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Register a new userVestigial nematicity from spin and/or charge order in the cuprates
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Nematic order has manifested itself in a variety of materials in the cuprate family. We propose an effective field theory of a layered system with incommensurate, intertwined spin- and charge-density wave (SDW and CDW) orders, each of which consists of two components related by $C_4$ rotations. Using a variational method (which is exact in a large $N$ limit), we study the development of nematicity from partially melting those density waves by either increasing temperature or adding quenched disorder. As temperature decreases we first find a transition to a nematic phase, but depending on the range of parameters (e.g. doping concentration) the strongest fluctuations associated with this phase reflect either proximate SDW or CDW order. We also discuss the changes in parameters that can account for the differences in the SDW-CDW interplay between the (214) family and the other hole-doped cuprates.
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We have carried out a theoretical analysis of the Landau-Ginzburg-Wilson effective field theory of a classical incommensurate CDW in the presence of weak quenched disorder. While the possibility a sharp phase transition and long-range CDW order are precluded in such systems, we show that any discrete symmetry breaking aspect of the charge order -- nematicity in the case of the unidirectional (stripe) CDW we consider explicitly -- generically survives up to a non-zero critical disorder strength. Such vestigial order, which is subject to unambiguous macroscopic detection, can serve as an avatar of what would be CDW order in the ideal, zero disorder limit. Various recent experiments in the pseudo-gap regime of the hole-doped cuprate high-temperature superconductors are readily interpreted in light of these results.
Charge-density wave order is now understood to be a widespread feature of underdoped cuprate high-temperature superconductors, although its origins remain unclear. While experiments suggest that the charge-ordering wavevector is determined by Fermi-surface nesting, the relevant sections of the Fermi surface are featureless and provide no clue as to the underlying mechanism. Here, focusing on underdoped YBa$_2$Cu$_3$O$_{6+x}$, we propose a scenario that traces the charge-density wave formation to the incipient softening of a bond-buckling phonon. The momentum dependence of its coupling to the electrons in the copper-oxygen planes favourably selects the incommensurate and axial ordering wavevector found in experiments. But, it requires strong electronic correlations via their cuprate-specific renormalization of the weight and the dispersion of quasiparticles to enable a unique enhancement of the charge susceptibility near the B$_{1g}$-phonon selected wavevector. The frequency of the B$_{1g}$ phonon softens by a few percent, and a lattice instability with concomitant finite-range charge-density wave correlations will form locally, if nucleated by defects or dopant disorder. These results offer the perspective that the complex phase diagram of underdoped cuprates cannot be understood in the context of strong electronic correlations alone.
Charge order has emerged as a generic feature of doped cuprates, leading to important questions about its origin and its relation to superconductivity. Recent experiments on two classes of hole doped cuprates indicate a novel d-wave symmetry for the order. These were motivated by earlier spin fluctuation theoretical studies based on an expansion about hot spots in the Brillouin zone that indicated such order would be competitive with d-wave superconductivity. Here, we reexamine this problem by solving strong coupling equations in the full Brillouin zone. Our results find that bond-oriented order, as seen experimentally, is strongly suppressed, indicating that the charge order must have a different origin.
Superconductivity in layered cuprates is induced by doping holes into a parent antiferromagnetic insulator. It is now recognized that another common emergent order involves charge stripes, and our understanding of the relationship been charge stripes and superconductivity has been evolving. Here we review studies of 214 cuprate families obtained by doping La$_2$CuO$_4$. Charge-stripe order tends to compete with bulk superconductivity; nevertheless, there is plentiful evidence that it coexists with two-dimensional superconductivity. This has been interpreted in terms of pair-density-wave superconductivity, and the perspective has shifted from competing to intertwined orders. In fact, a new picture of superconductivity based on pairing within charge stripes has been proposed, as we discuss.
Charge-density wave (CDW) modulations in underdoped high-temperature cuprate superconductors remain a central puzzle in condensed matter physics. However, despite a substantial experimental verification of this ubiquitous phase in a large class of high $T_{mathrm{c}}$ cuprates, a complete theoretical explanation of this phase is still missing. Here, we build upon our recent proposal that the CDW in underdoped cuprates (Y- and Bi- based compounds) emerges from a unique cooperation of the B$_{1g}$ bond-buckling phonon with strong electronic correlations. We assume a static mean-field lattice distortion with B$_{1g}$ symmetry, regardless of its origin, with a commensurate wave vector $mathbf{q}^*=(2pi/3,0)/(0,2pi/3)$. We show that such a phonon-induced CDW (both uni- and biaxial) reconstructs the Fermi surface, leading to electron and hole pockets, with relevant quantum oscillation frequencies in close consistency with the experiments. Furthermore, a systematic analysis of the symmetry of the intra-unit-cell charge modulations on the copper-oxygen planes is provided. We find that the atomic charge modulation on the CuO$_2$ unit cell is predominantly of $s$-wave character -- in support of the recent experimental observation.
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