First-principles study of a topological phase transition induced by image potential states in MXenes

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. The electronic properties of the free-standing OH-MXenes monolayers are different from their stacking multilayers. To emphasize the important role of the IP states on controlling the topological characteristics of materials, we have studied a set of hypothetical ${M}_{2}^{\ensuremath{'}}{M}^{\ensuremath{'}\ensuremath{'}}{\mathrm{C}}_{2}{(\mathrm{OH})}_{2}$ (${M}^{\ensuremath{'}}=\phantom{\rule{0.16em}{0ex}}\mathrm{V}$, Nb, Ta; ${M}^{\ensuremath{'}\ensuremath{'}}=$ Ti, Zr, Hf) MXenes using first-principles calculations. Their valence and conduction bands come from the IP states. We demonstrate that the energy bands of these free-standing OH-MXenes monolayers are topologically trivial. However, by stacking, the OH-MXenes multilayers possibly become nontrivial. In other words, the topological properties of the stacked multilayers depend on the interlayer distance. An energy-band inversion involving IP states is proposed. Our results are valid not only for MXenes, but for any materials whose IP states are energetically close to the Fermi level. We expect that these results can advance the future application of low work function materials as controllable TI devices.