Atomic-scale Interplay of the Charge Density Wave, Pair Density Wave and Nematic States of Cuprates.*

The antiferromagnetic insulator state of CuO₂ is transformed by hole-doping onto the oxygen sites, into an exotic quantum fluid that is usually referred to as the pseudogap (PG) phase. Its defining characteristic is a strong suppression of the electronic density-of-states for energies E<D, where D is the pseudogap energy scale. Within the pseudogap phase, complex broken-symmetry phases have been detected by a very wide variety of techniques. First, there is the finite-Q charge-density-wave (CDW) state that is locally commensurate and unidirectional, with 4a₀ periodicity and a d-symmetry form factor. Second, is the finite-Q pair-density-wave (PDW) state which is detected with superconducting-tip STM as having a 4a₀ periodicity in the magnitude of Josephson currents and an 8a₀ periodicity in its energy-gap modulations. Third, there is the nematic (NE) state which breaks rotational symmetry at Q=0.
Simultaneous measurements of the PDW and CDW phenomenology now reveal strong evidence that they are facets a single, fundamental, density wave (DW) state that breaks translational symmetry. More surprisingly, several characteristics of the NE state appear closely related to those of this DW state. For example, by simultaneously imaging the doping and energy dependence of the DW and NE states, we find that the maximum spectral intensity of these quite distinct forms of symmetry breaking always occurs at the same energy, and that this is always the pseudogap energy for hole-density p<0.19. We discuss how this perplexingly linked phenomenology of two highly distinct broken-symmetry states may be understood as the natural consequence of a vestigial nematic state within the pseudogap phase of Bi2Sr2CaCu2O8.