Tunable moiré materials for probing Berry physics and topology

Berry curvature physics and quantum geometric effects have been instrumental in advancing topological condensed matter physics in recent decades. Although Landau level-based flat bands and conventional 3D solids have been pivotal in exploring rich topological phenomena, they are constrained by their limited ability to undergo dynamic tuning. By stark contrast, moiré systems have risen as a versatile platform for engineering bands and manipulating the distribution of Berry curvature in momentum space. These moiré systems not only harbour tunable topological bands, modifiable through a plethora of parameters, but also provide unprecedented access to large length scales and low energy scales. Furthermore, they offer unique opportunities stemming from the symmetry-breaking mechanisms and electron correlations associated with the underlying flat bands that are beyond the reach of conventional crystalline solids. A diverse array of tools, encompassing quantum electron transport in both linear and nonlinear response regimes and optical excitation techniques, provide direct avenues for investigating Berry physics in these materials. This Review navigates the evolving landscape of tunable moiré materials, highlighting recent experimental breakthroughs in the field of topological physics. Additionally, we delineate the most pressing challenges and offer insights into promising avenues for future research. Moiré materials are a versatile and tunable platform that offers a wide variety of lattice constants, energy scales and symmetries, leading to a rich interplay of electron correlations and topology. This Review summarizes recent breakthroughs in topological and Berry physics in moiré materials.