Gotowa bibliografia na temat „Matter phases classification”

The physics of iron pnictides has been the subject of intense research for half a decade since the discovery of superconductivity in doped LaFeAsO in 2008. By now there exists a large number of different materials that are summarized under the term "pnictides'' with significant differences in their crystal structure, electronic properties, and their phase diagrams. This thesis is concerned with the investigation of the various phase transitions that are observed in the underdoped compounds of the pnictide subgroups RFeAsO, where R is a rare-earth element, and AFe_2As_2, where A is an alkaline-earth element. These compounds display two closely bound transitions from a tetragonal to an orthorhombic phase and from a paramagnetic to an antiferromagnetic metal. Both symmetry-broken phases are suppressed by doping or pressure and close to their disappearance superconductivity sets in. The superconducting state is stabilized until some optimal doping or pressure is reached and gets suppressed thereafter. The central goal of this thesis is to improve our understanding of the interplay between these three phases and to describe the various phase transitions. We start from an itinerant picture that explains the magnetism as a result of an excitonic instability and show how the other phases can be included into this picture. This approach is based on the the observation that the compounds we are interested in have a Fermi surface with multiple nested electron and hole pockets and that they have small to intermediate interaction strengths. The thesis starts with a study of the doping dependence of the antiferromagnetic phase transition in four different five-orbital models. We use the random-phase approximation to determine the transition temperature, the dominant ordering vector, and the contribution of the different orbitals to the ordering. This allows us to identify the more realistic models, which give results that are in good agreement with experimental observations. In addition to the frequently made assumption of orbital-independent interaction potentials we study the effect of a reduction of the interaction strengths that involve the d_{xy} orbital. We find that this tunes the system between two different nesting instabilities. A reduction of the interactions that involve the d_{xy} orbital also enhances the tendency towards incommensurate (IC) order. For a weak reduction this tendency is compensated by the presence of the orthorhombic phase. However, for a reduction of 30%, as it is suggested by constrained random-phase-approximation calculations, we always find large doping ranges, where a state with IC order has the highest transition temperature. We continue the investigation of the magnetic phase transition by studying the competition of different possible types of antiferromagnetic order that arises from the presence of two degenerate nesting instabilities with the ordering vectors (pi,0) and (0,pi). We derive a Ginzburg-Landau free energy from a microscopic two-band model and find that the presence of the experimentally observed stripe phase strongly depends on the number and size of the hole pockets in the system and on the doping. We show that within the picture of a purely magnetically driven nematic phase transition, which breaks the C_4 symmetry and induces the orthorhombic distortion, the nematic phase displays exactly the same dependence on the model parameters as the magnetic stripe phase. We propose that in addition to the purely magnetically driven nematic instability there is a ferro-orbital instability in the system that stabilizes the nematic transition and, thus, explains the experimentally observed robustness of the orthorhombic transition. We argue that including a ferro-orbital instability into the picture may also be necessary to reproduce the transition from simultaneous first-order transitions into an orthorhombic antiferromagnetic state to two separate second-order transitions, which is observed as a function of doping. Finally, a study of the superconducting phase transition inside the antiferromagnetic phase that is observed in some pnictide compounds is presented. We present an approach to calculate the fluctuation-mediated pairing interaction in the spin-density-wave phase of a multiband system, which is based on the random-phase approximation. This approach is applied to a minimal two-band model for the pnictides to study the effect of the various symmetry-allowed bare on-site interactions on the gap symmetry and structure. We find a competition between various even- and odd-parity states and over a limited parameter range a p_x-wave state is the dominant instability. The largest part of the parameter space is dominated by even parity states but the gap structure sensitively depends on the bare interactions. We propose that the experimentally observed transition from a nodeless to a nodal gap can be due to changes in the on-site interaction potentials.

