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 $T_{\mathrm{PS}}(p)$, near the pseudogap temperature $T^{\ast }(p)$. 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 $T_{\mathrm{c}}^{\max }(p)$. Using thermal activation expressions, along with quantum tunnelling between the charge domains, we successfully reproduce all Hall coefficient measurements $R_{\mathrm{H}}(p,T)$ 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 $T^{\ast }(p)\approx T_{\mathrm{c}}^{\max }(p)$. 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.

Latex, 7 pages, 2 figures

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