Optical absorption and luminescence of $α$-LiV$_2$O$_5$ from the Bethe Salpeter Equation

Abstract: $\alpha$-Li$x$V$_2$O$_5$ is obtained by intercalating Li between the layers of V$_2$O$_5$. The partial filling of the split-off conduction band by electron donation from Li leads to significant changes in optical properties. Here we study the electronic band structure of $\alpha$-LiV$_2$O$_5$ using quasiparticle self-consistent (QS) $GW$ calculations and the optical dielectric function by means of the Bethe Salpeter Equation (BSE). The half-filling of the narrow split-off band leads to a spin-splitting and formation of magnetic moments of 0.5 $\mu_B$ per V which order antiferromagnetically along the chain or $b$-direction. The imaginary part of the dielectric function shows a very strong optical absorption band near 2 eV for polarization along the $a$-direction. This absorptions stems from a localized transition between the occupied V-$d{xy}$ derived band, which is odd with respect to the $a$-mirrorplane to the higher lying empty band formed from the same V-$d_{xy}$ orbitals but even with respect to that mirror-plane, which explains its polarization and large oscillator strength. We relate this to a recent experimental study of cathodoluminescence (CL) in which a suppression of the lowest CL peak was observed upon addition of Li. The lowest CL peak near 1.8 eV, which lies well below the indirect absorption onset of V$_2$O$_5$ is proposed to be related to recombination of a self-trapped electron polaron, resulting from oxygen vacancies, with a hole at the valence band maximum and is suppressed in LiV$_2$O$_5$ by the strong self--absorption from the Li induced occupied band to the higher empty bands at about the same energy.