Coupled Hubbard ladders at weak coupling: Pairing and spin excitations

TL;DR

This study uses a weak-coupling approach to analyze how unidirectional hopping modulation in the Hubbard model enhances d-wave pairing correlations and affects spin excitations, revealing increased pairing strength and evolving neutron resonance features.

Contribution

It demonstrates that lattice modulation can enhance pairing correlations and alter spin excitation spectra in coupled Hubbard ladders, providing insights into tuning superconductivity mechanisms.

Findings

Pairing correlations are enhanced by lattice modulation.

Favorable Fermi surface nesting increases spin-fluctuation pairing.

Neutron resonance evolves into incommensurate resonances in weakly coupled ladders.

Abstract

The Hubbard model provides a simple framework in which one can study how certain aspects of the electronic structure of strongly interacting systems can be tuned to optimize the superconducting pairing correlations and how these changes affect the mechanisms giving rise to them. Here we use a weak-coupling random phase approximation to study a two-dimensional Hubbard model with a unidirectional modulation of the hopping amplitudes as the system evolves from the uniform square lattice to an array of weakly coupled two-leg ladders. We find that the pairing correlations retain their dominant $d_{x^2-y^2}$-wave like structure and that they are significantly enhanced for a slightly modulated lattice. This enhancement is traced backed to an increase in the strength of the spin-fluctuation pairing interacting due to favorable Fermi surface nesting in the modulated system. We then use a random-phase approximation BCS framework to examine the evolution of the neutron resonance in the superconducting state. We find that it changes only weakly for moderate modulations, but breaks up into two distinct resonances at incommensurate wave-vectors in the limit of weakly coupled ladders.