Tuning the metal-insulator transition in $d^1$ and $d^2$ perovskites by epitaxial strain: A first-principles-based study

We investigate the effect of epitaxial strain on the Mott metal-insulator transition (MIT) in perovskite systems with $d^1$ and $d^2$ electron configurations of the transition metal (TM) cation. We first discuss the general trends expected from the changes in the crystal-field splitting and in the hopping parameters that are induced by epitaxial strain. We argue that the strain-induced crystal-field splitting generally favors the Mott-insulating state, whereas the strain-induced changes in the hopping parameters favor the metallic state under compressive strain and the insulating state under tensile strain. Thus the two effects can effectively cancel each other under compressive strain, while they usually cooperate under tensile strain, in this case favoring the insulating state. We then validate these general considerations by performing electronic structure calculations for several $d^1$ and $d^2$ perovskites, using a combination of density functional theory (DFT) and dynamical mean-field theory (DMFT). We isolate the individual effects of strain-induced changes in either hopping or crystal-field by performing DMFT calculations where we fix one type of parameter to the corresponding unstrained DFT values. These calculations confirm our general considerations for ${\mathrm{SrVO}}_3$ ($d^1$) and ${\mathrm{LaVO}}_3$ ($d^2$), whereas the case of ${\mathrm{LaTiO}}_3$ ($d^1$) is distinctly different, due to the strong effect of the octahedral tilt distortion in the underlying perovskite crystal structure. Our results demonstrate the possibility to tune the electronic properties of correlated TM oxides by using epitaxial strain, which allows to control the strength of electronic correlations and the vicinity to the Mott MIT.

Figure 1

(Left) Ideal cubic perovskite structure. The TM cations (blue) form a simple cubic lattice and are octahedrally coordinated by anions (red). The larger $A$-site cations (green) occupy the voids formed in between eight anion octahedra. (Right) Distorted perovskite structure exhibiting tilted octahedra. The depicted case corresponds to $Pbnm$ space group symmetry.

Figure 2

Schematic depiction of the crystal-field splitting between $t_{2g}$ orbitals induced under compressive and tensile epitaxial strain, respectively. Here, the $x\text{−}y$ plane is oriented parallel to the surface of the hypothetical substrate.

Figure 3

Electronic structure of unstrained ${\mathrm{SrVO}}_3$ around the Fermi level, ${\varepsilon }_{\mathrm{F}}$, obtained from DFT. (Left) Total DOS (gray filled area) and partial DOSs (lines) projected onto atomic orbitals with V-$t_{2g}$ (solid red), V-$e_g$ (solid blue), and O-$p$ character (dashed green). (Right) Kohn-Sham eigenvalues along high-symmetry lines in $k$ space. The color represents the amount of V-$t_{2g}$ character within each bands (color scale on the right), with a value of 1 (0) corresponding to maximal (zero) overlap of the corresponding Bloch wave function with the V-$t_{2g}$ atomic orbitals.

Figure 4

Crystal-field splitting (a) and nearest-neighbor hopping amplitudes along one of the two equivalent in-plane directions (b) and along the out-of-plane direction (c) in ${\mathrm{SrVO}}_3$ as a function of epitaxial strain. The crystal-field levels in (a) are shown relative to the average $t_{2g}$ orbital energy for each strain.

Figure 5

DMFT results for unstrained ${\mathrm{SrVO}}_3$ (black) and for ${\mathrm{SrVO}}_3$ under tensile (red) or compressive (blue) epitaxial strain. (a) Trace of the Green's function $G\left(\tau \right)$ at $\tau =\beta /2$ and (b) orbitally resolved occupations, summed over both spin components, obtained from $-G\left(\beta \right)$, as a function of the interaction parameter $U$. The orbitally resolved spectral function $A\left(\omega \right)$ evaluated at $U=5.5$ eV is plotted as a function of $\omega$ for the unstrained case (c), under compressive strain (d), and under tensile strain (e). Different line styles in (b)–(e) differentiate between the $d_{xy}$ orbital (solid) and the degenerate $d_{xz}/d_{yz}$ orbitals (dashed).

Figure 6

Separate effects of the strain-induced changes of the crystal-field splitting (a) and of the hopping amplitudes (b), i.e., in (a), the hopping amplitudes are fixed to their unstrained values and in (b) the same is done for the crystal-field splitting. The plots show the evolution of the trace of $G(\beta /2)$ as a function of $U$ under compressive strain (blue) and tensile strain (red) in comparison to the unstrained case (black).

Figure 7

Strain-dependent crystal-field levels of the three TM $t_{2g}$ orbitals for ${\mathrm{LaTiO}}_3$ (left) and ${\mathrm{LaVO}}_3$ (right). For each strain, the orbital levels are shown with respect to the corresponding average value ${\varepsilon }_{\mathrm{avg}}$. The data for ${\mathrm{LaTiO}}_3$ is reproduced from Ref. [21].

Figure 8

Strain dependence of nearest-neighbor (NN, top) and next-nearest-neighbor (NNN, bottom) hopping amplitudes in ${\mathrm{LaVO}}_3$. The left panels corresponds to in-plane hoppings (along $x$ for NN and along $x+y$ for NNN), the right panels correspond to out-of-plane hoppings ($z$ for NN and $x+z$ for NNN). Orbital “1” roughly corresponds to $d_{xy}$ and is oriented mostly in-plane, while orbitals “2” and “3” derive from $d_{xz}$ and $d_{yz}$, respectively (see text).

Figure 9

Separate effects of the strain-dependent crystal-field splitting, i.e., hopping parameters fixed to the unstrained values, (top) and of the strain-dependent hopping parameters, i.e., crystal field fixed to the unstrained values, (bottom) for ${\mathrm{LaTiO}}_3$ (left) and ${\mathrm{LaVO}}_3$ (right).