| Summary: | We have investigated the structural, electronic and magnetic properties of the Mott insulator Ca<sub>2</sub>RuO<sub>4</sub> under the application of a static external electric field in two regimes: bulk systems at small fields and thin films at large electric fields. Ca<sub>2</sub>RuO<sub>4</sub> presents S- and L-Pbca phases with short and long c lattice constants and with large and small band gaps, respectively. Using density functional perturbation theory, we have calculated the Born effective charges as response functions. Once we break the inversion symmetry by off-centering the Ru atoms, we calculate the piezoelectric properties of the system that suggest an elongation of the system under an electric field. Finally, we investigated a four-unit cell slab in larger electric fields, and we found insulator–metal transitions induced by the electric field. By looking at the local density of states, we have found that the gap gets closed on surface layers while the rest of the sample is insulating. Correlated to the electric-field-driven gap closure, there is an increase in the lattice constant c. Regarding the magnetic properties, we have identified two phase transitions in the magnetic moments with one surface that gets completely demagnetized at the largest field investigated. In all cases, the static electric field increases the lattice constant c and reduces the band gap of Ca<sub>2</sub>RuO<sub>4</sub>, playing a role in the competition between the L-phase and the S-phase.
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