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Cuprate high-temperature superconductors are known to have a normal-statepseudogap but, after many years of intense research, its relation to thesuperconductivity is still a mystery. Similarly, the in-plane Hall coefficient$R_{\rm H}$ has a large temperature variation caused by changes in the carrierdensity which is also a long-standing puzzle. We approach both problems by akinetic theory of phase separation that reproduces the charge density wave by afree energy array of potential wells. The charge modulation favors localhole-hole attraction yielding local superconducting pairs and a transition bylong-range phase order at $T_{\rm c}$. As the temperature increases themodulations decrease and the charge density increases by thermal activation.This approach reproduces the $R_{\rm H}$ of La$_{2-x}$Sr$_x$CuO$_4$ compoundsof $x = 0.0 - 0.25$ and clarifies the role of the pseudogap and the disorder incuprates.

The role of the pseudogap in cuprate superconductors revealed by the Hall effect