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Low-valent nickelates R$_{n+1}$Ni$_n$O$_{2n+2}$ (R = rare earth) containingNi$^{1+}$ (d$^{9}$) with a quasi-two-dimensional (quasi-2D) square planarcoordination geometry possess structural and electronic properties that aresimilar to those of high-Tc cuprates, including superconductivity itself in thedoped infinite layer ($n = \infty$) RNiO$_2$ system. Within thisR$_{n+1}$Ni$_n$O$_{2n+2}$ nickelate family, the crystallographic isomorphsPr$_4$Ni$_3$O$_8$ and La$_4$Ni$_3$O$_8$ exhibit singularly different groundstates: Pr$_4$Ni$_3$O$_8$ is metallic and La$_4$Ni$_3$O$_8$ is a charge- andspin-stripe ordered insulator. To explore and understand the ground stateevolution from metallic Pr$_4$Ni$_3$O$_8$ to stripe-ordered La$_4$Ni$_3$O$_8$in the R$_4$Ni$_3$O$_8$ family, we have grown a series of isovalent-substitutedsingle crystals (Pr$_{1-x}$La$_x$)$_4$Ni$_3$O$_8$. Combining thermodynamic,transport, magnetic, and synchrotron X-ray single crystal diffractionmeasurements, we reveal a transition between metallic and stripe-insulatorphase regions, with a putative quantum phase transition at x = 0.4. We proposetwo possible models for (Pr$_{1-x}$La$_x$)$_4$Ni$_3$O$_8$: an electronicallyinhomogeneous system that could serve as a candidate for exploring quantumGriffiths phase physics and a homogeneous system with a putative quantumcritical point at the phase boundary.

Competing Charge/Spin-Stripe and Correlated Metal Phases in Trilayer Nickelates (Pr$_{1-x}$La$_x$)$_4$Ni$_3$O$_8$