating the emergence of Schottky phenomenology in a non–magnetic fluid. The third Chapter presents the case of an electrical resistor network featuring novel emergent properties, such as memristivity and the possibility to be used as a self–assembled logic gate; an article on this topic is currently in preparation. The growing difficulties arising in the improvement of the performance of standard computing architectures encouraged the quest for different approaches aiming at reproducing the computational capability and energy efficiency of the human brain, by mimicking neurons and synapses as probabilistic computing units [Markovic et al., Nat. Rev. Phys. 2, 499–510 (2020)]. Networks based on the bottom–up assembling of nanoscale building blocks and characterized by resistive switching (RS) activities are becoming increasingly popular as possible solutions for a straightforward fabrication of complex architectures with neuromorphic features [Wang et al., Nat. Rev. Mat. 5, 173-195 (2020)]. Specifically, it has recently been demonstrated that metallic nanostructured Au films, under certain conditions show a non–ohmic electrical behavior and complex and reproducible resistive switching, which can be exploited for the innovative realization of logic gates. In these devices, the nonlinear dynamic switching behavior resulting from an applied input voltage can be exploited for developing hardware for reservoir computing applications. In Chapter 3, I show how it is possible to simulate a complex model (Stochastic Resistor Network Model, SRNM) able to imi- tate the phenomenology and give hints for the development of experiments ongoing at the CIMaINa research laboratories, regarding the electrical current passage through nanostructured cluster gold films [Mirigliano et al., Nanotechnology, 31, 23, (2020)]. To this purpose, I personally contributed to develop from scratch a C++ code, parallelized via the Armadillo library (http://arma.sourceforge.net/). To study the electrical transport properties of this system, we modeled the experimental sample as a network of interconnected resistors whose effective resistance under a given voltage can be determined using spectral graph theory. The network state evolves stochastically via random physically–inspired update moves, and its effective total resistance (and the related Power Spectral Density) has been analyzed. The structure and the topology of the network were studied via the investigation of the shortest path connecting the source and the sink of the system, thus exploring the possible paths in which the current could flow. Moreover, we also applied Information Theory entropy–based tools to investigate the time evolution of network resistance at a local, coarse–grained, scale. We observed that specific input signals corresponding to 2 logical ‘bits’ pro- duce rich outputs associable to a logical NAND gate, which posses functional completeness. Given that relevant differences could be detected between the behavior of the network at low voltage before and after the so called ‘writing’ step (where the system is under a high applied voltage), memristive effects naturally emerge in the study of network properties. These results encourage further investigations, both experimental and via the innovative SRNM approach we developed, in order to exploit these RS devices in hardware computing applications as self–assembled logic gates. Last, in Chapter 4 I focus on another soft matter system, that I have started to investigate during my PhD research activity, regarding Monte Carlo simulations of low valence DNA–based colloidal particles. This last Chapter is mainly devoted to the description of the simulation method I have been developing during my more recent PhD research activities, while the preliminary results presented obviously need to be confirmed and extended by further studies. Particles with a limited number of attractive spots (patches) on their surface are generally characterized by non–crystalline low energy states; they rather generate a disordered 3D network in which all the sticky sites are engaged in (mutually exclusive) patch–patch bonds [Bianchi et al., Phys. Rev. Lett. (2006)]. One of the most promising experimental realizations of such peculiar colloids is extremely recent: laboratory synthesized DNA nanostars (NS) with fixed valence [Bi et al., PNAS (2013)]. In this field the landmark is represented by our collaborators from the group led by prof. T. Bellini. Recently, they started to investigate the behavior of mixtures of nanostars with leftwise or rightwise chirality of the DNA strands, characterized by a merely repulsive interspecies interaction. To date, our contribution mainly consisted in the development of an abstract model of these DNA nanostars, schematized as limited valence soft patchy particles, whose equilibrium configurations are sampled via a canonical Monte Carlo program. Their different chirality is represented by a mixed interaction which only comprises excluded volume terms. Our goal in this project is twofold: on the one hand, we aim to reconstruct the temperature–density phase diagram of such mixtures, also depending on the mixing ratio. Experiments revealed a critical behavior and a phase separation processes for dilute mono–component DNA solutions; the properties of a mixture of two components, each found in critical conditions, are studied in this work. In this Chapter, after a detailed overview of the experimental, computational and theoretical studies regarding low valence particles, the simulation code is described and it is presented a comparison between the simulation results and the experimental measurements at equilibrium. The peculiar structures found in the patchy particles network claim for further analysis, as well as the interesting behavior near the critical point for mono–component and bi–component systems both. The second perspective of this research regards the unexplored aggregation and cluster growth process of such particles. In this concern, part of the future research effort will be devoted to the transformation of our custom code into a Brownian Monte Carlo in order to unveil the mechanisms underlying the dynamics of such particles during their aggregation stages. The conclusions and further perspectives concerning each of the four topics addressed in this work can be retrieved at the end of each Chapter.

