Unified model of the Hall effect from insulator to overdoped compounds in cuprate superconductors

Measurements of the Hall coefficients in ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$, ranging from the undoped ($x=p=0$) Mott insulator to overdoped compounds, exhibit a temperature dependence that offers insights into these compounds' electronic structure. We interpret these results using a model based on the theory of phase-separation dynamics, which begins at half-filled ($n=1$) and at a temperature ${T}_{\mathrm{PS}}(p)$, near the pseudogap temperature ${T}^{*}(p)$. The $n=1$ holes have low mobility and provide the modulations of the charge density waves (CDW). As doping increases from $p=0$, these modulations guide the additional $p$ holes to occupy alternating CDW domains. This charge inhomogeneity may facilitate the formation of localized superconducting amplitudes below the critical onset temperature ${T}_{\mathrm{c}}^{\mathrm{max}}(p)$. Using thermal activation expressions, along with quantum tunneling between the charge domains, we successfully reproduce all Hall coefficient measurements ${R}_{\mathrm{H}}(p,T)$ and highlight the relevant energies of the cuprates. The calculations confirm three significant electronic features: the phase-separating role of the pseudogap temperature, the superconducting state achieved through phase coherence, and the two types of charge carriers whose energies and mobilities become comparable at $p\ensuremath{\approx}0.19$, where ${T}^{*}(p)\ensuremath{\approx}{T}_{\mathrm{c}}^{\mathrm{max}}(p)$. This results in a crossover from $n=p$ to $n=1+p$. These findings, along with the ${R}_{\mathrm{H}}(p,T)$ calculations from insulating to overdoped compounds, underscore the critical role of the electronic phase separation in the properties of cuprates.