Emergent States in Topological and Dirac Matter

This book explores diverse systems including carbon nanotubes, topological crystalline insulators, Dirac semimetals, and other more recently discovered topological phases, such as fragile and higher-order topology. Topological systems and moiré graphene-based materials form two intertwined branches of current interest in condensed matter physics. Various computational and analytical methods are extensively described and combined, providing new perspectives on these emerging fields. Regarding moiré materials, collapsed chiral carbon nanotubes are shown here to be one-dimensional analogues of twisted bilayer graphene, exhibiting magic angle physics. A wide-ranging overview of modern topological phases of matter is also presented, with an emphasis on crystalline symmetries. In this regard, the robustness of topological crystalline insulator SnTe under impurities, as well as its spin texture, is assessed. Additionally, over 50 two-dimensional materials with fragile topology are described, many of them for the first time, which can host fractionally filled corner states. In summary, this thesis constitutes an instructive presentation of novel theoretical advances in topological and Dirac matter, proposing several experimentally feasible material candidates for these exotic phases of matter. It is written in a clear manner and with a comprehensive introduction that will surely be of help for researchers and students entering these fields.

Olga Arroyo Gascón holds a BSc degree in Physics from Autonomous University of Madrid, and a MSc in Theoretical Physics from Complutense University of Madrid. During her MSc, under the guidance of Prof. Francisco Domínguez-Adame, she commenced her research on topological materials. She carried out her PhD at the Materials Science Institute of Madrid (Spanish National Research Council) and Complutense University of Madrid, under the supervision of Prof. Leonor Chico. Her research was developed at the Quantum Materials for Quantum Technologies group at the Materials Science Institute of Madrid and the Quantum Nanosystems Group at Complutense University of Madrid, with a research stay in Prof. Mónica Pacheco’s group at Federico Santa María University of Technology in Valparaíso (Chile). Her PhD research was focused on theoretical models and computational approaches to low-dimensional Dirac systems and symmetry-protected topological phases of matter. In September 2024, she defended her thesis with excellent cum laude grade and moved to University of Salamanca (Spain) as a postdoctoral researcher. At the end of this appointment, she will be starting a new postdoctoral position at the Institute of Theoretical Physics associated to the Paris-Saclay University and the French National Research Council. Olga’s thesis work has been awarded the XII Best Theoretical Thesis in Condensed Matter Physics by the Condensed Matter Physics Division of the Spanish Royal Physics Society. She is the first author of several scientific articles in peer-reviewed international journals, including high-impact journals such as Nano Letters and Carbon, and has also co-authored an outreach article based on novel results from her PhD research. She has presented her work in 12 international and 6 national conferences and workshops, including invited talks, and imparted seminars in universities inside and outside Spain. She is also a graduated flute player and enjoys synergies between art and science.