Imaging of electron forces, interactions, and topological states in designer quantum materials [electronic resource]

We have developed atomic manipulation with a scanning tunneling microscope (STM) into a compelling new tool to investigate the fundamental properties of condensed matter systems. Our new capability to assemble and fine-tune essentially any two-dimensional lattice combined with the ability to probe density of states at subatomic scale allows us to investigate the physics of electronic states with unprecedented freedom and precision. Here I aim to answer questions that so far proved too elusive for traditional material synthesis and measurement methods, in particular, questions about topological states in complex non-periodic systems and about many-body instabilities driven by electron interactions. In this thesis, I focus on corrals and lattices created by patterning a free electron gas of a Cu(111) surface with carbon monoxide (CO) molecules. The CO molecules provide act as potential wells and constrain the surface state electrons to an effective lattice or corral pattern. In the first part I explain a series of quantum force measurement experiments, where I try to shed some light on the quantum force distance dependence and focusing inside several corral structures. Next part describes charge fractionalization in molecular polyacetylene as well as in Kekule distorted molecular graphene. I discuss how a domain wall or a vortex defect in a bond strength wave, leads to an emergence of a mid-gap state, and the fractional charge associated with it. Following that, I talk about effective gauge fields in graphene induced by strain as well as through direct modulation in bond strength and on-site potential. I explain how these induced perturbations to the lattice can be described by gauge fields, equivalent to the ones associated electromagnetic fields. One remarkable consequence of this equivalence is strain gauge invariance that allows one to produce lattices with the same electronic energy spectrum, but very different local structure. In the next part, I show how electron-electron interactions lead to instabilities as the lattice constant changes. In particular, I show that in a honeycomb lattice doped to the Van Hove singularity, the instability leads to a spontaneous nematic and polarized pseudospin phase. I also research investigate the instability in the flat band of a honeycomb 5-5-8 grain boundary where the leading phase is likely magnetic. Next, I describe quasicrystalline molecular lattices based on Penrose tilings and the electron fractalization that happens in them. I show the deep connection between penteract and electrons in a Kite-and-Dart quasicrystal that form localized states at energies related by the golden ratio. I end by briefly discussing some possible future experiments that can exhibit an even larger variety of effects such as an emergence of a quantum spin Hall state or topological currents can be expected. These effects might show when one introduces stronger interactions and stronger spin-orbit coupling present for example on surfaces of gold and topological insulators.

Keywords: Physics.
Advisor: Manoharan Harindran C. (Harindran Chelvasekaran)
Fisher Ian
Qi Xiaoliang advisor. Thesis advisor