Abstract
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.
Highlights
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 lowenergy 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
We further show that this AP-charge density wave (CDW) state could be altered to become a superconducting state with a global d-wave pairing symmetry, while locally, each bond does not have the perfect d-wave symmetry
Summary
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 lowenergy charge-ordered states in a unidirectional charge density wave or a bidirectional checkerboard structure. Various calculations[29,30,31,32,33,34,35,36,37,38,39] on the Hubbard and t − J type models have revealed low-energy intertwined states appearing as stripes or bidirectional charge-ordered states, such as checkerboard (CB) These works usually involved different approximations and parameters, which often resulted in different types of charge-ordered patterns, and these studies were mostly concentrated at a hole concentration of 1/8, which is the most notable concentration in early experiments.
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