Tuning competition between charge order and superconductivity in the square-lattice t−t′−J model

Abstract

Recently, a flurry of works have found strong competition between charge density wave (CDW) and superconductivity (SC) in the doped Hubbard and t−J models on the square lattice. Interestingly, some recent results suggest that the electron-phonon coupling may suppress CDW order and enhance SC. In this work, we consider the square-lattice Hubbard model with the Holstein or Su-Schrieffer-Heeger electron-phonon coupling at the large-U and antiadiabatic (infinite phonon frequency) limits, which gives an effective t−J model with either a density attractive interaction V or a JP term that contributes a larger spin exchange and a density repulsive interaction. To explore how these effective couplings may tune the competition between CDW and SC, we implement the density matrix renormalization group simulations on the t−t′−J model with V or JP coupling. We focus on the six-leg cylinder system with the next-nearest-neighbor hopping t′, which hosts partially filled stripe and d-wave SC in phase diagram. By tuning t′/t>0 and V or JP, we establish two quantum phase diagrams at 112 doping ratio. In the SC phases, the increased V or JP coupling can enhance the quasi-long-range SC order, consistent with some previous findings. Nonetheless, no SC emerges when the partially filled stripe phase disappears with increased V or JP. Instead, the system has a transition to either a phase-separation-like regime or a filled stripe phase. On the other hand, with increased t′/t, not only the partially filled stripe but the phase separation and filled stripe can also be tuned to SC phase. Our results suggest that although V and JP couplings may strengthen hole binding, the hole dynamics controlled by t′/t appears to play a more crucial role for obtaining a SC in the t−J model.

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