  The quantum anomalous Hall (QAH) state is a two-dimensional topological
insulating state that has quantized Hall resistance of h/Ce2 and vanishing
longitudinal resistance under zero magnetic field, where C is called the Chern
number. The QAH effect has been realized in magnetic topological insulators
(TIs) and magic-angle twisted bilayer graphene. Despite considerable
experimental efforts, the zero magnetic field QAH effect has so far been
realized only for C = 1. Here we used molecular beam epitaxy to fabricate
magnetic TI multilayers and realized the QAH effect with tunable Chern number C
up to 5. The Chern number of these QAH insulators is tuned by varying the
magnetic doping concentration or the thickness of the interior magnetic TI
layers in the multilayer samples. A theoretical model is developed to
understand our experimental observations and establish phase diagrams for QAH
insulators with tunable Chern numbers. The realization of QAH insulators with
high tunable Chern numbers facilitates the potential applications of
dissipationless chiral edge currents in energy-efficient electronic devices and
opens opportunities for developing multi-channel quantum computing and
higher-capacity chiral circuit interconnects.
