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We performed density functional theory (DFT)+$U$ and dynamical mean fieldtheory (DMFT) calculations with continuous time quantum Monte Carlo impuritysolver to investigate the electronic properties of V$_2$O$_5$ andLi$_x$V$_2$O$_5$ ($x$ = 0.125 and 0.25). Pristine V$_2$O$_5$ is acharge-transfer insulator with strong O $p$-V $d$ hybridization, and exhibits alarge 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 calculationsare 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, theelectronic properties of V$_2$O$_5$ are mainly driven by a polaronic mechanism,the electron spin resonance and electron nuclear double resonancespectroscopies observed the coexistence of free and bound polarons. Notably,our DMFT results identify both polaron types, with the bound polaron beingenergetically preferred, while DFT+$U$ method predicts only the free polaron.Our DMFT analysis also reveals that increased Li doping leads to electronfilling in the conduction band, shifting the Fermi level, this resultconsistent with the observed Burstein-Moss shift upon enhanced Li doping and wethus demonstrate that the DFT+DMFT approach can be used for accurate andrealistic description of strongly correlated materials.

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