Delocalized polaron and Burstein-Moss shift induced by Li in α−V2O5 : A DFT+DMFT

We performed density functional theory (DFT)$+U$ and dynamical mean field theory (DMFT) calculations with a continuous-time quantum Monte Carlo impurity solver to investigate the electronic properties of ${\mathrm{V}}_{2}{\mathrm{O}}_{5}$ and ${\mathrm{Li}}_{x}{\mathrm{V}}_{2}{\mathrm{O}}_{5}\phantom{\rule{4pt}{0ex}}(x=0.125$ and 0.25). Pristine ${\mathrm{V}}_{2}{\mathrm{O}}_{5}$ is a charge-transfer insulator with strong O $p--\mathrm{V}\phantom{\rule{4pt}{0ex}}d$ hybridization, and it exhibits a large band gap $({E}_{\text{gap}})$ as well as a nonzero conduction-band (CB) gap. We show that the band gap, the number of $d$ electrons of vanadium, ${N}_{d}$, and the CB gap for ${\mathrm{V}}_{2}{\mathrm{O}}_{5}$ obtained from our DMFT calculations are in excellent agreement with the experimental values. While the $\mathrm{DFT}+U$ approach replicates the experimental band gap, it overestimates the value of ${N}_{d}$ and underestimates the CB gap. In the presence of low Li doping, the electronic properties of ${\mathrm{V}}_{2}{\mathrm{O}}_{5}$ are mainly driven by a polaronic mechanism, and electron spin resonance and electron nuclear double resonance spectroscopies observed the coexistence of free and bound polarons. Notably, our DMFT results identify both polaron types, with the bound polaron being energetically preferred, while the $\mathrm{DFT}+U$ method only predicts the free polaron. Our DMFT analysis also reveals that increased Li doping leads to electron filling in the conduction band, shifting the Fermi level. This result is consistent with the observed Burstein-Moss shift upon enhanced Li doping, and we thus demonstrate that the $\mathrm{DFT}+\mathrm{DMFT}$ approach can be used for an accurate and realistic description of strongly correlated materials.