Monte Carlo simulations used for representing dynamical physical phenomena are studied in terms of a Markov chain operator acting on the probability distrubution of the states of a given system. The most general transition rule satisfying detailed balance and leading to a canonical ensemble probability distribution is derived using this formalism. The explicit Markov chain representing the two most commonly used canonical algorithms, the Metropolis and the Glauber transition rules, is then constructed and numerically applied to the states of an Ising model. The dynamical properties of the system are studied for each algorithm. Various measures, such as time-time correlation functions, are estimated for different system sizes and finite-size sealing is applied. In particular, the effects of the transition rule on the dynamic critical exponent is investigated.
We at first examine one- and two-dimensional systems using periodic boundary conditions. Systems with free boundary conditions were also studied, and their results were equivalent with respect to the dynamical critical properties of the system. The effects of conservation laws were also investigated and both conserved and non-conserved systems were studied. Both local and non-local spin-exchange dynamics were investigated for conserved systems. Finally, our approach was used to simulate quenches on small systems.
This method is them used to analyze phenomenological transformations done by dynamical renormalization-group (RG) methods. It is found that, when the RG transformation is linear in probability space, there exists a corresponding Markov chain generating the time sequence of the renormalized systems. An example is given for the one-dimensional Ising model.

Although the study of thermal transport in condensed matter has a very long history, it continues to be an active field of work due to its importance in many applications. The research subject reported in this thesis is on theoretical investigations of thermal energy transport in systems whose linear dimension is less than the wavelength of thermal phonons. Such situations occur in mesoscopic and nanoscopic scale dielectric structures which can now be fabricated in a number of laboratories. Due to the small system dimensions, phonons must be treated as waves. Thermal energy transport, therefore, must be treated as phonon wave propagation through the system.
After reviewing the general physics of thermal energy transport in the classical regime, we derive, for dielectric materials, a formula for thermal energy flux in devices involving multi-terminals each connected to a thermal reservoir at local equilibrium. The energy flux is driven by a temperature bias and traverses the system by virtue of phonon wave scattering. A multi-terminal thermal conductance formula is derived in terms of phonon transmission coefficient. Using our theoretical formulation, we investigate thermal transport properties of both two-terminal and four-terminal dielectric devices by solving the quantum scattering problem using a mode matching numerical technique.
For thermal transport in a T-shaped dielectric nanostructure with two-terminals at low temperature, due to quantum interference the transmission coefficient of phonons becomes quite complicated. We found that the value of phonon transmission coefficients at zero energy may be unity or zero depending on a geometrical ratio of the nanostructure. The transmission has an oscillation behavior with quasi-periodicity and irregularity. The thermal conductance is found to increase monotonically with temperature---a result that we conclude to be generally true for any two-terminal device. We confirm the existence of the universal quantum of thermal conductance which exists at the low temperature limit, and such a quantum is robust against all the system parameters.
The physical behavior of four-terminal thermal conductance for mesoscopic dielectric systems with arbitrary shapes of scattering region is also investigated in detail. If we make a two-terminal measurement in the four-terminal device, the two-terminal conductance is a monotonically increasing function of temperature, and is equal to the universal quantum of thermal conductance masked by a geometric factor. If we make a four-terminal measurement, the four-terminal conductance has a non-monotonic dependence. In the low temperature limit, we predict that the four-terminal conductance diverges inversely proportional to temperature.
Finally, we discuss an interesting theoretical problem on the general behavior of thermal conductance for multi-terminal systems when thermal carriers satisfy fractional exclusion statistics. Our analysis allows us to conclude that results for fractional exclusion statistics are quite different from those of the Bose-Einstein statistics.

