A Unified Understanding of the Experimental Controlling of the T$_\text{c}$ of La$_3$Ni$_2$O$_7$

Abstract

Recently, a series of experiments have been conducted which control the superconducting T$_\text{c}$ of the bilayer nickelates La$_3$Ni$_2$O$_7$ through tuning the oxygen stoichiometry, the element substitution, the pressure or strain, catching great interests. Here, we provide a unified understanding toward these experiments based on the previously proposed effective $d_{x^2-y^2}$-orbital bilayer $t-J_\parallel-J_\perp$ model with model parameters input from first-principle calculations. This model exhibits a T$_\text{c}$-controlling behavior well analogous to the hole-doped overdoped cuprates, due to near quarter-filling of the $d_{x^2-y^2}$ orbital. For doping dependence, this mode exhibits a particle-hole asymmetry: The hole (electron) doping makes the system more (less) heavily overdoped and suppresses (enhances) T$_\text{c}$.This character well explains the experimental finding that hole doping introduced through increasing oxygen stoichiometry or alkaline-earth Ca$^{2+}$/Sr$^{2+}$ substitution of La suppresses T$_\text{c}$, and the ``half-dome'' behavior in the oxygen-stoichiometry controlling. For interaction dependence, T$_\text{c}$ follows the variation of $J_\perp$, which well explains the enhancement of bulk T$_\text{c}$ under pressure by Sm/Nd substitution of La, the ``right-triangle'' shaped bulk T$_\text{c}$-pressure relation and the enhancement of T$_\text{c}$ with compressive strain in the film. In comparison with weak-coupling theories in which T$_\text{c}$ mainly relies on the density of states and the $d_{z^2}$-orbital dominated pairing mechanism in which T$_\text{c}$ scales with $d_{z^2}$ hole density, our model provides a more natural and unified understanding toward experiments. We propose that electron doping implemented through approaches without inducing disorder, e.g. substitution of La by element with higher valence, can enhance T$_\text{c}$.