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

Abstract: Measurements of the Hall coefficient in La${2-x}$Sr$_x$CuO$_4$, ranging from the undoped ($x = p = 0$) Mott insulator to overdoped compounds, exhibit a temperature dependence that offers insights into their electronic structure. We interpret these results using a model based on the theory of phase-separation (PS) dynamics, which begins at half-filled ($n = 1$) and at a temperature $T{\rm PS}(p)$, 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 $T_{\rm c}^{\rm max}(p)$. Using thermal activation expressions, along with quantum tunnelling between the charge domains, we successfully reproduce all Hall coefficient measurements $R_{\rm H}(p,T)$ and highlight the relevant energies of 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 $p \approx 0.19$, where $T^*(p) \approx T_{\rm c}^{\rm max}(p)$. This results in a crossover from $n = p$ to $n = 1 + p$. These findings, along with the $R_{\rm H}(p,T)$ calculations from insulating to overdoped compounds, underscore the critical role of the electronic phase separation in the properties of cuprates.