We study theoretically a mechanical oscillator coupled to a superconducting single-electron transistor (SSET), focussing on the regime where incoherent Cooper pair tunnelling in the SSET leads to a negative damping instability of the oscillator. In this regime, large oscillator motion modulates tunnelling in the SSET, which in turn affects the oscillator. This interplay leads to interesting strong feedback effects, including a highly non-thermal stationary oscillator state and a significant enhancement of the low-frequency current noise in the SSET. These effects and others are reminiscent of laser physics: the SSET corresponds to population-inverted atoms while the oscillator corresponds to cavity electro-magnetic field modes. We discuss the extent of this analogy and investigate the linewidth of the oscillator's noise spectrum. Our results are relevant to current experiments, and we point out several feasible measurements that could be done to observe strong feedback effects.

We study the dynamics of an interface driven far from equilibrium in three dimensions. We first derive the equations of motion which describe this physics. Numerical results are then obtained for three models which simulate the growth of an interface: the Kardar-Parisi-Zhang equation, a discrete version of that model, and a solid-on-solid model with asymmetric rates of evaporation and condensation. We show that the three models belong to the same dynamical universality class by estimating the dynamical scaling exponents and the scaling functions. We confirm the results by a careful study of the crossover effects. In particular, we propose a crossover scaling ansatz and verify it numerically. Furthermore, the discrete models exhibit a kinetic roughening transition. We study this phenomenon by monitoring the surface step energy which shows a drastic jump at a finite temperature for a given driving force. At the same temperature, a finite size scaling analysis on the bond energy fluctuation shows a diverging peak.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2012.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references.
In this work, I describe experiments utilizing high-field terahertz (THz) pulses to initiate nonlinear responses in several classes of materials. We have developed several methods for interrogating the nonlinear THz response of materials including collinear and noncollinear THz-pump/THz-probe spectroscopy, and THz-pump/optical probe spectroscopies including THz Kerr effect spectroscopy. We have observed nonlinear free-carrier absorption, occurring through the saturation of free-carrier mobility in bulk semiconductors. We have demonstrated that highly energetic electrons in the conduction band can generate electron-hole pairs in indium antimonide, and have elucidated the dynamics of the carrier generation process. We have observed nonlinear conductivity responses in graphene, showing that a strong THz pulse can heat the electron distribution leading to saturable absorption in the THz range. We have demonstrated THz-induced optical anisotropy in simple liquids, allowing for the measurement of subsequent orientational dynamics. We have driven nonlinear vibrational dynamics in ferroelectrics, demonstrating that the strong anharmonicity of lattice vibrational modes can induce an anisotropic optical response. We have begun to study nonlinear vibrational responses in molecular crystals, which is of importance in mode coupling and energy transfer processes in the THz range. Finally, we have driven nonlinear metamaterial responses in gallium arsenide and vanadium dioxide. In GaAs, we have shown that metamaterial properties may be tuned by an intense THz field if the substrate material (GaAs) is changed by the incident THz pulse, and we have demonstrated carrier multiplication locally in the metamaterial split ring resonator gaps where substantial electric field enhancement occurs. In VO2, we have shown that THz radiation can drive an insulator-to-metal phase transition, opening up new possibilities in the control of the states of matter with THz fields. This work has demonstrated only a few of the capabilities made possible by the interaction of intense THz radiation with matter, and provides a general framework to open up new research in a nascent field.
by Harold Young Hwang.
Ph.D.

