Charge modulation in the background of depleted superconductivity inside vortices

We use the Bogoliubov-de Gennes (BDG) formalism to undertake a microscopic investigation of a vortex lattice in a strongly correlated, type-II, d-wave superconductor (SC) treating strong correlation within Gutzwiller formalism. We demonstrate that in the underdoped region, the vortex core changes from metallic-type to insulating-type in the presence of subdominant charge and bond order, in contrast to Mott-type, when these orders are absent. We have investigated that such subdominant order changes the structure and spectrum of the d-wave vortex in the underdoped region. We have demonstrated the formation of charge and bond modulation at the vortex center by decreasing the doping and reaching an underdoped zone.