<p>In this thesis, we study gapped topological phases of matter in systems with strong inter-particle interaction. They are challenging to analyze theoretically, because interaction not only gives rise to a plethora of phases that are otherwise absent, but also renders methods used to analyze non-interacting systems inadequate. By now, people have had a relatively systematic understanding of topological orders in two spatial dimensions. However, less is known about the higher dimensional cases. In Chapter 2, we will explore three dimensional long-range entangled topological orders in the framework of Walker-Wang models, which are a class of exactly solvable models for three-dimensional topological phases that are not known previously to be able to capture these phases. We find that they can represent a class of twisted discrete gauge theories, which were discovered using a different formalism. Meanwhile, a systematic theory of bosonic symmetry protected topological (SPT) phases in all spatial dimensions have been developed based on group cohomology. A generalization of the theory to group supercohomology has been proposed to classify and characterize fermionic SPT phases in all dimensions. However, it can only handle cases where the symmetry group of the system is a product of discrete unitary symmetries. Furthermore, the classification is known to be incomplete for certain symmetries. In Chapter 3, we will construct an exactly solvable model for the two-dimensional time-reversal-invariant topological superconductors, which could be valuable as a first attempt to a systematic understanding of strongly interacting fermionic SPT phases with anti-unitary symmetries in terms of exactly solvable models. In Chapter 4, we will propose an alternative classification of fermionic SPT phases using the spin cobordism theory, which hopefully can capture all the phases missing in the supercohomology classification. We test this proposal in the case of fermionic SPT phases with Z₂ symmetry, where Z₂ is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known fermionic SPT phases in space dimensions less than or equal to 3.</p>

The discovery of topological phases of quantum matter has brought about a new paradigm in the understanding of rich and exotic phases which fall outside the conventional classification of phases using Landau’s theory of broken symmetries. The thesis addresses various aspects of nonequilibrium and semiclassical dynamics in systems hosting such topological phases. While the study of nonequilibrium closed quantum systems is an exciting field in itself, it has gained a lot of importance in the context topological systems. Much of this has been fuelled by the immense progress in the experimental realisation of such topological systems with ultracold atoms in optical lattices. As measurements of real-time responses are natural in such experiments, they have served as ideal platforms to study the nonequilibrium responses of topological systems. The studies presented in this thesis can be brought under the umbrella of two broad questions, first, how non-equilibrium dynamics can be used to characterize topological phases or locate topological critical points, and second, what new topological phases can be realized out of equilibrium. Generally, non-trivial topology of a system manifests itself via quantised responses at the edges of a system or via appropriate non-local string order parameters which are rather difficult to measure in experiments. Local measurements in the bulk are more conducive to experiments. We address this question by showing that within a non-equilibrium setup obtained via a quantum quench, local bulk observables can show sharp signatures of topological quantum criticality via a non-analyticity in parameter space at the critical point. Although via non-local basis transformations, topological phase transitions can often be mapped onto conventional phase transitions, a remarkable aspect of this result is that within the non-equilibrium setup, the local bulk observables can locate the critical point in the natural basis where the phase transition is topological and not described by a local order parameter. The next question that the thesis explores is how nonequilibrium and semiclassical dynamics, more precisely wavepacket dynamics, can be used to probe topological phases with an emphasis on Chern insulators in two dimensions. Chern insulators are essentially similar to quantum Hall systems except that they show quantised Hall responses in the absence of external magnetic fields due to intrinsically broken time-reversal symmetry. The Hall conductance in these systems is related to an integer-valued topological invariant characterising the energy bands, known as the Chern number, which is the net flux of Berry curvature through the entire two-dimensional Brillouin zone. The Berry curvature modifies the semiclassical equations of motion describing the dynamics of a wavepacket. Hence, the real-time motion of a wavepacket is used to map out the Berry curvature and thence the topology of the band. Complementary to these bulk responses, spatially local quenches in Chern insulators are also shown as probes for the presence or absence of chiral edge modes. The idea of semiclassical equations of motion can be extended to the case of a three-dimensional Weyl semimetal. Weyl semimetals are a new class of gapless topological systems in three dimensions, elementary fermionic excitations of which are described by the Weyl equation. Since in cold atom experiments, magnetic fields are realized synthetically via phases in complex hoppings, exploring the Hofstadter limit is a natural scenario. When the magnetic field penetrating a two-dimensional system becomes so large that the associated magnetic length becomes comparable to the lattice spacing, the energy spectrum of the system is described by fractal known as the Hofstadter butterfly. We introduce the Weyl butterfly, a set of fractals which describes the spectrum of a Weyl semimetal subjected to a magnetic field, and we characterize the fractal set of Weyl nodes in the spectrum using wavepacket dynamics to reveal their chirality and location. Moreover, we show that the chiral anomaly -- a hallmark of the topological Weyl semimetal -- does not remain proportional to the magnetic field at large fields, but rather inherits a fractal structure of linear regimes as a function of external field. Finally, the thesis addresses the question of novel nonequilibrium topological phases of matter. In the context of phase structures of nonequilibrium systems, periodically driven, also known as Floquet systems, has received a lot of attention. Moreover, the role of disorder has been shown to be rather crucial as generically such Floquet systems heat up to featureless infinite temperature states. Also, in the context of topological systems like Chern insulators, disorder is expected to play an interesting role given that it is important in localising the bulk cyclotron orbits in an integer quantum Hall system. With this motivation, the phase diagram of the disordered Chern insulator with a Floquet drive is explored in the thesis. In the model considered there are indeed topological Floquet edge modes which are exclusive to Floquet systems, for instance, the edge modes in gaps of the quasienergy spectrum around ±pi. There are also disorder-induced topological transitions between different Floquet topological phases, due to a mechanism shown to be of levitation-annihilation type.

