High Chern number quantum anomalous Hall effect tunable by stacking order in van der Waals topological insulators

The discovery of van der Waals (vdW) ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ provides a platform for investigating the quantum anomalous Hall effect (QAHE), which is a candidate for quantum computation without dissipation. However, because of the topological requirement, the High Chern number QAHE with extended dissipation-free channels is hard to achieve in atomically thin samples, which can take full advantage of two-dimensional (2D) materials. In this work, by first-principles calculations, the variable stacking order (inherent to vdW materials) was proposed as a means of regulating the Chern number of the QAHE in ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}$ (MBT). The interlayer stacking order in the 2D limit dominates the orbital hybridization, resulting in a tunable topological property. Furthermore, the High Chern number QAHE with $C=N$ was achieved in ultrathin MBT ($2N$ septuple layers) with alternate stacking orders, which have different topological states. This scenario was extended to the vdW heterostructure of MBT-family materials for achieving a stable, zero-field, High Chern number QAHE. Our work reveals stacking tunable topological properties in vdW magnetic topological insulators and provides an effective means of regulating the QAHE.