Exploring the Mott coexistence region employing an energy-volume coupled Ising-like model

Strongly correlated electron systems continue attracting great interest from the scientific community. The strong interaction between electrons gives rise to several exotic phases of matter, including superconductivity and the Mott insulating phase. In this contribution, we explore the Mott coexistence region, where metallic $\textit{puddles}$ emerge in a ferroelectric insulating matrix upon pressurization. The Hubbard parameter $U/W \propto p^{-1}$ is the tuning parameter, being $U$ the inter-site Coulomb repulsion, $W$ the bandwidth and $p$ the applied pressure [1]. The coexistence region surrounds the spinodal line, i.e., the line that marks the first-order transition between the metallic and insulating phases [1, 2]. We propose a new type of Grüneisen parameter, which we call the dielectric Grüneisen parameter $\Gamma_{\varepsilon}$, obtained using an energy-volume coupled Ising-like model [3, 4]. Using scaling arguments, we show that the relaxation time depends on the entropy and that $\Gamma_{\varepsilon}$ can be recognized as the scaling exponent [5]. Upon approaching the critical Hubbard parameter, i.e., upon approaching the spinodal line, the relaxation time shows a divergent-like behavior. Considering the intrinsic spatial randomness in the coexistence region and the slowing-down of the electron dynamics, our findings suggest that this region can be identified as a Griffiths-like phase [6]. Also, we propose the electric Grüneisen parameter, which allows the quantification of the electrocaloric effect.

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[5] R. Casalini, C.M. Roland, Phys. Rev. E $\textbf{69}$, 062501 (2004).
[6] Robert B. Griffiths, Phys. Rev. Lett. $\textbf{23}$, 17 (1969).

E-mail for corresponding author: [email protected]