Genesis of charge orders in high temperature superconductors

One of the most puzzling facts about cuprate high-temperature superconductors in the lightly doped regime is the coexistence of uniform superconductivity and/or antiferromagnetism with many low-energy charge-ordered states in a unidirectional charge density wave or a bidirectional checkerboard structure. Recent experiments have discovered that these charge density waves exhibit different symmetries in their intra-unit-cell form factors for different cuprate families. Using a renormalized mean-field theory for a well-known, strongly correlated model of cuprates, we obtain a number of charge-ordered states with nearly degenerate energies without invoking special features of the Fermi surface. All of these self-consistent solutions have a pair density wave intertwined with a charge density wave and sometimes a spin density wave. Most of these states vanish in the underdoped regime, except for one with a large d-form factor that vanishes at approximately 19% doping of the holes, as reported by experiments. Furthermore, these states could be modified to have a global superconducting order, with a nodal-like density of states at low energy.