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Strongly correlated materials manifest some of the most intriguing behaviors found in condensed matter physics. However, their understanding remains a challenge because they cannot be described using standard theoretical approaches, as such systems are complex and typically have many competing degrees of freedom. Many strongly correlated systems are realized in layered or highly anisotropic materials, and they behave as effectively two-dimensional systems. When the dimensionality is reduced, fluctuations due to the competition between degrees of freedom are more pronounced and easier to observe. Anomalous transport properties are one of the hallmarks of strongly correlated materials; thus, charge transport measurements have proven remarkably effective for their study. This thesis focuses on three very different two-dimensional (2D) materials using charge transport to understand the origin of some of the observed behaviors. The electron system (ES) in Si metal-oxide-semiconductor field-effect transistors (MOSFETs) is a model strongly correlated system with only the interplay of Coulomb interactions and disorder. The insight from this simple system can help to build a more general picture of strongly correlated materials. Second, atomically thin layers of WSe2 produce a unique 2D system to study the universality of the correlated phenomena observed in Si MOSFETs. Finally, the Cu-O planes of La-214 compounds with charge and spin stripe order are complex materials, which behave effectively as 2D, with the interplay of many orders. By varying the dopant of the La-214 compound, the origin of the correlated behaviors can be probed. In the first two materials, the 2D MIT is controlled by applying a gate voltage. The existence of the 2D MIT is supported by an abundance of experimental data but remains poorly understood. Within experimental systems, both electron-electron interactions and disorder are present; however, the theory of their interplay is not fully developed. Studies performed on highly disordered Si MOSFETs suggest the importance of Coulomb interactions for the glassy dynamics observed at low electron densities. Therefore, the first study discussed in this thesis explores relaxations of conductivity in a strongly disordered 2DES with screened Coulomb interactions after the system is quenched-revealing the necessity of long-range Coulomb interactions for the existence of the collective (glassy) relaxation dynamics. Additionally, we have shown that, in the 2DES of the Si MOSFET weakly thermally coupled to the environment, abnormally long relaxations are observed in the presence of short-range interactions, suggesting that the system is in the proximity to a many-body-localized phase. Thus our results also demonstrate a promising new platform for exploring the breakdown of thermalization and MBL in real materials. Evidence of quantum criticality associated with the MIT has been almost exclusively studied in Si MOSFETs. Our second study reveals quantum criticality in WSe2 field-effect transistors showing that transition metal dichalcogenides are viable systems for the low-temperature investigation of the 2D MIT. Our scaling analysis found that the critical exponents agree with those found in low-disordered Si MOSFETs in the presence of local magnetic moments. These findings pave the way for further studies of the fundamental quantum mechanical properties of 2D transition metal dichalcogenides. The final study focuses on fluctuations of charge order (CO) and the magnetoresistance (MR) of stripe-ordered La-214 cuprates. The dynamics of CO are thought to be relevant for the unconventional properties of the normal state and high-temperature superconductivity. We report observations of dynamic charge stripes close to the charge order (and structural) transition in response to temperature perturbations but absent in magnetic field in La1.875Ba0.125CuO4. These dynamic behaviors are only observed when the transition is approached from the charge-ordered state. Additionally, a comparative analysis of the MR of several La-214 single crystals is presented to establish which behaviors are characteristic of the family of materials as opposed to dopant specific. Together, these three studies contribute to understanding the complex interplay of orders found in strongly correlated materials.
The two experimental studies reported in this thesis contribute important new knowledge about phase transitions in two-dimensional complex plasmas: in one case a determination of the coupling parameter (ratio of mean potential to mean kinetic energy of the particles in an ensemble), and in the other a detailed characterization of the non-equilibrium recrystallization of a two-dimensional system. The latter results are used to establish the connection between structural order parameters and the kinetic energy, which in turn gives novel insights into the underlying physical processes determining the two-dimensional phase transition.
Phase Transition Dynamics, first published in 2002, provides a fully comprehensive treatment of the study of phase transitions. Building on the statistical mechanics of phase transitions, covered in many introductory textbooks, it will be essential reading for researchers and advanced graduate students in physics, chemistry, metallurgy and polymer science.
Systems with competing energy scales are widespread and exhibit rich and subtle behaviour, although their systematic study is a relatively recent activity. This text presents lectures given at a NATO Advanced Study Institute reviewing the current knowledge and understanding of this fascinating subject, particularly with regard to phase transitions and dynamics, at an advanced tutorial level. Both general and specific aspects are considered, with competitions having several origins; differences in intrinsic interactions, interplay between intrinsic and extrinsic effects, such as geometry and disorder; irreversibility and non-equilibration. Among the specific physical application areas are supercooled liquids and glasses, high-temperature superconductors, flux or vortex pinning and motion, charge density waves, domain growth and coarsening, and electron solidification.