We study the dynamics of two reaction-diffusion phenomena driven by chemical activation and thermal dissipation and evolving, respectively, on a randomly distributed or continuous medium. The first system describes the process of slow combustion of a randomly distributed reactant. It is studied by a phase-field model built up from first principles and describes the evolution of thermal and reactant concentration fields. Our combustion model incorporates thermal diffusion, activation and dissipation. We examine it in a manner which makes a connection between the propagation of combustion fronts, their kinetic roughening and the percolation transition. In so doing, we examine slow combustion in the context phase transitions. The second system describes propagation of reaction fronts arising in transformations obeying the Arrhenius law of chemical reactions. It too is modelled by a set of phase-field equations describing the dynamics of both thermal and concentration fields. A typical example of this transformation is the crystallization of an amorphous material. In addition to the features of our combustion model, this model also incorporated a realistic treatment of mass diffusion. Front propagation of our model is shown to undergo period doubling bifurcations as one varies the background temperature at which the system is maintained. The signature of these bifurcations is the same as those of the logistics map. We study how the bifurcation structure changes as a function mass diffusion, focusing on changes of the background temperature for which period doubling first emerges. This temperature is the most easily obtained experimentally.

We study a number of quantum phase transitions, which are exotic in their nature and separates non-trivial phases of matter. Since quantum fluctuations, which drive these phase transitions, are stronger in low-dimensions, we concentrate on low-dimensional systems. We consider two different two-dimensional systems in this thesis and study their phase transition. First, we investigate a phase transition in graphene, one of the most famous two-dimensional systems in condensed matter. For a suspended bilayer graphene in ν = 0 quantum Hall regime, the conductivity data and mean-field analysis suggests a phase transition from an antiferromagnetic (AF) state to a valence bond solid (VBS) state, when perpendicular electric field is increased. This AF to VBS phase transition is reminiscent of deconfined criticality, which is a novel phase transition that cannot be explained by Landau’s theory of symmetry breaking. We show that in the strong coupling regime of bilayer graphene, the AF state is destabilized by the transverse electric field, likely resulting in a VBS state. We also consider monolayer and bilayer graphene in the large cyclotron gap limit and show that the effective action for the AF and VBS order parameters have a topological Wess-Zumino-Witten term, supporting that the phase transition observed in experiments is in the deconfined criticality class. Second, we study the model systems of cuprate superconductor, which is effectively a two-dimensionalal system in the CuO_2 plane. The proposal that the pseudogap metal is a fractionalized Fermi liquid described by a quantum dimer model is extended using the density matrix renormalization group. Measuring the Friedel oscillations in the open boundaries reveals that the fermionic dimers have dispersion minima near (π/2,π/2), which is compatible with the Fermi arcs in photoemission. Moreover, investigating the entanglement entropy suggests that the dimer model with low fermion density is similar to the free fermion system above the Lifshitz transition. We also study the phase transition from a metal with SU(2) spin symmetry to an AF metal. By applying the functional renormalization group to the two-band spin-fermion model, we establish the existence of a strongly coupled fixed point and calculate critical exponents of the fixed point.
Physics

