Electronic correlations in quantum materials: inhomogeneities and frustration

Abstract

Landau's theory of phase transitions is the cornerstone of our modern understanding of Condensed Matter Physics. The ability to characterize ordered states of matter, and their low-lying excitations, in terms of a local order parameter and the accompanying spontaneous symmetry breaking, is a very powerful and unifying idea. However, since the discovery of the quantum Hall effect, it was realized that this cherished theory is not enough to describe long-range entangled quantum phases and topological order. Over the last two decades, strongly correlated electronic systems have emerged as a fruitful platform to host a broad range of new and exotic solid and liquid phases; families of frustrated Mott insulators, as well as unconventional superconductors, have been predicted to host a variety of topological phases in the presence of spin-orbit coupling. Unlike quantum Hall systems, these correlated systems take advantage of the combinatorial richness of the periodic table, and the presence of sometimes large microscopic energy scales (hence, larger temperature scales), as well as being amenable to a variety of experimental probes. The central goal of this project is to find and study novel phases of matter in strongly correlated materials in the presence of frustration and/or inhomogeneities. We aim at a microscopic understanding of their low-energy excitation spectrum, thermodynamic response, transport properties, and relation to topology. The key ingredients are electron-electron interaction, geometrically frustrated lattices, and strong spin-orbit coupling. In describing and understanding the properties of promising materials, we will implement the following program. We start by investigating the experimental phase diagram, and the observed thermodynamic behavior, as a function of external parameters such as temperature, pressure, magnetic field, and doping. In this step, we want to assess the relative importance of the many competing ingredients and write a minimal theoretical model. Once we include the key ingredients in our theory, we can study the (unusual) character of the emergent low-energy excitations, their diverse manifestations, and their coupling to other degrees of freedom. Ultimately, we want to bridge the prediction of simplified models and the experimental results in complex quantum materials to increase our understanding of their microscopy properties. (AU)