Out-of-plane bond-order phase, superconductivity, and their competition in the $t$-$J_{\parallel }$-$J_{\perp }$ model: Possible implications for bilayer nickelates

Abstract

Almost four decades of intense research have been invested to study the physics of high-T${}_c$ cuprate superconductors. The recent discovery of high-T${}_c$ superconductivity in pressurized bilayer nickelates and its potential similarities with cuprate superconductors may open a new window to understand this long-standing problem. We have studied the proposed bilayer $t$-$J_{\parallel }$-$J_{\perp }$ model [where $J_{\parallel }$ ($J_{\perp }$) is the in-plane (out-of-plane) magnetic exchange] in a large-$N$ approach on the basis of the path integral representation for Hubbard operators, which allows to obtain results at mean-field and beyond mean-field level. We find that $J_{\perp }$ is a candidate for triggering high superconducting $T_c$ values at quarter filling (hole doping $\delta =0.5$) of the $d_{x^2-y^2}$ orbitals. Beyond mean-field level, we find a new phase, an out-of-plane bond-order phase (z-BOP), triggered also by $J_{\perp }$. z-BOP develops below a critical temperature which decreases with increasing doping and vanishes at a quantum critical point below quarter filling. The occurrence of this phase and its competition with superconductivity leads to a superconducting dome-shaped behavior as a function of doping and as a function of $J_{\perp }$. Qualitative comparisons with the physics of cuprates and the recent literature on the new pressurized nickelates are given along the paper.

7 pages (main text) + 8 pages (references + appendices), 7 figures

References in corpus (44)

