  We investigate the effect of localization on the local charging of quantum
batteries (QBs) modeled by disordered spin systems. Two distinct schemes based
on the transverse-field random Ising model are considered, with Ising couplings
defined on a Chimera graph and on a linear chain with up to next-to-nearest
neighbor interactions. By adopting a low-energy demanding charging process
driven by local fields only, we obtain that the maximum extractable energy by
unitary processes (ergotropy) is highly enhanced in the ergodic phase in
comparison with the many-body localization (MBL) scenario. As we turn off the
next-to-nearest neighbor interactions in the Ising chain, we have the onset of
the Anderson localization phase. We then show that the Anderson phase exhibits
a hybrid behavior, interpolating between large and small ergotropy as the
disorder strength is increased. We also consider the splitting of total
ergotropy into its coherent and incoherent contributions. This incoherent part
implies in a residual ergotropy that is fully robust against dephasing, which
is a typical process leading to the self-discharging of the battery in a real
setup. Our results are experimentally feasible in scalable systems, such as in
superconducting integrated circuits.