Systems modelling nanoscale structures have been studied in the context of the theory of energy level statistics in the ballistic and mesoscopic as well as the insulating regimes. Statistics were obtained using a new unfolding scheme based on the existence of a local stationary property for fluctuations of the energy spectra. Two different models were used in the study with particular emphasis on the relevance to the physics of nanoscale devices. Thus, a quantum billiard model composed of a quasi-two-dimensional tight-binding atomic lattice was introduced. The results of the statistical analysis of the spectra of the models were compared throughout the thesis with Random Matrix Theory (RMT). The applicability of RMT and the universality predicted by RMT were verified.
The statistical behavior of energy levels for systems in the crossover region between regular and chaotic behavior was studied in all three regimes. Gradual transitions were observed for both ballistic and mesoscopic systems, and found to be similar in the cases. For systems in the insulating regime, the statistical behavior of levels was found to be of Poisson type. The transition from GOE to Poisson behavior when the system is changed from the mesoscopic to the insulating regime was also studied, a spectral dependence of the local fluctuations of energy levels was found, indicating the break-down of translation invariance of the local fluctuations.
The transition due to time reversal invariant symmetry breaking was studied by applying a uniform magnetic field to systems constructed by using a tight-binding model with non-zero off-diagonal interactions. By rescaling the transition control parameter, it was found that for both ballistic and mesoscopic systems the transition behavior can be well described by RMT. For closed systems the transition is complete when the effective area of the system encloses a flux greater than one flux quantum.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2002.
Includes bibliographical references (leaves 131-137).
In this thesis properties of various condensed matter systems are studied, whose dependency on electronic behavior is incorporated through coarse-grained interactions. Three specific systems are considered. In the first system of study, high momentum, plane wave states of the electronic wave function are coarse-grained, while the low momentum states are fully resolved. Moreover, the coarse-graining procedure incorporates the response of the high momentum states to environmental changes and its couplings to changes in the low momentum states. Within density functional theory this allows the representation of the electronic wave function, when using a plane wave basis, to be computationally feasible without having to make the pseudopotential approximation. This coarse-graining procedure is beneficial for the study of high pressure systems, where the response of the core region is important. With this method we study a number of solid phases of boron and reveal a number of important structural and electronic properties on its high pressure and superconducting phase. The second system of study focuses on a slightly coarser scale, where a theory for the elasticity of nanometer sized objects is developed. This theory provides a powerful way of understanding nanoscale elasticity in terms of local group contributions and acts as a bridge between the atomic and the continuum regimes. This theory properly describes elastic fluctuations on length scales on the order of the decay length of the force constant matrix; allowing for straightforward development of new relations between the bending and stretching properties of nanomechanical resonators, which prove to be much more accurate than the continuum-based relations currently employed in experimental analysis.
(cont.) This theory is then used to link features of the underlining electronic structure to the local elastic response in silicon nanoresonators, emphasizing the importance of electronic structure on the local and overall elastic response. Our final system of study focuses on the longest length scales, the continuum. It is shown that the inclusion of electronic structure is crucial in the study of the role of dislocations on the macroscopic property of slip. This thesis explores the discrepancy between experimental data and theoretical calculations of the lattice resistance in bcc metals. This thesis presents results for the temperature dependence of the Peierls stress and the first ab initio calculation of the zero-temperature Peierls stress which employ periodic boundary conditions. The ab initio value for the Peierls stress is over five times larger than current extrapolations of experimental lattice resistance to zero-temperature. Although it is found that the common techniques for such extrapolation indeed tend to underestimate the zero-temperature limit, in this work it is shown that other mechanisms other than the simple Peierls mechanism are important in controlling the process of low temperature slip.
by Darren Eric Segall.
Ph.D.

A positive muon can be considered an isotope of hydrogen due to similarities in spin and charge. For metal hydride systems, the muon enters the sample "as the last hydrogen added," and competes for the same sites as the hydrogen atoms. to observe the site competition and diffusion of both particles (muon and proton), several FCC metal hydrides, TiH{dollar}\sb{lcub}1.83{rcub}{dollar}, TiH{dollar}\sb{lcub}1.97{rcub}{dollar}, TiH{dollar}\sb{lcub}1.99{rcub}{dollar}, YH{dollar}\sb{lcub}1.77{rcub}{dollar}, YH{dollar}\sb2{dollar}, ZrH{dollar}\sb{lcub}1.94{rcub}{dollar}, and LaH{dollar}\sb{lcub}2.06{rcub}{dollar}, were studied using transverse-, zero-, and low longitudinal-field {dollar}\mu{dollar}SR. The low temperature region results indicate that the muon predominately occupies octahedral sites for the FCC metal hydrides in this study. The probability for a muon to occupy a tetrahedral site in titanium and zirconium hydrides at these temperatures is proportional to the vacancy concentration. Whereas the probability for T site occupation in yttrium hydride is proportional to the number of protons not occupying these sites which increases with hydrogen concentration. Muon T site occupancy below room temperature for LaH{dollar}\sb{lcub}2.06{rcub}{dollar} was not observed and was not expected since these sites are occupied by protons. Around 300 K, the muon diffuses over interstitial O sites to vacancies in the H sublattice of TiH{dollar}\sb{lcub}1.99{rcub}.{dollar} The vibration of the hydrogen lattice is found to be the mechanism responsible for the activation of the muon out of the O site. Above room temperature, the muon occupies tetrahedral sites in yttrium and titanium hydrides. at high temperatures, the field-correlation time for a muon in titanium and yttrium hydrides is approximately one to two orders of magnitude greater than for a proton as measured by NMR. The results of a Monte Carlo simulation indicate that the presence of the muon inhibits the motion of the nearest-neighbor protons at high temperatures. The dynamics of the proton spins are observed by zero- and low longitudinal-field {dollar}\mu{dollar}SR through the oscillation of the muon polarization at long times for a static muon in a T or O site. This observation is not predicted by the Kubo-Toyabe treatment for a stationary muon.

