Nearly free electron states in MXenes

Using a set of first-principles calculations, we studied the electronic structures of two-dimensional transition metal carbides and nitrides, so called MXenes, functionalized with F, O, and OH. Our projected band structures and electron localization function analyses reveal the existence of nearly free electron (NFE) states in a variety of MXenes. The NFE states are spatially located just outside the atomic structure of MXenes and are extended parallel to the surfaces. Moreover, we found that the OH-terminated MXenes offer the NFE states energetically close to the Fermi level. In particular, the NFE states in some of the OH-terminated MXenes, such as $\mathrm{T}{\mathrm{i}}_{2}\mathrm{C}{(\mathrm{OH})}_{2},\mathrm{Z}{\mathrm{r}}_{2}\mathrm{C}{(\mathrm{OH})}_{2},\mathrm{Z}{\mathrm{r}}_{2}\mathrm{N}{(\mathrm{OH})}_{2},\mathrm{H}{\mathrm{f}}_{2}\mathrm{C}{(\mathrm{OH})}_{2},\mathrm{H}{\mathrm{f}}_{2}\mathrm{N}{(\mathrm{OH})}_{2},\mathrm{N}{\mathrm{b}}_{2}\mathrm{C}{(\mathrm{OH})}_{2}$, and $\mathrm{T}{\mathrm{a}}_{2}\mathrm{C}{(\mathrm{OH})}_{2}$, are partially occupied. This is in remarkable contrast to graphene, graphane, and $\mathrm{Mo}{\mathrm{S}}_{2}$, in which their NFE states are located far above the Fermi level and thus they are unoccupied. As a prototype of such systems, we investigated the electron transport properties of $\mathrm{H}{\mathrm{f}}_{2}\mathrm{C}{(\mathrm{OH})}_{2}$ and found that the NFE states in $\mathrm{H}{\mathrm{f}}_{2}\mathrm{C}{(\mathrm{OH})}_{2}$ provide almost perfect transmission channels without nuclear scattering for electron transport. Our results indicate that these systems might find applications in nanoelectronic devices. Our findings provide new insights into the unique electronic band structures of MXenes.