${\mathrm{Sr}}_2\mathrm{V}{\mathrm{O}}_4$ and ${\mathrm{Ba}}_2\mathrm{V}{\mathrm{O}}_4$ under pressure: An orbital switch and potential $d^1$ superconductor

We study ${\mathrm{Sr}}_2\mathrm{V}{\mathrm{O}}_4$ and ${\mathrm{Ba}}_2\mathrm{V}{\mathrm{O}}_4$ under high pressure by means of the local-density $\text{approximation}+\text{dynamical}$ mean-field theory method. While ${\mathrm{Sr}}_2\mathrm{V}{\mathrm{O}}_4$ is a $1∕6$-filling three-band system at ambient pressure with a small level splitting between the $d_{xy}$ and $d_{yz∕zx}$ bands, we show that an orbital polarization occurs under uniaxial pressure, which will lead to dramatic changes of the magnetic and transport properties. When pressure is applied in the $c$ direction, a $d^1$ analog of $d^9$ cuprates is realized, making ${\mathrm{Sr}}_2\mathrm{V}{\mathrm{O}}_4$ a possible candidate for a $d^1$ superconductor. We also study the effect of chemical pressure by substituting Sr by Ba, and find that a $d^1$ analog of cuprates can be realized more easily by growing ${\mathrm{Ba}}_2\mathrm{V}{\mathrm{O}}_4$ on a substrate with lattice constant of $4.1–4.2\mathrm{\AA }$.

Figure 1

(Color online) (a) NMTO Wannier function of the V $d_{xy}$ orbital for ${\mathrm{Sr}}_2\mathrm{V}{\mathrm{O}}_4$, shown together with the oxygen and Sr ions. The position of Sr and the apical oxygen are optimized by a plane-wave GGA calculation. (b) GGA-optimized distance between O and V along the $c$ direction (open squares) and in the $ab$ plane (open circles) as a function of the $c$-axis elongation $c∕c_0$.

Figure 2

(Color online) Density of states of the $t_{2g}$ band obtained by LDA calculation for (a) atmospheric pressure, (b) uniaxial pressure in the $c$ direction $(c∕c_0=0.9)$, and (c) uniaxial pressure in the $ab$ plane $(c∕c_0=1.1)$. The solid (dashed) line is for the $d_{xy}$ orbital ($d_{yz∕zx}$ orbitals). Inset: LMTO band structure for atmospheric pressure.

Figure 3

(a) NMTO crystal-field splitting between the $d_{xy}$ and $d_{xz∕yz}$ orbitals. (b) Electron occupations for the $d_{xy}$ (squares) and $d_{xz∕yz}$ orbitals (circles).

Figure 4

(Color online) $\mathrm{LDA}+\mathrm{DMFT}$ spectral function for atmospheric pressure, where the dashed, dotted, and solid lines are for $d_{xy}$, $d_{xz∕yz}$, and the total ${\mathrm{Sr}}_2\mathrm{V}{\mathrm{O}}_4$ spectrum, respectively. For $U^{\prime }=2.8\mathrm{eV}$, two solutions [(b) metallic and (c) insulating] coexist.

Figure 5

(Color online) Same as Fig. 4 but for (a) uniaxial pressure in the $ab$ plane $(c∕c_0=1.1)$ with $U^{\prime }=2.8\mathrm{eV}$ and (b) uniaxial pressure in the $c$ direction $(c∕c_0=0.9)$ with $U^{\prime }=2.5\mathrm{eV}$.

Figure 6

(Color online) Density of states of the $t_{2g}$ band of ${\mathrm{Ba}}_2\mathrm{V}{\mathrm{O}}_4$ obtained by LDA for (a) atmospheric pressure and (b) uniaxial pressure in the $c$ direction $(c∕c_0=0.95)$. (c) and (d) are $\mathrm{LDA}+\mathrm{DMFT}$ spectral function for (a) and (b), respectively, with $U^{\prime }=2.5\mathrm{eV}$.