Quantum phenomena in topological materials

Jincheng Zhang

This paper investigates the application of Quantum Field Theory (QFT) to the study of topological materials, aiming to provide a framework for predicting emergent properties and stability based on non-linear quantum effects. We formalize the concept of topology to quantum systems, enabling the prediction of material behavior driven by quantum field dynamics. The core claim is that a QFT approach will significantly enhance our understanding and design of topological materials, offering a novel means of predicting and controlling their characteristics. This research explores the potential for utilizing QFT to uncover the underlying mechanisms governing topological phenomena, moving beyond traditional material modeling approaches.

Bing Liu, Wenjun Zhang

The exploration of topologically nontrivial states in condensed matter systems, along with their novel transport properties, has garnered significant research interest. This review aims to provide a comprehensive overview of representative topological phases, starting from the initial proposal of the quantum Hall insulator. We begin with a concise introduction, followed by a detailed examination of first-order topological quantum phases, including gapped and gapless systems, encompassing relevant materials and associated phenomena in experiment. Subsequently, we delve into the realm of exotic higher-order topological quantum phases, examining both theoretical propositions and experimental findings. Moreover, we discuss the mechanisms underlying the emergence of higher-order topology, as well as the challenges involved in experimentally verifying materials exhibiting such properties. Finally, we outline future research directions. This review not only systematically surveys various types of topological quantum states, spanning from first-order to higher-order, but also proposes potential approaches for realizing higher-order topological phases, thereby offering guidance for the detection of related quantum phenomena in experiments.

David S. Simon

Anantha Hegde, Adarsh Kumar, Adhip Agarwala +1 more

Annica M. Black‐Schaffer, Oscar Grånäs, Anders Bergman

Materials display an astonishing range of phenomena, many of them with no classical description. These are quantum materials: superconductors, magnets, topological insulators and beyond. Discovering, understanding, and exploiting materials with dominating quantum effects is key for future quantum technologies. To make progress, theory and modeling is essential.