Titanium nitride: A correlated metal at the threshold of a Mott transition

We investigate electron correlation effects in stoichiometric titanium nitride (TiN) using a combination of electronic structure and many-body calculations. In a first step, the $N\text{th}$-order muffin-tin-orbital technique is used to obtain parameters for the low-energy Hamiltonian in the $\text{Ti-}d\left(t_{2g}\right)$-band manifold. The Coulomb interaction $U$ and Hund’s rule exchange parameter $J$ are estimated using a constrained local-density-approximation calculation. Finally, the many-body problem is solved within the framework of the variational cluster approach. Comparison of our calculations with different spectroscopy results stresses the importance of electronic correlation in this material. In particular, our results naturally explain a suppression of the TiN density of states at the Fermi level (pseudogap) in terms of the proximity to a Mott-metal-insulator transition.

Figure 1

(Color online) Octahedral environment formed by the Ti atoms (large, red spheres) around the N atom (small, blue sphere). The unit cell is represented by the black lines; the subset of Ti atoms connected by dashed lines shows the cluster geometry that was used as reference system for the VCA calculation (see text).

Figure 2

(Color online) Orbital-resolved density of states for Ti obtained by LDA and $\text{LDA}+U$. The upper (lower) panel shows the $t_{2g}\left(e_g\right)$ contribution. The upper panel also displays the $\text{N-}p$ density of states and the experimental XPS spectrum (Ref. 3) (experimental data reproduced with kind permission of the authors).

Figure 3

(Color online) Band structure of TiN calculated for a path in the BZ going from the $L$ point (0.5,0.5,0.5) through the $\Gamma$ (0,0,0), $X$ (0,1,0), $W$ (0.5,1,0), $L$ (0.5,0.5,0.5), $K$ (0,0.75,0.75) points, and ending at the $\Gamma$ point (0,0,0). The bands are obtained from the LDA calculation (dashed/green line) for the complete orbital basis set. The NMTO bands (full/red line) are obtained after downfolding to the $\text{Ti-}3d\left(t_{2g}\right)$ orbitals.

Figure 4

(Color online) TiN density of states calculated with $\text{LDA}+\text{VCA}$ for different values of the Coulomb-interaction parameter $U$ and for $J=1.3$.

Figure 5

(Color online) TiN density of states calculated within $\text{LDA}+\text{VCA}$ for $U=8.5\text{eV}$ and $J=1.3$ compared with measured XPS (Ref. 3) and K-ELNES (Ref. 17) spectra (experimental data reproduced with kind permission from the authors).

Figure 6

(Color online) Spectral function of TiN for $U=8.5$ and $J=1.3$ shown as density plot for the same path in the BZ as in Fig. 3. The bands obtained from downfolding (dashed, green lines) are shown as reference.

Figure 7

Imaginary part of the self-energy calculated for the same parameters and along the same BZ path as in Fig. 6, and presented in a three-dimensional plot.