Micro- and nano-mechanical resonators with low mass and high vibrational frequency are often studied for applications in mass and force detection where they can offer unparalleled precision. They are also excellent systems with which to study nonlinear phenomena and fundamental physics due to the numerous routes through which they can couple to each other or to external systems.

In this work we study the structural, thermal, and nonlinear properties of various micro-mechanical systems. First, we present a study of graphene-coated silicon nitride membranes; the resulting devices demonstrate the high quality factors of silicon nitride as well as the useful electrical and optical properties of graphene. We then study nonlinear mechanics in pure graphene membranes, where all vibrational eigenmodes are coupled to one another through the membrane tension. This effect enables coherent energy transfer from one mechanical mode to another, in effect creating a graphene mechanics-based frequency mixer. In another experiment, we measure the resonant frequency of a graphene membrane over a wide temperature range, 80K - 550K, to determine whether or not it demonstrates the negative thermal expansion coefficient predicted by prevailing theories; our results indicate that this coefficient is positive at low temperatures – possibly due to polymer contaminants on the graphene surface – and negative above room temperature. Lastly, we study optically-induced self-oscillation in metal-coated silicon nitride nanowires. These structures exhibit self-oscillation at extremely low laser powers (~1μW incident on the nanowire), and we use this photo-thermal effect to counteract the viscous air-damping that normally inhibits micro-mechanical motion.

The propsect of designing technologies around the quantum behavior of mesoscopic devices is enticing. This thesis present several tools to facilitate the process of calculating and analyzing the quantum properties of such devices – resonance, boundary conditions, and the quantum-classical correspondence are major themes that we study with these tools. In Chapter 1, we begin by laying the groundwork for the tools that follow by defining the Hamiltonian, the Green’s function, the scattering matrix, and the Landauer formalism for ballistic conduction. In Chapter 2, we present an efficient and easy-to-implement algorithm called the Outward Wave Algorithm, which calculates the conductance function and scattering density matrix when a system is coupled to an environment in a variety of geometries and contexts beyond the simple two-lead schematic. In Chapter 3, we present a unique geometry and numerical method called the Boundary Reflectin Matrix that allows us to calculate the full scattering matrix from arbitrary boundaries of a lattice system, and introduce the phenomenon of internal Bragg diffraction. In Chapter 4, we present a new method for visualizing wavefunctions called the Husimi map, which uses measurement by coherent states to form a bridge between the quantum flux operator and semiclassics. We extend the formalism from Chapter 4 to lattice systems in Chapter 5, and comment on our results in Chapter 3 and other work in the literature. These three tools – the Outward Wave Algorithm, the Boundary Reflection Matrix, and the Husimi map – work together to throw light on our interpretation of resonance and scattering in quantum systems, effectively codifying the expertise developed in semiclassics over the past few decades in an efficient and robust package. The data and images that they make available promise to help design better technologies based on quantum scattering.
Physics

