Order by Disorder in Topological Quantum Materials

Abstract

Topological materials are a promising platform for next-generation devices, ranging from optoelectronics to interconnects. In these materials, the interplay between magnetic, electronic, and lattice degrees of freedom presents an opportunity to discover new phases with enhanced tunability and performance. In this thesis, I discuss the role of fluctuations — deviations from global order in space and time— in promoting incipient phases in topological materials, such as incommensurate magnetism and nematicity, which are probed through an ensemble of experimental techniques, including electrical and thermal transport as well as time-resolved X-ray scattering. In the first part of the dissertation, I explore the role of thermally-activated, geometrically frustrated carriers in driving rotational symmetry-breaking. Geometric frustration from the kagomé lattice localizes modes onto specific crystallographic regions in real-space, leading to flat-bands with quenched kinetic energy in reciprocal space. These electronic flat-bands are so sensitive to any lattice perturbation that they can drive a profound reconstruction of the entire crystal. When the temperature is raised such that electronic flat-bands below the Fermi-level are activated, the localized electrons conspire to form nematic state where rotational symmetry is broken. At lower temperatures, these carriers are not active and thus no nematic state is formed. In contrast to systems in which interactions with the lattice actually slow down quasiparticle transport, here we find that the flat-electrons are actually mobilized by their interaction with the lattice. These findings have the potential to lead to highly entropic carriers for thermoelectric applications. In the second part of the thesis, I discuss the way in which thermally enabled scattering amongst topological electrons fundamentally change the interactions in magnetic domains, leading to their enhanced stability. Unlike conventional electrons, which have a doubly degenerate parabolic dispersion for each spin, topological fermions in Weyl semimetals are characterized by the chiral, linear dispersion dictated by the relativistic Weyl equation. The properties of these Weyl fermions propagate through to the exchange interactions experienced by a material's magnetic moments, leading to small domains of incommensurate magnetism which are locally stable but globally unstable. These domains have a distinct impact on the thermal and electronic transport through the crystal, showing how deviations from the global order can still strongly affect macroscopic properties of the material. Finally, in the last chapter of the thesis, I explore new techniques for observing fluctuations with time-resolved X-ray scattering. Technological advancements in the time-resolution, repetition rate, and brilliance of X-ray scattering sources--chiefly among them X-ray Free Electron Lasers (XFELs)-- are enabling observations of time-dependent phenomena from timescales of femtoseconds all the way to minutes. While these experiments promise to elucidate new physical behavior of systems ranging from biological proteins to topological magnets, a key challenge in their execution is analyzing the massive troves of data that result from taking a time-series of detector images. In parallel with the rise of time-resolved X-ray scattering, there have been numerous machine learning techniques that have the potential to revolutionize the way these massive troves of time-series data are analyzed. I demonstrate the utility and promise of non-linear embedding methods popularized in machine learning communities by applying them to nano-second resolution data from the EU-XFEL. These methods are a departure from typical analysis methods based on statistical correlation functions, and unveil distinct fluctuations of magnetic-stripes in a topological magnet. Taken together, these results point to the unexpected ways in which quantum materials can be engineered such that their characteristic thermal fluctuations aid, rather than hinder, their performance in applications such as spintronics and thermoelectrics. Furthermore, by utilizing a wide array of experimental and computational techniques accessible through National Laboratory User facilities, I hope to show how productive it can be to approach scientific problems from as many angles as possible, leading to robust inductive discoveries.