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Triple-well ferroelectricity and kagome-like Chern flat band in two-dimensional multiferroic CuVP$_2$Se$_6$

Two-dimensional multiferroics that host nontrivial topological bands offer a rich platform for correlated and tunable quantum phenomena, yet such materials remain rare. Here, using first-principles calculations, we reveal that monolayer CuVP$_2$Se$_6$ unites a tunable triple-well ferroelectric transition with a spin-polarized Chern flat band. The ferroelectric and paraelectric phases are close in energy and can be reversibly switched by moderate strain or an electric field. During the transition, a kagome-like flat band emerges near the Fermi level, which we describe via a minimal three-orbital tight-binding model on a triangular lattice. Furthermore, the system exhibits sizable magnetic anisotropy and a magnetization-dependent Chern insulating state: the Chern number is $C = \pm 1$ for out-of-plane magnetization but becomes trivial when the moments rotate in-plane. These findings establish CuVP$_2$Se$_6$ as a promising candidate for exploring electrically tunable flat-band correlations and topological magnetism in a multiferroic monolayer.