  The non-equilibrium boron nitride (BN) phase of zinc oxide (ZnO) has been
reported for thin films and nanostructures, however, its properties are not
well understood due to a persistent controversy that prevents reconciling
experimental and first-principles results for its atomic coordinates. We use
first-principles theoretical spectroscopy to accurately compute electronic and
optical properties, including single-quasiparticle and excitonic effects: Band
structures and densities of states are computed using density functional
theory, hybrid functionals, and the $GW$ approximation. Accurate optical
absorption spectra and exciton binding energies are computed by solving the
Bethe-Salpeter equation for the optical polarization function. Using this data
we show that the band-gap difference between BN-ZnO and wurtzite (WZ) ZnO
agrees very well with experiment when the theoretical lattice geometry is used,
but significantly disagrees for the experimental atomic coordinates. We also
show that the optical anisotropy of BN-ZnO differs significantly from that of
WZ-ZnO, allowing to optically distinguish both polymorphs. By using the
transfer-matrix method to solve Maxwell's equations for thin films composed of
both polymorphs, we illustrate that this opens up a promising route for tuning
optical properties.
