Supplementary material

1.  ZrO2-x cell building and DFT calculations

Calculations were performed at the DFT level using the 3.2 version of the SIESTA code [1] including periodic boundary conditions. The calculations were made in the Generalized Gradient Approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE) functional [2]. Trouillier-Martins pseudopotentials were used to simulate the ion and core electrons. We used 5s2 4d2 as valence configuration for Zr with 3.04, 3.19 and 2.68 bohr for s, p and d channels, respectively. For oxygen we have used 1.14 bohr for all channels. The atomic basis set was described using a double zeta basis plus polarization orbitals (DZP).

ZrO2 supercell of cubic, tetragonal and monoclinic polymorphs was build using 96 atoms (32 Zr and 64 O) by a duplication of the experimental unit cell in the three directions. The final lattice vectors of the three polymorphs are: a = 10.14 Å for cubic; a = b = 10.10 Å, c = 10.36 Å for tetragonal; a = 10.29 Å, b = 10.42 Å, c = 10.62 Å, β = 99.23° for monoclinic. Oxygen vacancies were created randomly in the zirconia lattice by removing O atoms to assess the Influence of O vacancies on the phase constitution.

The optimization of the structure and the calculation of the electronic structure were performed at 0 K using a mesh cut-off of 190 Ry and a Monhkorst-Pack grid of (2x2x2) k-point. The atomic positions were relaxed until the forces on the atom were less than 0.04 eV/Ang while the lattice vectors of the unit cell were fixed during the calculation.

2.  Effect of O vacancies on electronic states

Density of states (DOS) of cubic structure were also calculated for various O vacancy concentration from DFT calculation, shown in Fig. S1. One can observe the generation of new electronic states appearing in the band gap, as oxygen vacancies are generated. This is a consequence of the presence of the free electrons coming from the zirconium atoms. The later are not trapped by the oxygen atoms and are more free to move in the material.

Fig. S 1: DOS of the relaxed cubic structures having (a) 0 at.% (b) 2 at.% (c) 4 at.% (d) 10 at.% O vacancies.

Reference

[1] J.M. Soler, E. Artacho, J.D. Gale, A. Garcìa, J. Junquera, P. Ordejòn, D. Sànchez-Portal, J. Phys. Condens. Matter 14 (2002) 2745–2779.

[2] J. Perdew, K. Burke, Y. Wang, Phys. Rev. B 54 (1996) 16533–16539.