The recent chemical exfoliation of layered MAX phase compounds to novel two-dimensional transition metal carbides and nitrides, the so-called MXenes, has brought a new opportunity to materials science and technology.

MXenes are a set of two-dimensional transition metal carbides and nitrides that offer many potential applications in energy storage and electronic devices. As an important parameter to design new electronic devices, we investigate the work functions of bare MXenes and their functionalized ones with F, OH, and O chemical groups using first-principles calculations. From our calculations, it turns out that the OH-terminated MXenes attain ultralow work functions between 1.6 and 2.8 eV. Moreover, depending on the type of the transition metal, the F or O functionalization affects increasing or decreasing the work functions. We show that the changes in the work functions upon functionalizations are linearly correlated with the changes in the surface dipole moments. It is shown that the work functions of the F- or O-terminated MXenes are controlled by two factors: the induced dipole moments by the charge transfers between F/O and the substrate, and the changes in the total surface dipole moments caused by surface relaxation upon the functionalization. However, in the cases of the OH-terminated MXenes, in addition to these two factors, the intrinsic dipole moments of the OH groups play an important role in determining the total dipole moments and consequently justify their ultralow work functions.

Two-dimensional (2D) topological insulators (TIs) have been recognized as a new class of quantum state of matter. They are distinguished from normal 2D insulators with their nontrivial band-structure topology identified by the $Z_2$ number as protected by time-reversal symmetry (TRS). Two-dimensional TIs have intriguing spin-velocity locked conducting edge states and insulating properties in the bulk. In the edge states, the electrons with opposite spins propagate in opposite directions and the backscattering is fully prohibited when the TRS is conserved. This leads to a quantized dissipationless “two-lane highway” for charge and spin transportation and promises potential applications. Up to now, only very few 2D systems have been discovered to possess this property. The lack of suitable material obstructs further study and application. Here, by using first-principles calculations, we propose that functionalized MXenes with oxygen, ${\mathrm{M}}_2{\mathrm{CO}}_2$ (M=W, Mo, and Cr), are 2D TIs with the largest gap of 0.194 eV in the W case. They are dynamically stable and natively antioxidant. Most importantly, they are very likely to be easily synthesized by recently developed selective chemical etching of transition-metal carbides (the ${\mathrm{M}}_{n+1}{\mathrm{AX}}_n$ phase). This will pave the way to tremendous applications of 2D TIs, such as “ideal” conducting wire, multifunctional spintronic devices, and the realization of topological superconductivity and Majorana modes for quantum computing.

Chemical exfoliation of MAX phases into two-dimensional (2D) MXenes can be considered as a major breakthrough in the synthesis of novel 2D systems. To gain insight into the exfoliation possibility of MAX phases and to identify which MAX phases are promising candidates for successful exfoliation into 2D MXenes, we perform extensive electronic structure and phonon calculations, and determine the force constants, bond strengths, and static exfoliation energies of MAX phases to MXenes for 82 different experimentally synthesized crystalline MAX phases. Our results show a clear correlation between the force constants and the bond strengths. As the total force constant of an “A” atom contributed from the neighboring atoms is smaller, the exfoliation energy becomes smaller, thus making exfoliation easier. We propose 37 MAX phases for successful exfoliation into 2D Ti₂C, Ti₃C₂, Ti₄C₃, Ti₅C₄, Ti₂N, Zr₂C, Hf₂C, V₂C, V₃C₂, V₄C₃, Nb₂C, Nb₅C₄, Ta₂C, Ta₅C₄, Cr₂C, Cr₂N, and Mo₂C MXenes. In addition, we explore the effect of charge injection on MAX phases. We find that the injected charges, both electrons and holes, are mainly received by the transition metals. This is due to the electronic property of MAX phases that the states near the Fermi energy are mainly dominated by d orbitals of the transition metals. For negatively charged MAX phases, the electrons injected cause swelling of the structure and elongation of the bond distances along the c axis, which hence weakens the binding. For positively charged MAX phases, on the other hand, the bonds become shorter and stronger. Therefore, we predict that the electron injection by electrochemistry or gating techniques can significantly facilitate the exfoliation possibility of MAX phases to 2D MXenes.

The family of two-dimensional transition metal carbides, so called MXenes, has recently found new members with ordered double transition metals $M_2^{\prime }{M}^{″}{\mathrm{C}}_2$, where $M^{\prime }$ and $M^{″}$ stand for transition metals. Here, using a set of first-principles calculations, we demonstrate that some of the newly added members, oxide $M_2^{\prime }{M}^{″}{\mathrm{C}}_2$ ($M^{\prime }=\mathrm{Mo}$, W; $M^{″}=\mathrm{Ti}$, Zr, Hf) MXenes, are topological insulators. The nontrivial topological states of the predicted MXenes are revealed by the $Z_2$ index, which is evaluated from the parities of the occupied bands below the Fermi energy at time reversal invariant momenta, and also by the presence of the edge states. The predicted $M_2^{\prime }{M}^{″}{\mathrm{C}}_2{\mathrm{O}}_2$ MXenes show nontrivial gaps in the range of 0.041–0.285 eV within the generalized gradient approximation and 0.119–0.409 eV within the hybrid functional. The band gaps are induced by the spin-orbit coupling within the degenerate states with $d_{x^2-y^2}$ and $d_{xy}$ characters of $M^{\prime }$ and $M^{″}$, while the band inversion occurs at the $\mathrm{\Gamma }$ point among the degenerate $d_{x^2-y^2}/d_{xy}$ orbitals and a nondegenerate $d_{3z^2-r^2}$ orbital, which is driven by the hybridization of the neighboring orbitals. The phonon dispersion calculations find that the predicted topological insulators are structurally stable. The predicted W-based MXenes with large band gaps might be suitable candidates for many topological applications at room temperature. In addition, we study the electronic structures of thicker ordered double transition metals $M_2^{\prime }{M}_2^{″}{\mathrm{C}}_3{\mathrm{O}}_2$ ($M^{\prime }=\mathrm{Mo}$, W; $M^{″}=\mathrm{Ti}$, Zr, Hf) and find that they are nontrivial topological semimetals. Among the predicted topological insulators and topological semimetals, ${\mathrm{Mo}}_2{\mathrm{TiC}}_2$ and ${\mathrm{Mo}}_2{\mathrm{Ti}}_2{\mathrm{C}}_3$ functionalized with a mixture of F, O, and OH have already been synthesized, and therefore some of the topological materials proposed here can be experimentally accessed.

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 $\mathrm{T}{\mathrm{i}}_2\mathrm{C}{\left(\mathrm{OH}\right)}_2,\mathrm{Z}{\mathrm{r}}_2\mathrm{C}{\left(\mathrm{OH}\right)}_2,\mathrm{Z}{\mathrm{r}}_2\mathrm{N}{\left(\mathrm{OH}\right)}_2,\mathrm{H}{\mathrm{f}}_2\mathrm{C}{\left(\mathrm{OH}\right)}_2,\mathrm{H}{\mathrm{f}}_2\mathrm{N}{\left(\mathrm{OH}\right)}_2,\mathrm{N}{\mathrm{b}}_2\mathrm{C}{\left(\mathrm{OH}\right)}_2$, and $\mathrm{T}{\mathrm{a}}_2\mathrm{C}{\left(\mathrm{OH}\right)}_2$, 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 $\mathrm{H}{\mathrm{f}}_2\mathrm{C}{\left(\mathrm{OH}\right)}_2$ and found that the NFE states in $\mathrm{H}{\mathrm{f}}_2\mathrm{C}{\left(\mathrm{OH}\right)}_2$ 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.