Topological quantum matter with designer materials

Topological quantum matter, where topological concepts are exploited to discover and classify new phases of matter, has emerged as one of the most important topics in condensed-matter physics in recent years. Topological states with exotic properties are robust to local perturbations, which is important for a multitude of applications. In particular, topological superconductors have attracted a lot of interest as they are predicted to host zero-energy Majorana bound states which could make it possible to construct topological qubits. However, the realization of these exotic states is often challenging in naturally occurring materials. This can be overcome using the designer materials approach, where the desired physics emerges from the engineered interactions between different components. This thesis demonstrates the experimental realization of topological modes in one-dimensional artificial lattices with atomic level control using chlorine vacancies in the c(2x2) adsorption layer on Cu(100). In Publication I (PI), we show that while the edge modes in the Su-Schrieffer-Heeger (SSH) model are exactly at the mid-gap energy, other paradigmatic 1D models such as trimer and coupled dimer chains have non-zero energy boundary states. This allows wide tuneability of the domain wall modes that we experimentally demonstrate using low-temperature scanning tunneling microscopy (STM). Subsequently in PII, we experimentally realize both gapped and gapless flat band systems with single or multiple flat bands. Atomic level structural control allows us to demonstrate the broad tuneability of the realized flat bands. In PIII and PIV, we use the designer approach in two-dimensional van der Waals heterostructures. The combination of ferromagnetic materials and superconductors suggests the possibility of realizing topological superconductivity. We present the direct synthesis of the magnet-superconductor heterostructures using molecular beam epitaxy (MBE) by combining superconducting NbSe2 with VSe2 or CrBr3. In the case of VSe2/NbSe2 heterostructures, the STM and bulk magnetization measurements suggest the magnetization of the VSe2 island on the local scale, but we do not observe topological edge modes in this system. On the other hand, CrBr3 islands show strong out-of-plane ferromagnetic ordering, which allows the realization of topological superconductivity. The low-temperature STM and STS measurements demonstrate the existence of the one-dimensional Majorana zero modes along the edges of the CrBr3 islands, which the key signature of topological superconductivity. Two-dimensional vdW heterostructures offer a broad range of materials properties, high flexibility in fabrication pathways, and the ability to form artificial states of quantum matter, which can be not only studied in controlled laboratory settings but also provide.