Pairing susceptibility in the weakly interacting multilayer Hubbard model evaluated by direct perturbative expansion

Abstract

We present a systematic study of the interaction, doping, and layer dependence of the $d_{x^2-y^2}$-wave pairing susceptibility of the Hubbard model for a stacked 2D square lattice. We perform a multi-index perturbative expansion up to fourth-order to obtain coefficients in powers of the Hubbard $U$, the inter-layer $V$, and the pair-hopping $J$ interactions. We evaluate the vertex diagrams that contribute to the pairing susceptibility for $\ell =2,3,4$ layered models in the $U$-$V$-$J$ interaction space. This provides unprecedented access to the pairing amplitudes, allowing us to identify the processes that enhance or reduce pairing. We distinguish pairing within the diagonal channel, $P_d^{\parallel }$, and off-diagonal channel, $P_d^{\perp }$, and find that, in the absence of $J$, the qualitative behavior of the layered system is equivalent to the single-layer model. In the presence of $J$, we show that pairing is enhanced sublinearly with increasing $\ell$ and is primarily mediated by the $P_d^{\perp }$ component and find which coefficients and diagram sets are responsible. Finally, we construct a generalized $\ell$-dependent equation for $P_d^{\perp }$ to speculate pairing beyond $\ell =4$.

21 pages, 9 figures in the main text, 10 figures in the supplemental material (appended)

References in corpus (46)

• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Superconductivity and the Pseudogap in the two-dimensional Hubbard model
• Absence of superconductivity in the pure two-dimensional Hubbard model
• Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods
• Superconductivity in the Hubbard model and its interplay with charge stripes and next-nearest hopping t'
• Local Electronic Correlation at the Two-Particle Level
• Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory
• One-band tight-binding model parametrization of the high-$T_c$ cuprates, including the effect of $k_z$-dispersion
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model
• New Perspective on the Phase Diagram of Cuprate High-Temperature Superconductors
• High-Tc Superconductivity and Antiferromagnetism in Multilayered Copper Oxides - A New Paradigm of Superconducting Mechanism -
• Ground state phase diagram of the doped Hubbard model on the 4-leg cylinder
• Mott physics and first-order transition between two metals in the normal state phase diagram of the two-dimensional Hubbard model
• Plaquette versus ordinary $d$-wave pairing in the $t^{\prime }$-Hubbard model on a width 4 cylinder
• Direct comparison of many-body methods for realistic electronic Hamiltonians
• Emergent BCS regime of the two-dimensional fermionic Hubbard model: ground-state phase diagram
• Enhanced Superconductivity in Superlattices of High-$T_c$ Cuprates
• Superconducting state of Sr${}_2$RuO${}_4$ in the presence of longer-range Coulomb interactions
• Magnetic and Transport Properties of a Coupled Hubbard Bilayer with Electron and Hole Doping
• Electronic Origin of High-Tc Maximization and Persistence in Trilayer Cuprate Superconductors
• Algorithmic Matsubara Integration for Hubbard-like models
• Superconducting Fluctuations in the Normal State of the Two-Dimensional Hubbard Model
• Enhanced superconductivity by near-neighbor attraction in the doped Hubbard model
• Pair density wave in doped three-band Hubbard model on two-leg square cylinders
• Resistivity phase diagram of cuprates revisited
• Optimal grouping of arbitrary diagrammatic expansions via analytic pole structure
• Superconductivity assisted by inter-layer pair hopping in multi-layered cuprates
• Quantifying the role of antiferromagnetic fluctuations in the superconductivity of the doped Hubbard model
• Algorithmic approach to diagrammatic expansions for real-frequency evaluation of susceptibility functions
• Role of the van Hove Singularity in the Quantum Criticality of the Hubbard Model
• Effect of interlayer processes on the superconducting state within t-J-U model: Full Gutzwiller wave-function solution and relation to experiment
• Uniform Mixing of Antiferromagnetism and High-Tc Superconductivity in Electron-doped Layers in Four-layered Ba2Ca3Cu4O8F2 : A New Phenomenon in an Electron Underdoped RegimePhenomenon in an Electron Underdoped Regime
• Pairing correlations in the cuprates: a numerical study of the three-band Hubbard model
• Magnetic Susceptibility and Simulated Neutron Signal in the 2D Hubbard Model
• Many-variable variational Monte-Carlo study of superconductivity in two-band Hubbard models with an incipient band
• Hybridization of Bogoliubov-quasiparticles between adjacent CuO${}_2$ layers in the triple-layer cuprate Bi${}_2$Sr${}_2$Ca${}_2$Cu${}_3$O${}_{10+\delta }$ studied by ARPES
• Spin susceptibility in bilayered cuprates: resonant magnetic excitations
• Multiband mean-field theory of the $d+ig$ superconductivity scenario in Sr${}_2$RuO${}_4$
• Single particle properties of the 2D Hubbard model for real frequencies at weak coupling: Breakdown of the Dyson series for partial self-energy expansions
• Renormalized Perturbation Theory for Fast Evaluation of Feynman Diagrams on the Real Frequency Axis
• Pair-Hopping Mechanism for Layered Superconductors
• Superconductivity in bilayer $t$-$t^{\prime }$ Hubbard models
• Superconductivity arising from layer-differentiation in multi-layer cuprates
• Pairing susceptibility of the two-dimensional Hubbard model in the thermodynamic limit
• Coexistence of superconductivity and antiferromagnetism in self-doped bilayer t-t'-J model
• Self-doping effect arising from electron correlations in multi-layer cuprates

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