Electronic structure of superconducting copper intercalated transition metal dichalcogenides: First-principles calculations

We report first-principles calculations, within density functional theory, of copper intercalated titanium diselenides, ${\text{Cu}}_x{\text{TiSe}}_2$, for values of $x$ ranging from 0 to 0.11. The effect of intercalation on the energy bands and density of states of the host material is studied in order to better understand the cause of the superconductivity that was recently observed in these structures. We find that charge transfer from the copper atoms to the metal dichalcogenide host layers leads to the formation of Cu-Se bonds that stabilize most of the transferred charge on Se atoms and lead to a relatively large lowering of the Se-derived hole bands. The suppression of the hole bands, the increase in the number of electrons, and the corresponding enhancement of the density of states at the Fermi energy may contribute to the emergence of superconductivity in these systems.

Figure 1

(Color online) The unit cell of ${\text{TiSe}}_2$ is shown in (a), while the Brillouin zone and the $k$ path along which the energy bands are calculated are shown in (b). In (c), the unit cell for $\text{Cu}{\left({\text{TiSe}}_2\right)}_9$ is shown.

Figure 2

Band character plot for ${\text{TiSe}}_2$ along high-symmetry directions in the Brillouin zone (BZ). In (a), the contribution from $\text{Ti}3d$ states is shown. The width of the band lines is proportional to the contribution of the $\text{Ti}3d$ states to these bands. In a band character plot, every point is replaced by a circle whose radius is proportional to the contribution of the emphasized state to the Bloch wave function at the corresponding $k$ point in the BZ. In (b), the contribution of the $\text{Se}4p$ states to the energy bands is emphasized. The Fermi level is at zero energy.

Figure 3

(Color online) Total and atomic densities of states in ${\text{TiSe}}_2$. More than half of the total DOS at the Fermi energy is due to the Ti states.

Figure 4

Energy bands for the $4\times 4\times 1$ ${\text{TiSe}}_2$ superlattice are shown in (a), while those for $\text{Cu}{\left({\text{TiSe}}_2\right)}_{16}$ are shown in (b). The Fermi level is at zero energy.

Figure 5

Energy bands for the $\sqrt{13}\times \sqrt{13}\times 1$ ${\text{TiSe}}_2$ superlattice obtained by zone folding of the ${\text{TiSe}}_2$ bands and the energy bands for $\text{Cu}{\left({\text{TiSe}}_2\right)}_{13}$ are shown in (a) and (b), respectively. The Fermi level is at zero energy. Note that while the Fermi level rises by only 0.06 eV, as a result of Cu intercalation, the hole band—with a maximum at 0.17 eV at $\Gamma$ in (a)—shifts down in energy to just below Fermi level.

Figure 6

Energy bands for the $3\times 3\times 1$ ${\text{TiSe}}_2$ superlattice, obtained by zone folding of the ${\text{TiSe}}_2$ bands, are shown in (a), while the bands of the copper intercalated compound $\text{Cu}{\left({\text{TiSe}}_2\right)}_9$ are shown in (b). The Fermi level is at zero energy. Note the rise by 0.08 eV of the Fermi level in (b) as compared to (a). The hole band, with a maximum at 0.17 eV at $\Gamma$ in (a), shifts down in energy to $-0.08\text{eV}$ as a result of copper intercalation. A similar fate meets the hole band at A.

Figure 7

Band character plot for $\text{Cu}{\left({\text{TiSe}}_2\right)}_9$ along high-symmetry directions in the Brillouin zone. In (a) the Se(1) 4p character is emphasized while in (b) the $\text{Cu}3d$ character is displayed. For energies well below the Fermi energy there are bands with mixed $\text{Se}4p$ and $\text{Cu}3d$ character, reflecting the significant hybridization between Se and Cu states.

Figure 8

(Color online) Electron density plot (in $e/{\text{a}}_0^3$) for $\text{Cu}{\left({\text{TiSe}}_2\right)}_9$. The density is plotted in a plane formed by Cu, Se(1), and Ti(1) atoms. Along a contour the electron density is constant.

Figure 9

(Color online) Total and atomic densities of states for $\text{Cu}{\left({\text{TiSe}}_2\right)}_9$. The atomic DOS are shown for three out of the seven inequivalent atoms.