The structures of two electron defect systems in alkali halide crystals are studied. The systems which have been studied include: two electrons localized at an anion vacancy (F$\sp\prime$-centre); positronium self-trapped at an anion vacancy (Fe$\sp+$-centre); positron self-trapped at a cation vacancy (F$\sb{\rm anti}$-centre); positronium self-trapped at an interstice; and positronium in a Bloch state. An improved version of the extended-ion method which is based on the one electron Hartree-Fock approximation is used to perform these calculations. Its main feature is the exclusive use of floating 1s Gaussian functions as basis. For the multi-electron defect systems, the calculation of matrix elements of two electron interaction terms is a most difficult problem. We developed an effective approach to treat this interaction approximately. The correlation effect of defect electrons is partly accounted for by properly arranged Gaussian basis. The binding energy, thermal dissociation energy, and transition energy between ground state and excited state are calculated for F$\sp\prime$-centres. A defect model with negative-U properties was introduced to interpret the deeply bound F$\sp\prime$-centre. Calculations of positron binding energies are made for Fe$\sp+$-centres and F$\sb{\rm anti}$-centres. In addition, we evaluate the angular correlation and lifetime of an annihilated electron-positron pair for Fe$\sp+$-centres, localized positronium and Bloch state positronium. The observed phenomena such as the transition of positronium from Bloch state to localized state, and the crystallographic effect are examined theoretically. The calculated results regarding various properties of crystals are in reasonably good agreement with experiment.

This thesis delves into a study of phases of strongly correlated quantum matter confined to two spatial dimensions. The thesis can broadly be divided into three parts. In the first part, comprising of chapters 2 and 3, we investigate some interesting aspects of symmetry breaking and quantum criticality in the superconducting phase of the iron-based superconductors. In particular, motivated by tunneling microscopy measurements on FeSe, in chapter 2 we study the effect of spontaneously broken rotational symmetry on the structure of the superconducting vortex. In chapter 3, we study the critical singularities associated with the superfluid-density at a wide class of symmetry-breaking and topological phase transitions in a clean superconductor. Inspired by experiments on BaFe$_2$(As$_{1-x}$P$_x$)$_2$, we also analyze the effect of quenched disorder on the superfluid-density in the vicinity of magnetic quantum critical points. The second part of this thesis, consisting of chapters 4 and 5, is devoted to a study of the pseudogap phase in the underdoped cuprates. In chapter 4 we study the effect of thermal fluctuations of various competing order parameters, including preformed superconductivity and short-ranged charge-density wave, on the electronic excitations. In chapter 5 we analyze the feedback of pairing fluctuations on the landscape of various competing charge-density wave order parameters within the framework of fermi-liquid theory. In the final part of the thesis, consisting of chapters 6 and 7, we propose an alternative picture for describing the pseudogap metal. In chapter 6, we study a quantum-disordered phase of matter---the fractionalized fermi-liquid (FL*)---where the electrons are coupled to the fractionalized excitations of a strongly fluctuating antiferromagnet and propose it to be a candidate state for the pseudogap. We investigate instabilities of the FL* to density-wave order and compare with experiments. In chapter 7, we describe a framework for describing a novel quantum phase transition without any broken-symmetries---a Higgs transition---that describes a transition from a conventional fermi-liquid to a parent phase of the FL* state via an intermediate non-fermi liquid. We discuss its possible connection to the optimal doping critical point in the cuprates.
Physics

