Publications

Popular summary: In all kinds of materials, there are defects. Some of these are topological and are somewhat hard to describe mathematically - partly because they are usually described in terms of point objects. In this paper, we addressed this issue by introducing a framework where the defects have some extent, which enables a deeper understanding into how they interact with each other. 

Technical summary: Topological defects and smooth excitations determine the properties of systems showing collective order. We introduce a generic non-singular field theory that comprehensively describes defects and excitations in systems with O(n) broken rotational symmetry. Within this formalism, we explore fast events, such as defect nucleation/annihilation and dynamical phase transitions where the interplay between topological defects and non-linear excitations is particularly important. To highlight its versatility, we apply this formalism in the context of Bose-Einstein condensates, active nematics, and crystal lattices.

Symmetry, topology, and crystal deformations: a phase-field crystal approach 

Popular summary: Crystalline materials are the backbone of modern technology, from semiconductors to structural materials. The properties of these materials, including their strength, conductivity, and optical properties, are strongly influenced by their defects, such as dislocations. Despite their importance, our understanding of these defects still needs to be improved. The phase-field crystal approach is a relatively new tool that has emerged as a promising way to study crystalline materials. It is a remarkably versatile model, which allows for capturing both the elastic properties of crystals and the dynamics of their defects, including dislocations.In this thesis, we have used the phase-field crystal approach to study the nucleation and motion of dislocations under imposed stress and their interaction with elastic fields. Furthermore, we have extended this approach to various crystal symmetries and higher dimensions. As a result, the research provides new insights into the behavior of crystals under stress and strain. By improving our understanding of dislocation behavior and its impact on material properties, we can develop new materials with improved properties for various applications, such as electronics, energy storage, and transportation, which in turn may contribute to critical societal and economic issues, including sustainability, energy security, and technological innovation.

Technical summary: Crystalline materials are the backbone of modern technology, from semiconductors to structural materials. The properties of these materials, including their strength, conductivity, and optical properties, are strongly influenced by their defects, such as dislocations. Despite their importance, our current understanding of these defects still needs to be improved. The phase-field crystal approach is a relatively new tool that has emerged as a promising way to study crystalline materials. It is a remarkably versatile model, which allows for capturing both the elastic properties of crystals and the dynamics of their defects, including dislocations. In this thesis, I have used the phase-field crystal approach to study the nucleation and motion of dislocations under imposed stress and their interaction with elastic fields. Furthermore, I have extended this approach to various crystal symmetries and dimensions. As a result, my research provides new insights into the behavior of crystals under stress and strain. By improving our understanding of dislocation behavior and its impact on material properties, we can develop new materials with improved properties for various applications, such as electronics, energy storage, and transportation, which in turn may contribute to critical societal and economic issues, including sustainability, energy security, and technological innovation.

Symmetry, topology, and crystal deformations: a phase-field crystal approach 

Popular summary: If you press your ear to a railroad track, you can hear the sound of a hammer hitting it several miles away. The reason is that sound travels much faster in solids (like metal) than in air. In this article, we fixed a major deficiency with the phase-field crystal (PFC) models of solids, namely that they don't have sound waves in them.

Technical summary: Using principles of free energy minimization, we derive a phase-field crystal model coupled to a macroscopic velocity field that relaxes elastic waves. The motion of dislocations is driven by classical dissipative gradient descent PFC dynamics. We show that the model reproduces the behavior of dislocation dipoles that annihilate under imposed mechanical equilibrium and explicitly show how the elastic force density relaxes thereafter (picture). While similar approaches have been developed for the amplitude PFC models, these are not applicable to polycrystalline materials. Hence, we show that we can successfully apply the model also to such systems. 

Hydrodynamic phase field crystal approach to interfaces, dislocations and multi-grain networks 

Popular summary: Defects (weaknesses) in crystals form in lines, loops and squiggles (dislocation lines). In the third paper of my PhD we studied how these loops behave. The article uses notions from topology (a field of mathematics) to describe and track the evolution of these lines.

Technical summary: We derive a description of the dislocation density tensor in terms of the slowly varying amplitudes derived from the phase-field in a phase-field crystal (PFC) model. By differentiation with respect to time, we find a closed-form expression for the velocity of the dislocation lines, which are shown to move in response to the applied Peach-Koehler force. We then verify our results by studying the shrinkage of a shear dislocation loop.

A phase field crystal theory of the kinematics of dislocation lines 

Popular summary: In the second paper of my Ph.D. we explored how different types of crystals are stressed. In particular, we found an exact expression for the crystal stress in any phase-field crystal! 

Technical summary: We derive an expression for the stress tensor in any field theory based on a gradient expansion of the interaction (Ginzberg-Landau type) by using a variational formalism that also takes into account variations in the coarse-grained density. We apply the result to 5 different phase-field crystal (PFC) models, giving closed-form expressions for the stress tensor. 

Stress in ordered systems: Ginzburg-Landau-type density field theory 

Popular summary: What does creating a crystal crack from nowhere take? The first paper of my Ph.D. was devoted to finding answers to this question. We studied the defects' (dislocations, the two symbols in the figure) creation of defects using the phase-field crystal as a model for a real solid. 

Technical summary: We employ a model that constrains the phase-field crystal (PFC) model to mechanical equilibrium to add an external localized stress (indentation) to produce the nucleation of dislocations. We show that the lattice incompatibility field signals the onset of nucleation and that a simple Schmidt-based criterion is sufficient to determine the threshold stress needed to nucleate in this case. 

Dislocation nucleation in the phase-field crystal model 

Popular summary:  When rotating boson system lives in a complex multidimensional space. Based on the work of my Master's degree, we were able to identify certain simple structures that describe the lowest energy states.

Composite fermion basis for M-component Bose gases 

Popular summary: There are two types of particles in the universe - fermions and bosons. When squeezed into small spaces, fermions refuse to come close while bosons don't mind. In my Master's degree in theoretical physics, we tried to understand what happens when you take bosons of different species, squeeze them together like a pancake, and spin them around. At least theoretically.

Three M-Species Generalizations for Rotating Bose Gases in the Lowest Landau Level