Commensurate 4 a ₀ -period charge density modulations throughout the Bi ₂ Sr ₂ CaCu ₂ O _8+x pseudogap regime

Abstract

Theories based upon strong real space (r-space) electron-electron interactions have long predicted that unidirectional charge density modulations (CDMs) with four-unit-cell (4a 0 ) periodicity should occur in the hole-doped cuprate Mott insulator (MI). Experimentally, however, increasing the hole density p is reported to cause the conventionally defined wavevector Q A of the CDM to evolve continuously as if driven primarily by momentum-space (k-space) effects. Here we introduce phase-resolved electronic structure visualization for determination of the cuprate CDM wavevector. Remarkably, this technique reveals a virtually doping-independent locking of the local CDM wavevector at jQ 0 j = 2π=4a 0 throughout the underdoped phase diagram of the canonical cuprate Bi 2 Sr 2 CaCu 2 O 8 . These observations have significant fundamental consequences because they are orthogonal to a k-space (Fermi-surface)-based picture of the cuprate CDMs but are consistent with strong-coupling r-space-based theories. Our findings imply that it is the latter that provides the intrinsic organizational principle for the cuprate CDM state.CuO 2 pseudogap | commensurate charge density modulation | phase discommensuration S trong Coulomb interactions between electrons on adjacent Cu sites result in complete charge localization in the cuprate Mott insulator (MI) state (1). When holes are introduced, theories based upon the same strong r-space interactions have long predicted a state of unidirectional modulation of spin and charge (2-11), with latticecommensurate periodicity for the charge component. Experimentally, it is known that even the lightest hole doping of the MI state produces nanoscale clusters of charge density modulations (CDMs) (12, 13), which implies immediately that r-space interactions predominate. However, with increasing hole density p, the conventionally defined wavevector Q A of the CDM is reported to increase (14) or diminish (15) continuously as if driven primarily by k-space (Fermi surface) effects. Distinguishing between the r-space and k-space theoretical perspectives is critical to identifying the correct fundamental theories for the phase diagram and Cooper pairing mechanism in underdoped cuprates. Here we introduce an approach to this challenge by applying phase-resolved electronic structure visualization (16-18) in combination with the technique of phase demodulation-residue minimization, to explore the CDM wavevector. Using these methods, we visualize the phase discommensurations (19) and their influence on the doping dependence of both the conventionally defined Q A and the fundamental local wavevector Q 0 of the underdoped cuprate CDM state. CDMs in the Pseudogap PhaseAs holes are introduced into the CuO 2 plane of the MI, the first nonmagnetic state to appear is the pseudogap (PG) phase (Fig. 1A). It contains nanoscale CDM clusters (12, 13) even at lowest hole-density p; near p = 0.06 these CDM clusters percolate and the superconducting state appears (12). X-ray scattering experiments (15) now report a robust ...

Dispersive charge density wave excitations in Bi2Sr2CaCu2O8+δ

“…Additionally, if confirmed, the surprising change of Q CDW from incommensurate at low temperature towards commensurate at high temperature is reminiscent of the temperature dependence observed in stripe-phased nickelates, where the charge order is strongly coupled to a spin order, which originates from strong real-space interactions 30 . These results may be consistent with the proposal that the incommensurate Q CDW forms from a discommensuration of a universal period 4a o modulations 31 . Finally, the CDW signatures survive up to at least 240 K ∼ T * , which taken together with the similarities to striped nickelates indicates a close relationship between the CDW, spins, and the pseudogap.…”

Direct observation of charge order in underdoped and optimally doped Bi2(Sr,La)2CuO6+δPeng1, Salluzzo2, Sun3 et al. 2016Phys. Rev. B6913560View full textAdd to dashboardCite

“…The CDW order arising from the charge modulations can reflect this dichotomy: indeed at low doping p 0.11 the Q CDW vectors are similar between RXS and STM results, while they separate into two trends and departs further with doping. A recent STM work, by utilizing the phase-resolved electronic structure visualization, has revealed a surprising doping independent locking of the local CDW wavevector at 0.25 rlu throughout the underdoped phase diagram of (bi-layer) Bi2212 [42]. While the generality of this latticecommensurability CDW in other cuprates, and the supposed correlation with x-ray scattering results through phase slips between different short-ranged correlated domains remain to be explored, at least the conventional CDW amplitudes probed by x-ray and STM look different.…”

Dual gauge field theory of quantum liquid crystals in two dimensions

“…There are still fierce debates over the question whether this charge order should be understood as a weak-coupling 'Peierls-like' charge density wave (CDW) instability, or as a strongly-coupled affair arising in a doped Mott insulator [30]. The latest experimental results appear to largely support the strong coupling view [31]. Similarly, impressive progress has been made studying doped Mott insulators using several numerical methods.…”