Tuning superconductivity and charge density wave order by next-nearest-neighbor hopping integral in honeycomb Holstein model

By using unbiased determinant quantum Monte Carlo simulations, we investigate the interplay between superconductivity and charge density wave order in the Holstein model on a honeycomb lattice with next-nearest-neighbor hopping $t^{\mathrm{\prime }}$. We find that a finite negative $t^{\mathrm{\prime }}$ enhances $s$-wave superconducting pairing susceptibility near the van Hove fillings in the weak electron-phonon coupling regime, while it suppresses superconductivity and promotes charge density wave order at intermediate electron-phonon coupling strengths. The effect of $t^{\mathrm{\prime }}$ on a charge density wave is filling-dependent: It suppresses the charge density wave at half filling but enhances it near the van Hove singularities. A spectral analysis reveals the opening of a gap at low temperatures, highlighting the competitive relationship between superconducting and charge density wave orders mediated by electron-phonon coupling and tuned by $t^{\mathrm{\prime }}$.