Possible Liquid-Nitrogen-Temperature Superconductivity Driven by Perpendicular Electric Field in the Single-Bilayer Film of La$_3$Ni$_2$O$_7$ at Ambient Pressure

TL;DR

This work proposes a practical route to realize superconductivity above liquid-nitrogen temperature in a La$_3$Ni$_2$O$_7$ single-bilayer at ambient pressure by applying a perpendicular electric field. Using both a simplified one-orbital bilayer model and a comprehensive two-orbital framework, the authors show that field-driven charge transfer increases bottom-layer $d_{x^2-y^2}$ filling, suppresses interlayer $s$-wave pairing, and promotes intralayer $d$-wave superconductivity, with estimated $T_c$ around $80$ K for realistic voltages ($\sim0.1$--$0.2$ V). The results, validated by slave-boson mean-field theory and density-matrix renormalization group calculations, reveal a transition from $s$-wave to $d$-wave pairing and, in the two-orbital case, a time-reversal-symmetry-breaking $s+\mathrm{i}d$ admixture at intermediate fields. The findings suggest a robust, disorder-free method to tune high-$T_c$ superconductivity in oxide heterostructures and invite experimental verification at ambient pressure with plausible field strengths.

Abstract

Recently, high-temperature superconductivity (HTSC) is found in the La$_3$Ni$_2$O$_7$/SrLaAlO$_4$ ultrathin film with critical temperature $T_c$ above the McMillan limit at ambient pressure (AP). It is eager to enhance $T_c$ of La$_3$Ni$_2$O$_7$ at AP. We propose that a perpendicular electric field strongly enhances $T_c$ in the single-bilayer film of La$_3$Ni$_2$O$_7$ at AP. Under electric field, the layer with lower potential energy will accept electrons flowing from the other layer to fill in the Ni-$3d_{x^2-y^2}$ orbitals, as the nearly half-filled Ni-$3d_{z^2}$ orbital cannot accommodate more electrons. With the enhancement of the filling fraction in the $3d_{x^2-y^2}$ orbitals in this layer, the interlayer $s$-wave pairing is suppressed, but the intralayer $d$-wave pairing in this layer is strongly enhanced. We numerically verify this idea and yield that an imposed voltage of about $0.1\sim0.2$ volt between layers is enough to realize liquid-nitrogen-temperature HTSC in this single bilayer at AP. Our results appeal for experimental verification.

Figures (17)

• Figure 1: Schematic diagrams of the model. (a) Schematic diagram for the dominant hopping integrals and superexchange interactions between the $E_g$ orbitals in La$_3$Ni$_2$O$_7$. (b) Schematic diagram illustrating that the Hund's rule coupling transmits the interlayer perpendicular superexchange interaction $J_\perp$ between the $3d_{z^2}$ orbitals to the effective one $\tilde{J}_\perp$ between the $3d_{x^2-y^2}$ orbitals.
• Figure 2: Schematic diagrams of particle number and pairing configuration before and after introducing perpendicular electric field. (a) Particle numbers of the four $E_g$ orbitals within an unit cell without electric field. (b) The dominant pairing configuration for (a). (c) Schematic diagram showing how the electrons flow under the perpendicular electric field $\bm{\upvarepsilon}$ pointing upward. (d) The dominant pairing configuration for (c).
• Figure 3: The SBMF results for the single-orbital model. (a) The pairing amplitude $\tilde{\Delta}$ (in unit of $t_{\parallel}$) as function of the bottom-layer particle number per site $n_{bx}$. Different pairing symmetries are distinguished by color. (b) The $T_c$ as function of $n_{bx}$, in comparison with $0.42\tilde{\Delta}$ for the $d$-wave and $0.9\tilde{\Delta}$ for the $s$-wave regime. Inset: the spinon pairing temperature $T_{\mathrm{pair}}$ and the holon condensation temperature $T_{\mathrm{BEC}}$ as function of $n_{bx}$. In (a,b), we set $J_{\parallel}=0.4t_{\parallel}$ and $\tilde{J}_{\perp}=(1-\delta_{tz})\times1.3J_{\parallel}$. (c)-(d) The pairing configurations of the $s$-wave and $d$-wave, respectively.
• Figure 4: The DMRG results. (a) The $\delta-\varepsilon$ phase diagram of the ground state. The red region corresponds to the $s$-wave pairing and the blue region to the $d$-wave pairing. (b)-(c) The absolute value of the intra-bottom-layer pairing correlation functions $|\Phi^{\parallel}_b(r)|$ under different electric fields $\varepsilon=0, 0.4t_\parallel, 0.8t_\parallel, 1.2t_\parallel, 1.6t_\parallel$ for $\delta=0$ in (b) and $\delta=1/16$ in (c). (d)-(e) $|\Phi^{\parallel}_b(r)|$ for different transferred $d_{x^2-y^2}$-electron-doping levels $\delta=0,1/16,1/8$ under $\varepsilon=0.4t_\parallel$ in (d) and $\varepsilon=0.8t_\parallel$ in (e). The algebraic decay exponents $K_\text{SC}$ are written in the four figures as well, reflecting the decay rate of the pairing correlation function with spatial distance, negatively correlated with the corresponding pairing strength. In (a-e), $\delta$ and $\varepsilon$ are set as independent variables, since their exact relationship is unclear.
• Figure 5: The SBMF results for the two-orbital model. (a) The hole densities $\delta_{\mu\alpha}$ for the three orbitals as functions of the strength of the electric field $\varepsilon$. (b) The pairing gap amplitude of the bottom-layer $3d_{x^2-y^2}$-orbital as function of $\varepsilon$. (c)-(d) The pairing configurations of the $s$-wave and the $d$($3d_{x^2-y^2}$)+i$s$($3d_{z^2}$)-wave, respectively.