<p>We study aspects of gapped phases of matter, focusing on their classification, including the group law under stacking, and their relation to topological quantum field theories (TQFT). In one spatial dimension, it is well-known that Matrix Product States (MPS) efficiently approximate ground states of gapped systems; by showing that these states arise naturally in 1 + 1-dimensional lattice TQFT, which in turn are closely related to continuum TQFT, we provide a concrete connection between ground states of lattice systems and TQFT in 1 + 1 dimensions. We generalize this to systems with symmetries and fermions, and obtain a classification and group law for the stacking of 1 + 1-dimensional symmetry-protected topological phases. Further, we study the effect of turning on/off interactions for the classification: the phase classification of a given symmetry class of Hamiltonians can be different depending on whether we allow interactions or not, and in low dimensions we provide some concrete formulas relating the phases under the non-interacting classification and those under the interacting classification. Lastly, we study the phases of the 2 + 1-dimensional topological superconductor, and show that for all 16 phases braiding statistics of vortices, which determine the underlying TQFT, can be obtained by stacking layers of the basic <i>p</i> + <i>ip</i> superconductor.</p>

Classification of phases of matter has long been a central point of interest in the research community in condensed matter physics. Over the past several decades mainly two kinds of classification schemes have emerged, namely, one related to spontaneous symmetry breaking and the other to symmetry invariant topological classification. Although the latter one is fairly new, a lot of progress has been made over the past couple of decades, but still these two classification schemes are generally treated separately. In this thesis, I discuss systems where both the classification schemes need to be invoked due to the interplay of interaction and topology and their effect on each other. In the first piece of work, I present the theory of a new type of topological quantum order which is driven by the spin-orbit density wave order parameter and distinguished by Z2 topological invariant. The resulting quantum order parameters break translational symmetry but preserve time-reversal symmetry. Consequently, the system is inherently associated with a Z2 topological invariant along each density wave propagation direction which makes it a weak topological insulator in two dimensions, with an even number of spin-polarized boundary states. In the second work, I discuss the effect of the parent topological ground state on the local order. In particular, I focus on a well-studied (experimentally) material TlCuCl3 and show that it has unique unexplored topological properties which arise when a time-reversal breaking antiferromagnetic order parameter sets into the system and how they can explain the uncanny properties of this material such as unconventional paramagnon lifetime, finite Higgs mass across the phase transition, among other. In the last work, I discuss our attempt to confirm the presence of bosonic integer and fractional quantum hall effect in an interacting lattice model. The model consists of bosons spread over the honeycomb lattice with the nearest neighbour and next nearest correlated hopping with flux per hexagon. I provide evidence for the presence of integer as well as fractional quantum Hall states and also a superfluid state, for different fillings and tuning parameters. I have used mean-field theory and path integral methods as the theoretical tools to study the above problems. Furthermore, I have also used numerical methods such as Density Functional Theory (DFT, as implemented in VASP) and exact diagonalization (using Lanczos algorithm) where appropriate. As I have shown in the thesis, a large number of interesting results emerge from these studies, leading to a better understanding of the problems and uncovering some interesting underlying physics. Overall, this thesis brings forth some notable and interesting possibilities in understanding the physics of topological state of mater. An idea that stands out is that effect of topological phase onto the symmetry breaking phase and vice-versa. This will have an important impact on the future studies in the related area and to find a unified theory of phase transitions which incorporate both symmetry breaking and topological transition together along with more sophisticated like inclusion of Gaussian fluctuations on the top of the mean-field.

