Many theoretical descriptions of ordered systems, such as magnetic or ferroelectric systems, start from a homogeneous, low energy description of a system and then discuss excitations and perturbations to this homogeneous state. This greatly contrasts with the experimentally observed pristine order in crystals that are grown in labs with methods such as molecular beam epitaxy (MBE) or pulsed lased deposition (PLD). Such order, as e.g. shown in the image above, is often inhomogeneous on microscopic length scales and perturbative descriptions starting from homogeneous systems are unsuitable to describe them. My research focuses on simulations of microscopically inhomogeneously ordered systems in order to gain a theoretical understanding of the underlying mechanisms of the formation and manipulation of inhomogeneous order. 

Many microscopically inhomogeneous systems exhibit topological defects, such as vortices or skyrmions. These topological defects cannot be removed with a small local perturbation of the order parameter — they are topologically protected. This distinguishes them from other defects, such as bubble defects. In many cases, they become the defining feature of inhomogeneous order. In systems such as hexagonal manganites, the local domain pattern is completely dominated by vortex-antivortex pairs. Since vortices and antivortices are topologically protected, they exhibit very long relaxation times and, although technically not in a local minimum, can stabilize inhomogeneous order. I study systems with topological defects, and am particularly interested in simulating their dynamics.

The form and behavior of topological defects are strongly coupled to the dimensionality of a system. We can, for example, consider vortices and antivortices, which take the form of zero-dimensional singularities in a 2D system. If one takes exactly the same system, but in 3D, vortices and antivortices no longer exist; instead now one-dimensional vortex lines appear. These vortex lines show fundamentally different behavior as they are no longer singular particles with a topological charge, but rather oriented strings. Simulating systems in 2D and 3D and understanding their similarities and differences is one of my main research topics. Simulation and visualization of 3D systems has been particularly challenging due to computational requirements and difficulties in visualizing them, and in my research I aim to tackle these challenges.

I simulate my systems using phase-field methods, also known as time-dependent Ginzburg-Landau simulations, using high performance computing. I write and use GPU codes that are written in CUDA or other GPU frameworks. I combine my expertise in physics with methods from the field of Scientific Visualization to bring out the beauty of inhomogeneous order. I use frameworks such as the Visualization Toolkit (VTK) and custom ray-tracing shaders adapted from those included in VTK to create the visualizations shown on this page.