A Unified Understanding of the Experimental Controlling of the T$_\text{c}$ of Bilayer Nickelates

Abstract

Recently, a series of experiments which control the T$_\text{c}$ of the bilayer nickelates La$_3$Ni$_2$O$_7$ through varying environmental conditions, including the rare-earth Sm/Nd substitution, the pressure on the bulk material, the compressive strain on the film and the hole doping through over-oxidation or alkaline earth element substitution have caught great interests. Here, we provide a unified understanding toward all these experiments based on the minimal single $d_{x^2-y^2}$-orbital bilayer $t-J_\parallel-J_\perp$ model proposed previously. With model parameters input from density-functional-theoretical calculations under varying experimental conditions, we adopt combined slave-boson-mean-field and density-matrix-renormalization-group approaches to solve the model and compare with experiments. Our results yield that, the bulk T$_\text{c}$ under pressure enhances with the Sm/Nd substitution fraction, the bulk T$_\text{c}$-pressure relation takes a dome shaped curve, the T$_\text{c}$ of the thin film enhances with compressive strain. The obtained parameters dependence of T$_\text{c}$ in these three experiments mainly originates from the variation of $J_\perp$ with experimental conditions. As for the hole doping, our results provide that T$_\text{c}$ decreases with the hole doping level $δ$, due to reduced density of state for the $d_{x^2-y^2}$-orbital. All these results are qualitatively consistent with experiments. We further conduct a comparative weak-coupling random-phase-approximation (RPA) based study on these experiments and find that our strong-coupling $t-J_\parallel-J_\perp$ model provides a more natural understanding of the experiments. We propose that electron doping implemented through substitution of La by element with higher valence, or further enhancement of the compressive strain in the film, can enhance T$_\text{c}$.

Figures (9)

• Figure 1: Schematic diagram and properties of the models. (a) Schematic diagram of the two-orbital $t-J-J_H$ model (left) and the one-orbital $t-J_{\parallel}-J_{\perp}$ model (right). (b) The relationship between T$_\text{c}$ (red line) and SC gap $\Delta$ (blue line) of the $t-J_{\parallel}-J_{\perp}$ model and the interlayer superexchange parameter $J_\perp$. The inset compares between the BEC temperature T$_\text{BEC}$ and pairing temperature T$_\text{pair}$, and the results show that T$_\text{c}$ is determined by T$_\text{pair}$. (c) The relationship between T$_\text{c}$ (red line) and SC gap $\Delta$ (blue line) of the $t-J_{\parallel}-J_{\perp}$ model and the filling fraction $n$. The inset shows the relationship between DOS and the filling fraction. In (b) and (c), the left and right arrows point to the $y$-axis correspond to the two lines.
• Figure 2: Mechanism and results on Nd substitution in bulk. (a) The interlayer superexchange parameters $J_\perp^z = 4t_z^{\perp\ 2} / U$ (black line) and $J_\perp$ (red line) change with Nd substitution, where $U = 5$ eV. (b) The T$_\text{c}$ as a function of Nd substitution calculated by SBMF theory. (c) The SC gap as a function of Nd substitution calculated by SBMF theory. (d) The interlayer pairing correlation function $|\Phi^\perp(r)|$ calculated by DMRG. The decay power exponents $K_\text{SC}$ are plotted in the inset as a function of Nd substitution. The legend "log $\sim$ log" corresponds to a log-log plot. The line legends in the figures indicate their meanings.
• Figure 3: Mechanism and results on pressure-dependence in bulk. (a) The interlayer superexchange parameters $J_\perp^z$ (black line) from DFT and $J_\perp$ (red line) calculated by DMRG change with pressure. The gray dash line and black arrow label the structural transition. (b) The T$_\text{c}$ as a function of pressure calculated by SBMF theory. (c) The SC gap as a function of pressure calculated by SBMF theory. (d) The interlayer pairing correlation function $|\Phi^\perp(r)|$ calculated by DMRG.
• Figure 4: Mechanism and results on strain-dependence in the film. (a) The interlayer superexchange parameters $J_\perp^z$ (black line) from DFT and $J_\perp$ (red line) calculated by DMRG change with strain. (b) The T$_\text{c}$ as a function of strain calculated by SBMF theory. (c) The SC gap as a function of strain calculated by SBMF theory. (d) The interlayer pairing correlation function $|\Phi^\perp(r)|$ calculated by DMRG.
• Figure 5: Mechanism and results on hole doping in the film. (a) The filling fraction of $d_{x^2-y^2}$-orbital electrons changes with hole doping. (b) The DOS of $d_{x^2-y^2}$-orbital as a function of hole doping. (c) The T$_\text{c}$ and SC gap as functions of hole doping calculated by SBMF theory. (d) The interlayer pairing correlation functions $|\Phi^\perp(r)|$ with different hole doping level $\delta$ calculated by DMRG.