Active matter describes systems that convert energy from their environment into directed motion. Therefore, these systems are in intrinsic nonequilibrium, unlike their passive counterparts. From a theoretical point of view, such active systems have been modeled by agent-based models, as well as hydrodynamic approaches, which allowed for the investigation of a wide range of observed collective phenomena characterizing active matter. In this thesis we develop a microscopic field-theoretical approach to describe generic properties of active systems. This description combines the phase field crystal model with a polar order parameter and a self-propulsion term. First, we validate this approach by reproducing results obtained with corresponding agent-based models, such as binary collisions, collective migration and vortex formation. We also perform a direct comparison between our model and a microscopic phase field description of active matter. Next, we use this continuum approach to simulate some larger active systems and to analyze the coarsening process in active crystals, as well as the mechanisms leading to mobile clusters. We show the generality of our approach by extending it to binary mixtures of interacting active and passive particles. Also in this case, we first validate the model by reproducing known results, such as enhanced crystallization via active doping and the suppression of collective migration in an active bath in the presence of fixed obstacles. Interestingly, for the regime of mobile passive particles in an active bath a laning state is found, which is characterized by an alignment of the active particles that is globally nematic, but polar within each lane. This state represents a theoretical prediction feasible to be validated experimentally. Finally, we explore the field of topological active matter. We develop an agent-based model to describe self-propelled particles on curved surfaces and study the complex spatiotemporal patterns that emerge.<br>Aktive Materie beschreibt Systeme, die Energie aus ihrer Umgebung in gerichtete bewegung umwandeln. Im Gegensatz zur passiven Materie befinden sich diese Systeme nie im physikalischen Gleichgewicht und offenbaren dadurch interessante physikalische Phänomene. Vom theoretischen Standpunkt her wurde aktive Materie bereits simuliert, typischerweise durch agenten-basierte Modelle oder hydrodynamische Ansätze, die es ermöglichen eine Vielzahl der auftretenden kollektiven Bewegungsprinzipien zu untersuchen. In dieser Doktorarbeit entwickeln wir einen mikroskopischen Kontinuumsansatz um die generischen Eigenschaften von aktiven Systemen zu untersuchen. Unsere Beschreibung kombiniert das Phasenfeld-Kristall Modell mit einem polaren Ordnungsparameter und einem Antriebsterm. Zuerst validieren wir den Ansatz durch Reproduktion bekannter Ergebnisse agenten-basierter Modelle, wie binäre Kollisionen, kollektive Bewegung und Wirbelformationen. Des Weiteren führen wir einen direkten Vergleich zwischen unserem Modell und einer mikroskopischen Phasenfeldbeschreibung aktiver Materie durch. Danach nutzen wir den kontinuierlichen Ansatz um große aktive Systeme zu simulieren und analysieren den Vergröberungsprozess in aktiven Kristallen und Mechanismen der mobilen Aggregatbildung. Wir illustrieren die Allgemeingültigkeit unseres Simulationsansatzes durch die Erweiterung auf binäre Systeme, in denen sowohl aktive als auch passive Partikel enthalten sind. Auch in diesem Fall validieren wir das Modell durch Vergleiche mit bekannten Resultaten, wie zum Beispiel die verstärkte Kristallisation durch aktives Doping oder die Unterdrückung kollektiver Bewegung durch die Einführung von Hindernissen in einem aktiven Bad. Interessanterweise finden wir bei der Präsenz mobiler passiver Partikel in einem aktiven Bad einen Fahrspur-Zustand, in welchem die aktiven Partikel nematische Fahrspuren bilden und sich nur jeweils innerhalb einer Fahrspur nematisch polar anordnen. Dieser bisher unbekannte Zustand stellt eine theoretische Vorhersage dar, die experimentell geprüft werden kann. Schließlich begeben wir uns auf das Gebiet der topologischen aktiven Materie. Wir entwickeln ein agenten-basiertes Modell um selbst-angetriebene Partikel auf gekrümmten Oberflächen zu beschreiben und untersuchen die dabei auftretenden zeitlich und räumlich komplexen Muster.%, die dabei auftreten.