Charge, bond, and pair density wave orders in a strongly correlated system

TL;DR

This study demonstrates that in a strongly correlated system modeled by the $t-t^\prime-J$-model, spatially modulated charge, bond, and pairing orders can be stabilized and are energetically favorable over uniform states in the underdoped regime, revealing complex incommensurate orders.

Contribution

The paper introduces a microscopic approach using the $t-t^\prime-J$-model with repulsion and self-consistent Hartree-Fock-Bogoliubov treatment to stabilize and analyze spatially modulated orders in strongly correlated materials.

Findings

Unidirectional bond density states coexist with charge and pairing modulations.

Modulating states vanish with increased doping, leading to a vestigial nematic phase.

Spatially modulating states are absent when strong correlations are relaxed.

Abstract

The coexistence of multiple quasi-degenerate orders is the hallmark of the strongly correlated materials. Experiments often reveal several spatially modulated orders in the underdoped cuprates. This has come to the forefront with the possible detection of the pair density wave states. However, microscopic calculations often struggle to stabilize such spatially modulating orders as the ground state in the strong correlation limit. This work uses the $t-t^\prime-J$-model with an additional nearest-neighbor repulsion to stabilize spatially oscillating charge, bond, and pairing orders in the underdoped regime. We employ the standard Gutzwiller approach while treating the inhomogeneity for the spatial orders using the self-consistent Hartree-Fock-Bogoliubov methodology. Our calculations reveal that unidirectional bond density states coexisting with charge and pairing modulations can have lower energy than the uniform superconducting state over an extensive doping range. These modulating states vanish monotonically as the modulation wavevector becomes shorter with increased dopings. The finite momentum orders melt upon increasing doping to a vestigial nematic state which breaks the rotational symmetry of the system. The spatial features of the ground state at each doping reveal multiple wavevectors, which potentially drives the incommensuration of charge orders. Interestingly, the spatially modulating states are absent when the strong correlations criteria are relaxed, suggesting that the removal of double occupancy aids the stabilization of density wave orders.