MXenes, a family of two-dimensional transition metal carbides and nitrides, have various tunable physical and chemical properties. Their diverse prospective applications in electronics and energy storage devices have triggered great interests in science and technology. MXenes can be functionalized by different surface terminations. Some O and F functionalized MXenes monolayers have been predicted to be topological insulators (TIs). However, the reported OH functionalized MXenes TIs are very few and their electronic structures need to be investigated in more detail. It has been revealed that the work functions of MXenes are reduced significantly by OH termination and the image potential (IP) states move close to the Fermi level. The wave functions of these IP states are spatially extensive outside the surfaces. By stacking the OH-functionalized MXenes, the energies of the IP states can be modulated by the interlayer distances of multilayers, because the overlap and hybridization of the wave functions between the neighboring layers are significant. Therefore, these stacking layers are interacted and coupled with IP states. Here, based on first-principles calculations, we demonstrate that the stacking of two-dimensional topologically trivial OH-functionalized MXenes, such as V$_2$HfC$_2$(OH)$_2$, possibly gives rise to the topologically nontrivial energy bands. In other words, the topological properties of V$_2$HfC$_2$(OH)$_2$ multilayers can be modulated by its interlayer distance. An energy band inversion involving IP states is proposed. We expect that these results can advance the future application of MXenes or other low work function multilayer materials as controllable TI devices.
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