Quantum states engineering in graphene nanoribbons
Keywords: Graphene nanoribbons
Quantum coherence
Spin states
Vibrational states
Topological states

The new upcoming generation of quantum devices requires the creation of solid state systems that display prominent quantum properties. This search, which is intensifying, has allowed identifying excellent quantum systems in molecular magnets, defect centres, low-dimensional materials, among others. Most efforts are directed towards systems produced with a top-down approach, e.g. by exfoliation or shaping of two-dimensional materials. This, however, prevents achieving the precise atom-by-atom control of the morphology that is usually necessary for topological and quantum properties to emerge distinctively in experiments.
One class of systems that holds the promise of overcoming many present difficulties are graphene nanoribbons (GNRs) made by molecular synthesis. GNRs display a graphitic backbone, whose edges, terminations, and morphology can all be altered synthetically, with atomic precision, thus changing the electronic, optical, and magnetic properties. Synthesis of these systems is booming, as new pathways for the bottom-up synthesis of novel systems are reported frequently. At the same time, new theoretical developments now allow understanding that GNRs can also display non-trivial topologies. On the other hand, their quantum behaviour, and the relationship with theoretically-predicted topological and quantum properties remain largely unexplored.
In this thesis I present a theoretical and experimental investigation of molecular GNRs, integrating computation and experiments, so as to unravel the interplay between morphology and quantum properties. The focus of my thesis lies on their electronic properties, with attention to topological phases, quantum spin, and vibrational states.
The development of theoretical methods and programs for numerical calculations allowed classifying and understanding the topological phases in GNRs, and we could use these tools to design novel structures exhibiting distinct topological phases, and directly suggest innovative applications for topological states. Most importantly, we could relate the topological properties to some of the old rules concerning the stability of aromatic compounds, producing a direct connection between modern theoretical physics and the very empirical, rule-of-thumb guidelines developed at the organic synthesis hoods in the 1970s. We also find that dissipationless transport becomes possible, under certain conditions, and that different compounds known since decades, such as fused porphyrin tapes, can display interesting topological states. As the quantum properties are most evident in spin states, we first investigate theoretically how topology can influence them. Then we investigate experimentally, using pulsed EPR techniques, two types of spin centres introduced through external functionalisation groups in GNRs.
In the final part we examine two ways of probing directly the electronic states: through optical spectroscopy and through electron transport in devices. We show how, in both cases, the vibrational states are fundamental, and we can identify unambiguously their role in ultra-clean quantum transport devices at millikelvin temperatures and in optical spectra. We extract the electron–phonon coupling strength and offer a unified vision, which could set the interpretative basis for both transport and optical measurements.