Originally proposed in high energy physics as particles, which are their own anti-particles, Majorana fermions have never been observed in experiments. However, possible signatures of their condensed matter analog, zero energy, charge neutral, quasiparticle excitations, known as Majorana zero modes (MZMs), are beginning to emerge in experimental data. The primary method of engineering topological superconductors capable of supporting MZMs is through proximity-coupled semiconductor nanowires with strong Rashba spin-orbit coupling and an applied magnetic field. Recent tunneling transport experiments involving these materials, known as semiconductor-superconductor heterostructures, were capable for the first time of measuring quantized zero bias conductance plateaus, which are robust over a range of control parameters, long believed to be the smoking gun signature of the existence of MZMs. The possibility of observing Majorana zero modes has garnered great excitement within the field due to the fact that MZMs are predicted to obey non-Abelian quantum statistics and therefore are the leading candidates for the creation of qubits, the building blocks of a topological quantum computer. In this work, we first give a brief introduction to Majorana zero modes and topological quantum computing (TQC). We emphasize the importance that having a true topologically protected state, which is not dependent on local degrees of freedom, has with regard to non-Abelian braiding calculations. We then introduce the concept of partially separated Andreev bound states (ps-ABSs) as zero energy states whose constituent Majorana bound states (MBSs) are spatially separated on the order of the Majorana decay length. Next, through numerical calculation, we show that the robust 2 e²/h zero bias conductance plateaus recently measured and claimed by many in the community to be evidence of having observed MZMs for the first time, can be identically created due to the existence of ps-ABSs. We use these results to claim that all localized tunneling experiments, which have been until now the main way researchers have tried to measure MZMs, have ceased to be useful. Finally, we outline a two-terminal tunneling experiment, which we believe to be relatively straight forward to implement and fully capable of distinguishing between ps-ABSs and true topologically protected MZMs.

The coherent response of a semiconductor three-state system to one or two intense light pulses is investigated experimentally on a 100 fs time scale. Three experiments constitute this dissertation: observation of excitonic Rabi oscillations, measurement of two-exciton coupled Stark shifting, and an attempt to observe dark states. Basic concepts of time-resolved ultrafast semiconductor spectroscopy are explained, followed by an analysis of semiconductor two- and three-state systems. Pure two- and three-state dynamics are derived from first principles, followed by the development of the appropriate semiconductor Bloch equations (SBE). Two-color pump-probe, two-color pump-pump, and pump-pump-probe techniques are explained in the context of three-state semiconductor experiments. The experimental setup is explained in detail. Resonant two-color pump-probe measurements resulted in the first observation of multiple excitonic Rabi oscillations. The common conduction band shared by the light-hole and heavy-hole excitons of an InGaAs multiple quantum well allowed us to measure hh-exciton density (Rabi) oscillations by probing lh-exciton absorption. By studying the intensity dependence of the Rabi frequency, we showed the important role of many-body effects in renormalizing the dipole energy. The shared conduction band also causes the lh-exciton resonance to Stark shift when the hh exciton is Stark shifted. We measured a transient Stark shifting of both resonances due to virtual hh-exciton transitions. We observed that the ratio of the hh-exciton shift to lh-exciton shift was 2:1 at large pump-exciton detuning, as predicted from a simple three-state dressed exciton picture. For smaller detunings we saw an increase in the ratio and a redshift of the non-dipole coupled exciton state. Both of these observations are consistent with the most recent theories and experiments on excitonic Stark shifting. For strong near-resonant pumping of both lh- and hh-exciton transitions, an intervalence-band Raman-type coherence follows from the SBE that results in a transparent eigenstate (dark state) when both pumps are equally detuned from resonance. The existence of this coherence is well-known in atomic-optical systems, but has been elusive in semiconductors. Our inconclusive experimental result is presented along with an evaluation of experimental shortcomings. In brief, the expected change is absorption was too small to see.

We have studied the exchange bias interaction in metal bilayers IrMn/Co and FeMn/Co using the static and ultrafast pump-probe Kerr effects. Experiments conducted on wedged Co samples show that the exchange bias interaction is sensitive to the buffer layers grown beneath it when the antiferromagnetic layer is FeMn. The exchange bias strength, as measured by the shift in the magnetic hysteresis loop, follows a 1/tFM dependence as reported in the literature. The time-domain pump-probe experiments reveal coherent magnetization oscillations, whose frequencies are comparable to those measured by frequency-domain FMR measurements, and they fit well to FMR equations for the frequency. We have also been able to use the pump beam to permanently alter the exchange bias interface which leads to the launching of oscillations along new geometries, particularly along the easy axis where magnetization is aligned with the applied field. This is explained qualitatively by showing that the pump has enough energy to overcome the energy barrier in the AF, allowing it to flip and provide a torque on the magnetization that launches oscillations.