= Formal hole count in a cuprate
{title2=$p_{\mathrm{formal}}=x-2\delta$}
For a chosen homogeneous composition $\mathrm{La}_{2-x}\mathrm{Ba}_x\mathrm{CuO}_{4-\delta}$, assign formal <oxidation states> $+3$ to <lanthanum>, $+2$ to <barium> and $-2$ to <oxygen>. If $v$ is the mean formal <copper> <oxidation state>, <charge neutrality> requires
$$
3(2-x)+2x+v-2(4-\delta)=0,
\qquad v=2+x-2\delta.
$$
The excess formal positive charge per <copper> relative to $+2$ is therefore $p_{\mathrm{formal}}=x-2\delta$. For stipulated $x=0.12$ and $\delta=0.01$, it is $0.10$; at $\delta=0.06$, it is zero. These are bookkeeping examples, not measurements of mobile carriers. The symbol $x$ here belongs to this declared formula, not the original mixed-phase recipe. A whole-pellet elemental ratio cannot simply be assigned to each constituent phase.
<Charge neutrality> alone does not locate holes. The lecture reviews <oxygen>-related carrier evidence and charge-$2e$ pairing from the <Josephson effect> and <fluxoid and flux quantization in a superconductor>. Pair charge does not establish <phonon>-mediated <BCS theory> for <cuprate superconductors>.<Perovskite-type oxides: The new approach to high-Tc superconductivity by Johannes Georg Bednorz and Karl Alexander Müller>[Part 2, pp.444–446, 450; pairing, carriers and mechanism]{ref}
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