The Advanced Study Institute (AS I) entitled "Phase Transitions in Surface Films" was held at the Ettore Majorana Centre for Scientific Culture in Erice, Sicily from June 19 to June 29, 1990. It reviewed the present understanding (experimental and theoretical) of phase transitions of surfaces, interfaces, and thin ftlms as well as the related structural and dynamical properties of these systems. From its inception, this ASI was envisioned as a sequel to one of the same title organized eleven years earlier by J. G. Dash and J. Ruvalds which was also held at the Ettore Majorana Centre. The previous ASI reflected the progress which had been made in understanding quasi two-dimensional (2D) states of matter, particularly adsorbed monolayers, and the phase transitions which occur in them. At that time, the field was barely ten years old. The modern field to which we are referring here can be traced to the landmark experiments of A. Thorny and X. Duval. Beginning in 1967, they published a series of papers presenting evidence from vapor pressure measurements of 2D phases of krypton and other gases adsorbed on polycrystalline (exfoliated) graphite. Their work led to a large number of thermodynamic and scattering experiments on physisorbed ftlms. This in turn motivated a great deal of theoretical interest in 2D systems and their phase transitions.
Describing the physical properties of quantum materials near critical points with long-range many-body quantum entanglement, this book introduces readers to the basic theory of quantum phases, their phase transitions and their observable properties. This second edition begins with a new section suitable for an introductory course on quantum phase transitions, assuming no prior knowledge of quantum field theory. It also contains several new chapters to cover important recent advances, such as the Fermi gas near unitarity, Dirac fermions, Fermi liquids and their phase transitions, quantum magnetism, and solvable models obtained from string theory. After introducing the basic theory, it moves on to a detailed description of the canonical quantum-critical phase diagram at non-zero temperatures. Finally, a variety of more complex models are explored. This book is ideal for graduate students and researchers in condensed matter physics and particle and string theory.
This work addresses dynamical aspects of quantum criticality in two space dimensions. It probes two energy scales: the amplitude (Higgs) mode, which describes fluctuations of the order parameter amplitude in the broken symmetry phase and the dual vortex superfluid stiffness. The results demonstrate that the amplitude mode can be probed arbitrarily close to criticality in the universal line shape of the scalar susceptibility and the optical conductivity. The hallmark of quantum criticality is the emergence of softening energy scales near the phase transition. In addition, the author employs the charge-vortex duality to show that the capacitance of the Mott insulator near the superfluid to insulator phase transition serves as a probe for the dual vortex superfluid stiffness. The numerical methods employed are described in detail, in particular a worm algorithm for O(N) relativistic models and methods for numerical analytic continuation of quantum Monte Carlo data. The predictions obtained are particularly relevant to recent experiments in cold atomic systems and disordered superconductors.
This book discusses some scaling properties and characterizes two-phase transitions for chaotic dynamics in nonlinear systems described by mappings. The chaotic dynamics is determined by the unpredictability of the time evolution of two very close initial conditions in the phase space. It yields in an exponential divergence from each other as time passes. The chaotic diffusion is investigated, leading to a scaling invariance, a characteristic of a continuous phase transition. Two different types of transitions are considered in the book. One of them considers a transition from integrability to non-integrability observed in a two-dimensional, nonlinear, and area-preserving mapping, hence a conservative dynamics, in the variables action and angle. The other transition considers too the dynamics given by the use of nonlinear mappings and describes a suppression of the unlimited chaotic diffusion for a dissipative standard mapping and an equivalent transition in the suppression of Fermi acceleration in time-dependent billiards. This book allows the readers to understand some of the applicability of scaling theory to phase transitions and other critical dynamics commonly observed in nonlinear systems. That includes a transition from integrability to non-integrability and a transition from limited to unlimited diffusion, and that may also be applied to diffusion in energy, hence in Fermi acceleration. The latter is a hot topic investigated in billiard dynamics that led to many important publications in the last few years. It is a good reference book for senior- or graduate-level students or researchers in dynamical systems and control engineering, mathematics, physics, mechanical and electrical engineering.
This article reviews recent experimental studies of the phase transitions which occur on reconstructed surfaces and in layers of chemisorbed atoms. Emphasis is given to systems which exhibit continuous transitions. The experimental results are presented in the context of current theories which emphasize the roles of symmetry, dimensionally and universality. The limitations currently imposed by sample quality and experimental techniques are also discussed. Results from individual systems are surveyed and promising future directions including studies of finite size effects are discussed.