Designing guidance for multiple valley-based topological states driven by magnetic substrates: potential applications...

Valley-based topological phases offer a wealth of exotic quantum states with tunable functionalities, driven by the valley degree of freedom. In this work, by constructing heterostructures of germanene (silicene, stanene) on various magnetic substrates, we address key tuning factors such as the spin-orbit coupling (SOC) strength of the substrate, magnetic orientations, and stacking orders, all of which govern multiple valley-based topological features. We present a comprehensive guiding principle for the efficient manipulation of these features, achieved simply by designing and modulating the magnetic properties of the underlying substrates. Specifically, increasing the SOC strength of the magnetic substrate facilitates a range of topological phase transitions characterized by different Chern numbers, with many systems exhibiting a transition from quantum valley Hall to quantum anomalous Hall (QAH) states. Additionally, rotating the in-plane magnetic orientation of the substrate enables tunability of the Chern number and chirality, within a moderate range of SOC strength. Furthermore, the antiferromagnetic coupling of the magnetic substrate can induce valley-based QAH states with substantial valley gaps, leveraging its high Curie temperature (TC) to enable the realization of multiple tunable magnetic topologies at elevated temperatures. Our findings provide a straightforward strategy for the design and manipulation of spintronic and valleytronic devices that can potentially operate under high-temperature conditions.