Interacting quantum materials and their acoustic analogs

Abstract

When electrons in solids interact strongly with one another, they often produce unexpected, emergent phases, like high-temperature superconductivity or fractional quantum Hall states. In this thesis, I approach this strongly interacting regime from two directions: by searching for materials with naturally occurring strong interactions, and by developing new strategies to enhance existing interactions. In the first approach, I focus on lanthanide or actinide metals that host 4f or 5f magnetic moments, such as SmB6 or URu2Si2. At temperatures of around a few Kelvin, the conduction electrons in these materials coherently screen the magnetic moments, becoming entangled with them. This strong interaction has dramatic consequences. The once-mobile electrons in URu2Si2 suddenly struggle to move, appearing as though they have an effective mass nearly a hundred times higher than a free electron does! Whereas in SmB6, this interaction drives a topological phase transition that yields heavy Dirac states at the material's surface. At milliKelvin temperatures, the interactions between these Dirac states may promote even stranger behavior, like a spontaneously generated quantum anomalous Hall effect, fractionalization, or a phase with non-Abelian quantum statistics. In chapters 1-4 of this thesis, I present the first images of heavy Dirac fermions ever taken, and I describe how atomic-scale defects influence their fate. In the second approach, I search for ways to decrease an electron’s kinetic energy so that its interactions with other electrons play a more prominent role in determining its behavior. One way to slow electrons down is to trap them in certain spatial regions, either by creating a moiré pattern or by using their own destructive wave interference to prevent them from moving away. As it turns out, these methods are just as effective at slowing sound waves as they are at slowing electron waves. A carefully constructed acoustic metamaterial can reshape the flow of sound to closely resemble how electrons move in a solid. Using acoustic metamaterials to mimic electron behavior is certainly appealing: it can take years to find a reliable recipe for growing new quantum materials, whereas a new acoustic metamaterial might take only a few hours to 3D print. In chapters 5-8 of this thesis, I present designs for acoustic metamaterials that exploit topological protection to create a robust logic gate, that mimic generic van der Waals heterostructures, and that can slow sound to a few centimeters per second---only mildly outpacing a garden snail! If combined, these two approaches could create a platform for engineering designer quantum phases with strong electron interactions, opening a path towards future technology such as custom-built unconventional superconductors, robust quantum computers, and antiferromagnetic spintronic devices for efficient information storage and processing.