Delocalized polaron and Burstein-Moss shift induced by Li in $\alpha$-$\textrm{V}_{2}\textrm{O}_{5}$: DFT+DMFT study

We performed density functional theory (DFT)+$U$ and dynamical mean field theory (DMFT) calculations with continuous time quantum Monte Carlo impurity solver to investigate the electronic properties of V$_2$O$_5$ and Li$_x$V$_2$O$_5$ ($x$ = 0.125 and 0.25). Pristine V$_2$O$_5$ is a charge-transfer insulator with strong O $p$-V $d$ hybridization, and exhibits a large band gap ($E_{\textrm{gap}}$) as well as non-zero conduction band (CB) gap. We show that the band gap, the number of $d$ electrons of vanadium, $N_d$, and conduction band (CB) gap for V$_2$O$_5$ obtained from our DMFT calculations are in excellent agreement with the experimental values. While the 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 V$_2$O$_5$ are mainly driven by a polaronic mechanism, the 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 DFT+$U$ method predicts only 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 consistent with the observed Burstein-Moss shift upon enhanced Li doping and we thus demonstrate that the DFT+DMFT approach can be used for accurate and realistic description of strongly correlated materials.