  Quantum anomalous Hall (QAH) insulators with high Chern number host multiple
dissipationless chiral edge channels, which are of fundamental interest and
promising for applications in spintronics and quantum computing. However, only
a limited number of high-Chern-number QAH insulators have been reported to
date. Here, we propose a dynamic approach for achieving high-Chern-number QAH
phases in periodically driven two-dimensional higher-order topological
insulators (HOTIs).In particular, we consider two representative kinds of HOTIs
which are characterized by a quantized quadruple moment and the second
Stiefel-Whitney number, respectively. Using the Floquet formalism for
periodically driven systems, we demonstrate that QAH insulators with tunable
Chern number up to four can be achieved. Moreover, we show by first-principles
calculations that the monolayer graphdiyne, a realistic HOTI, is an ideal
material candidate. Our work not only establishes a strategy for designing
high-Chern-number QAH insulators in periodically driven HOTIs, but also
provides a powerful approach to investigate exotic topological states in
nonequilibrium cases.
