Progress in topological physics based on artificial gauge fields

Topological physics with artificial gauge fields has emerged as a pivotal frontier in condensed matter physics and quantum simulation, offering profound insights into quantum phenomena and materials science. Artificial gauge fields have been realized on a variety of electrically neutral platforms through methods such as Raman laser coupling, strain engineering, and Floquet modulation. These approaches facilitate the discovery and manipulation of exotic quantum phases, including the quantum Hall effect, topological insulating states, and Weyl semimetals. Such phenomena not only shed light on fundamental aspects of topology in quantum systems but also enable analog quantum simulations, thereby allowing the emulation of complex quantum behaviors in tunable laboratory settings. Considering the importance of the research field and to cover its fast development, we have reviewed the progress of this field. First, we examine the theoretical underpinnings of topological states and artificial gauge fields, introducing their mathematical frameworks, implementation strategies, and synergistic interplay. Next, we introduce different topological phenomena based on artificial gauge fields and their experimental platform. Finally, we summarize the application achievements in this field and outline prospects for future development. Our work systematically and comprehensively elucidates how to employ artificial gauge fields to investigate topological effects, offering a detailed reference for future advancements in this field.