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. In stark contrast, moir\'e systems have risen as a versatile platform for engineering bands and manipulating the distribution of Berry curvature in momentum space. These moir\'e systems not only harbor 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 non-linear response regimes and optical excitation techniques, provide direct avenues for investigating Berry physics. This review navigates the evolving landscape of tunable moir\'e materials, highlighting recent experimental breakthroughs in the field of topological physics. Additionally, we delineate several challenges and offer insights into promising avenues for future research.