• Superconductivity near 80 Kelvin in single crystals of La3Ni2O7 under pressure
• High-temperature superconductivity with zero-resistance and strange metal behavior in La${}_3$Ni${}_2$O${}_{7-\delta }$
• Bilayer two-orbital model of La${}_3$Ni${}_2$O${}_7$ under pressure
• Superconductivity in pressurized trilayer La${}_4$Ni${}_3$O${}_{10-\delta }$ single crystals
• Possible $S_{\pm }$-wave superconductivity in La${}_3$Ni${}_2$O${}_7$
• The s${}^{\pm }$-Wave Pairing and the Destructive Role of Apical-Oxygen Deficiencies in La${}_3$Ni${}_2$O${}_7$ Under Pressure
• Possible high $T_c$ Superconductivity in La${}_3$Ni${}_2$O${}_7$ under High Pressure through Manifestation of a Nearly-Half-Filled Bilayer Hubbard Model
• Electronic correlations and superconducting instability in La${}_3$Ni${}_2$O${}_7$ under high pressure
• Interlayer Coupling Driven High-Temperature Superconductivity in La${}_3$Ni${}_2$O${}_7$ Under Pressure
• Orbital-Dependent Electron Correlation in Double-Layer Nickelate La3Ni2O7
• Bilayer $t$-$J$-$J_{\perp }$ Model and Magnetically Mediated Pairing in the Pressurized Nickelate La${}_3$Ni${}_2$O${}_7$
• Effective bi-layer model Hamiltonian and density-matrix renormalization group study for the high-Tc superconductivity in La${}_3$Ni${}_2$O${}_7$ under high pressure
• Electronic structure, dimer physics, orbital-selective behavior, and magnetic tendencies in the bilayer nickelate superconductor La${}_3$Ni${}_2$O${}_7$ under pressure
• Pressure-induced superconductivity in polycrystalline La3Ni2O7
• Signature of superconductivity in pressurized La${}_4$Ni${}_3$O${}_{10}$
• Electronic and magnetic excitations in La${}_3$Ni${}_2$O${}_7$
• High Temperature Superconductivity in La${}_3$Ni${}_2$O${}_7$
• High-$T_c$ superconductivity by mobilizing local spin singlets and possible route to higher $T_c$ in pressurized La${}_3$Ni${}_2$O${}_7$
• Theoretical analysis on the possibility of superconductivity in a trilayer Ruddlesden-Popper nickelate La${}_4$Ni${}_3$O${}_{10}$ under pressure and its experimental examination: comparison with La${}_3$Ni${}_2$O${}_7$
• Electronic correlations and partial gap in the bilayer nickelate La${}_3$Ni${}_2$O${}_7$
• Charge Transfer and Zhang-Rice Singlet Bands in the Nickelate Superconductor $\mathrm{L}{\mathrm{a}}_3\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_7$ under Pressure
• Polymorphism in Ruddlesden-Popper $L{a}_{3}N{i}_2{O}_7$: Discovery of a Hidden Phase with Distinctive Layer Stacking
• Normal and superconducting properties of La${}_3$Ni${}_2$O${}_7$
• Electron correlations and superconductivity in La${}_3$Ni${}_2$O${}_7$ under pressure tuning
• High-T${}_C$ superconductivity in $\mathrm{L}{\mathrm{a}}_3\mathrm{N}{\mathrm{i}}_2{\mathrm{O}}_7$ based on the bilayer two-orbital t-J model
• Unconventional crystal structure of the high-pressure superconductor La${}_3$Ni${}_2$O${}_7$
• Neutron Scattering Studies on the High-$T_c$ Superconductor La${}_3$Ni${}_2$O${}_{7-\delta }$ at Ambient Pressure
• Pressure-enhanced spin-density-wave transition in double-layer nickelate $L{a}_{3}N{i}_2{O}_{7-\delta }$
• Detection of Acoustic Plasmons in Hole-Doped Lanthanum and Bismuth Cuprate Superconductors Using Resonant Inelastic X-Ray Scattering
• Multiband Metallic Ground State in Multilayered Nickelates La${}_3$Ni${}_2$O${}_7$ and La${}_4$Ni${}_3$O${}_{10}$ Probed by ${}^{139}$La-NMR at Ambient Pressure
• Superconductivity in trilayer nickelate La4Ni3O10 under pressure
• Non-Fermi Liquid and Hund Correlation in La${}_4$Ni${}_3$O${}_{10}$ under High Pressure
• Effect of Rare-earth Element Substitution in Superconducting R${}_3$Ni${}_2$O${}_7$ Under Pressure
• Density-wave-like gap evolution in La${}_3$Ni${}_2$O${}_7$ under high pressure revealed by ultrafast optical spectroscopy
• Design and synthesis of three-dimensional hybrid Ruddlesden-Popper nickelate single crystals
• Superconductivity in the Bilayer Two-orbital Hubbard Model
• Gapped collective charge excitations and interlayer hopping in cuprate superconductors
• Effective model and electron correlations in trilayer nickelate superconductor La${}_4$Ni${}_3$O${}_{10}$
• Evolution of plasmon excitations across the phase diagram of the cuprate superconductor La${}_{2-x}$Sr${}_x$CuO${}_4$
• Growth and characterization of the La${}_3$Ni${}_2$O${}_{7-\delta }$ thin films: dominant contribution of the $d_{x^2-y^2}$ orbital at ambient pressure
• Impact of electron correlations on two-particle charge response in electron- and hole-doped cuprates
• Electron self-energy from quantum charge fluctuations in the layered t-J model with long-range Coulomb interaction
• Superconductivity with and without glue and the role of the double-occupancy forbidding constraint in the t-J-V model
• Plasmarons in high-temperature cuprate superconductors

Cited by in corpus (6)

• $t$-$J$ model for strongly correlated two-orbital systems: Application to bilayer nickelate superconductors
• Superexchanges and Charge Transfer in the La${}_3$Ni${}_2$O${}_7$ Thin Films
• Robust $s_{\pm }$-wave pairing in a bilayer two-orbital model of pressurized La${}_3$Ni${}_2$O${}_7$ without the $\gamma$ Fermi surface
• Strong-coupling theory of bilayer plasmon excitations
• Raman response in superconducting multiorbital systems with application to nickelates
• Weak coupling theory of nickel-based 327 superconductors