Properties at the interface of graphene and ${\mathrm{Ti}}_2\mathrm{C}$ MXene

Employing ab initio calculations, we characterize the interfaces formed between graphene, a much discussed two-dimensional material, and MXene, another two-dimensional material of recent interest. Our study considering the specific case of ${\mathrm{Ti}}_2\mathrm{C}$, a member of the MXene family, shows the formation of chemical bonds between Ti atoms and C atoms of graphene. This results in reconstruction of the electronic structure at the interface, making the interface metallic, though graphene is a zero-gap semiconductor and ${\mathrm{Ti}}_2\mathrm{C}$ is an antiferromagnetic insulator in their respective native form. The optical and phonon properties of the interfaces are found to be strongly dependent on the stacking arrangement, driven by the nature of chemical-bond formation. Consideration of O-passivated ${\mathrm{Ti}}_2\mathrm{C}$ is found to weaken the interaction between graphene and ${\mathrm{Ti}}_2\mathrm{C}$ substantially, making it a physisorption process rather than chemisorption in the unpassivated situation. Our first-principles study is expected to motivate future experimental investigation.

Figure 1

Left panels: The overlayer geometries of graphene/${\mathrm{Ti}}_2\mathrm{C}$ in three possible stacking configurations, i.e., conf-1, conf-2, and conf-3 (from top to bottom), in side and top views. The large balls represent Ti atoms, while the small balls represent C atoms. The Ti atoms belonging to the top and bottom layers of ${\mathrm{Ti}}_2\mathrm{C}$ have been colored differently. The carbon atoms belonging to A and B sublattices of graphene have been marked as well as colored differently [green (light gray) and gray], while the C atoms belonging to ${\mathrm{Ti}}_2\mathrm{C}$ have been distinguished with a different color [brown (dark gray)]. Also the magnetic moment at a given site is marked. Middle panels: The density of states projected onto C $p$ states of graphene in graphene/${\mathrm{Ti}}_2\mathrm{C}$ heterostructure (in black) as compared to that of freestanding, unstrained graphene structure [brown (gray color)] for conf-1, conf-2, and conf-3 (from top to bottom). The inset in the top panel shows the plot of the charge density at the graphene and top layer of ${\mathrm{Ti}}_2\mathrm{C}$ obtained from the contribution of states close to the Fermi level. The isosurface value has been set to 0.02 $e^{-}/{\AA }^3$. Right panels: Same as in middle panels, but plotted for the density of states projected onto Ti $d$ states of freestanding, unstrained ${\mathrm{Ti}}_2\mathrm{C}$.

Figure 2

Top panels: Partial density of states (pDOS) plotted against the energy, with zero of energy set at $E_F$ for conf-1, conf-2, and conf-3 of the overlayer geometry of graphene/${\mathrm{Ti}}_2\mathrm{C}$ (from left to right). The pDOS for top-layer Ti $d$, bottom-layer Ti $d$, and C $p$ states of ${\mathrm{Ti}}_2\mathrm{C}$ are shown in black line, shaded area, and red (dark gray) line, respectively. The pDOS for C $p$ states of graphene is shown in green (light gray) line. Marked are the various possible optical transitions. Bottom panels: The corresponding optical conductivity.

Figure 3

Left panels: Phonon density of states for pristine graphene, pristine ${\mathrm{Ti}}_2\mathrm{C}$, and graphene/${\mathrm{Ti}}_2\mathrm{C}$ heterostructures in conf-1, conf-2, and conf-3 of the overlayer geometry. The various infrared (IR)-active and Raman (R)-active modes have been marked. The doubly degenerate modes are marked as $dd$. The graphene and ${\mathrm{Ti}}_2\mathrm{C}$ modes are shown in black and green (light gray) colors, respectively, while the joint graphene-${\mathrm{Ti}}_2\mathrm{C}$ modes are shown in part black and part green (light gray) colors. Right panels: The atomic displacements corresponding to the phonon modes in heterostructures having displacements confined solely to the graphene layer (topmost panel), solely to the ${\mathrm{Ti}}_2\mathrm{C}$ layer (one below the topmost panel), and to both the ${\mathrm{Ti}}_2\mathrm{C}$ and graphene layers (bottom three panels).

Figure 4

Top panels: The sandwich geometries of graphene/${\mathrm{Ti}}_2\mathrm{C}$/graphene considering two similar interfaces between graphene and ${\mathrm{Ti}}_2\mathrm{C}$ in 1-1, 2-2, and 3-3 configurations (from left to right). As in Fig. 1, large balls represent Ti atoms, while the small balls represent C atoms. Middle panels: The density of states projected to C $p$ states of graphene in graphene/${\mathrm{Ti}}_2\mathrm{C}$/graphene heterostructure (in black) as compared to that of graphene in isolation [brown (gray) color] for 1-1, 2-2, and 3-3 stacking configurations (from left to right). Bottom panels: Same as in the middle panels, but plotted for Ti $d$ states of ${\mathrm{Ti}}_2\mathrm{C}$.

Figure 5

Same as in Fig. 4, but shown for sandwich geometries of graphene/${\mathrm{Ti}}_2\mathrm{C}$/graphene considering two dissimilar interfaces between graphene and ${\mathrm{Ti}}_2\mathrm{C}$ in 1-2, 1-3, and 2-3 stacking configurations (from left to right).

Figure 6

Left panel: The stacking of graphene on ${\mathrm{Ti}}_2{\mathrm{CO}}_2$ in configurations I, II, and III (from top to bottom). The large balls represent Ti atoms with Ti atoms belonging to the top and bottom layers of ${\mathrm{Ti}}_2\mathrm{C}$ colored differently, while the small balls represent C and O atoms. The C atoms belonging to the A and B sublattice of graphene layer are marked in gray and green colors, while the C atoms belonging to ${\mathrm{Ti}}_2\mathrm{C}$ are colored in brown. The oxygen atoms are colored in red. Right panel: The band structure of graphene/${\mathrm{Ti}}_2{\mathrm{CO}}_2$ in configuration I with the composite band structure shown as a black dashed line, that projected to ${\mathrm{Ti}}_2{\mathrm{CO}}_2$ as a red (dark gray) solid line, and that projected to graphene as a brown (light gray) solid line, respectively.