Study of vortices-PDW mixed state predicted by the t-J model via renormalized mean-field theory

Recent spectroscopic imaging scanning tunneling microscopy (SISTM) results show evidence of pair density wave (PDW) or checkerboard near the SC vortex halos [1]. The key finding in the work is that the CDW vector  Q_c may exist half of the PDW vector Q_p, which is the same as predicted by previous Ginzburg-Landau theories [2].

This work is to investigate the prediction of the t-J model under magnetic field about the mixed state that uniform and PDW superconducting order parameters may co-exist inside a vortex core. As in our previous study [3], we study the model within the Gutzwiller approximation (GA), which follows the standard renormalized mean-field theory (RMFT). In addition, the Peierls phase factor has been introduced to RMFT. In this work, the microscopic nature will be investigated, including the size of the vortices, the form factor, and the local density of states.