Interplay Between Stripe Order and Superconductivity in a Modulated XY Model

In strongly correlated electron systems, superconductivity and charge density waves often coexist in close proximity, suggesting a deeper relationship between these competing phases. Recent research indicates that these orders can intertwine, with the superconducting order parameter coupling to modulations in the electronic density. To investigate this interplay, we employ a microscopic model derived from the Hubbard model in the strong coupling limit, formulating the system as a two-dimensional modulated XY model with periodic coupling strength in one spatial direction. Using a combination of tensor network methods and Monte Carlo simulations, we find that the superconducting transition temperature Tc​ decreases as the modulation amplitude increases. More intriguingly, our results reveal a non-monotonic, dome-like dependence of Tc​ on the modulation wavelength, with the peak Tc​ shifting to longer wavelengths as the modulation strength grows. These findings shed new light on the phase behavior of intertwined superconducting and charge-ordered states, offering a deeper understanding of their complex interactions.