Atomic-scale Electronic Structure of the Cuprate d-Symmetry Form Factor Density Wave State

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Extensive research into high temperature superconducting cuprates is now focused upon identifying the relationship between the classic 'pseudogap' phenomenon¹,² and the more recently investigated density wave state³⁻¹³. This state always exhibits wave vector Q parallel to the planar Cu-O-Cu bonds⁴⁻¹³ along with a predominantly d-symmetry form factor¹⁴⁻¹⁷ (dFF-DW). Finding its microscopic mechanism has now become a key objective¹⁸⁻³⁰ of this field. To accomplish this, one must identify the momentum-space (k-space) states contributing to the dFF-DW spectral weight, determine their particle-hole phase relationship about the Fermi energy, establish whether they exhibit a characteristic energy gap, and understand the evolution of all these phenomena throughout the phase diagram. Here we use energy-resolved sublattice visualization¹⁴ of electronic structure and show that the characteristic energy of the dFF-DW modulations is actually the 'pseudogap' energy Δ₁. Moreover, we demonstrate that the dFF-DW modulations at E=-Δ₁ (filled states) occur with relative phase π compared to those at E=Δ₁ (empty states). Finally, we show that the dFF-DW Q corresponds directly to scattering between the 'hot frontier' regions of k-space beyond which Bogoliubov quasiparticles cease to exist³¹,³²,³³. These data demonstrate that the dFF-DW state is consistent with particle-hole interactions focused at the pseudogap energy scale and between the four pairs of 'hot frontier' regions in k-space where the pseudogap opens.