Split Ga vacancies and the colossal anisotropy of positron annihilation spectra in $\boldsymbol{\beta}$-Ga$_2$O$_3$

We report a systematic first principles study on positron annihilation parameters in the $\beta$-Ga$_2$O$_3$ lattice and Ga mono-vacancy defects complemented with direction-dependent experiments of the Doppler broadening of the positron-electron annihilation. We find that both the $\beta$-Ga$_2$O$_3$ lattice and the considered defects exhibit colossal anisotropy in their Doppler broadening signals. This anisotropy is associated with the unusual kind of low symmetry of the $\beta$-Ga$_2$O$_3$ crystal structure that leads to one-dimensional confinement of positrons even in the delocalized state in the lattice. In particular, the split Ga vacancies recently observed by scanning transmission electron microscopy produce unusually anisotropic positron annihilation signals. We show that in experiments, the positron annihilation signals in $\beta$-Ga$_2$O$_3$ samples are dominated by split Ga vacancies.