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In a recent Letter Ando et al (cond-mat/9905071) discovered an anomalous magnetoresistance(MR) in hole doped antiferromagnetic YBa$_2$Cu$_3$O$_{6+x}$, which they attributed to charged stripes, i.e., to segregation of holes into lines. In this Comment we show that the experiments, albeit being interesting, do not prove the existence of stripes. In our view the anomalous behavior is due to an (a,b) plane anisotropy of the resistivity in the bulk and to a magnetic field dependent antiferromagnetic (AF) domain structure. It is unlikely that domain walls are charged stripes.
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We report novel features in the in-plane magnetoresistance (MR) of heavily underdoped YBa_2Cu_3O_{6+x}, which unveil a developed ``charged stripe structure in this system. One of the striking features is an anisotropy of the MR with a d-wave symmetry upon rotating the magnetic field H within the ab plane, which is caused by the rotation of the stripes with the external field. With decreasing temperature, a hysteresis shows up below ~20 K in the MR curve as a function of H and finally below 10 K the magnetic-field application produces a persistent change in the resistivity. This memory effect is caused by the freezing of the directionally-ordered stripes.
Polarized and unpolarized neutron diffraction has been used to search for magnetic order in YBa$_2$Cu$_3$O$_{6+x}$ superconductors. Most of the measurements were made on a high quality crystal of YBa$_2$Cu$_3$O$_{6.6}$. It is shown that this crystal has highly ordered ortho-II chain order, and a sharp superconducting transition. Inelastic scattering measurements display a very clean spin-gap and pseudogap with any intensity at 10 meV being 50 times smaller than the resonance intensity. The crystal shows a complicated magnetic order that appears to have three components. A magnetic phase is found at high temperatures that seems to stem from an impurity with a moment that is in the $a$-$b$ plane, but disordered on the crystal lattice. A second ordering occurs near the pseudogap temperature that has a shorter correlation length than the high temperature phase and a moment direction that is at least partly along the c-axis of the crystal. Its moment direction, temperature dependence, and Bragg intensities suggest that it may stem from orbital ordering of the $d$-density wave (DDW) type. An additional intensity increase occurs below the superconducting transition. The magnetic intensity in these phases does not change noticeably in a 7 Tesla magnetic field aligned approximately along the c-axis. Searches for magnetic order in YBa$_2$Cu$_3$O$_{7}$ show no signal while a small magnetic intensity is found in YBa$_2$Cu$_3$O$_{6.45}$ that is consistent with c-axis directed magnetic order. The results are contrasted with other recent neutron measurements.
The possibility of enhancing desirable functional properties of complex materials by optical driving is motivating a series of studies of their nonlinear terahertz response. In high-Tc cuprates, large amplitude excitation of certain infrared-active lattice vibrations has been shown to induce transient features in the reflectivity suggestive of non-equilibrium superconductivity. Yet, a microscopic mechanism for these observations is still lacking. Here, we report measurements of time- and scattering-angle-dependent second-harmonic generation in YBa$_2$Cu$_3$O$_{6+x}$, taken under the same excitation conditions that result in superconductor-like terahertz reflectivity. We discover a three-order-of-magnitude amplification of a 2.5-terahertz electronic mode, which is unique because of its symmetry, momentum, and temperature dependence. A theory for parametric three-wave amplification of Josephson plasmons, which are assumed to be well-formed below T$_c$ but overdamped throughout the pseudogap phase, explains all these observations and provides a mechanism for non-equilibrium superconductivity. More broadly, our work underscores the role of parametric mode mixing to stabilize fluctuating orders in quantum materials.
The competition between superconductivity and charge density wave (CDW) order in underdoped cuprates has now been widely reported, but the role of disorder in this competition has yet to be fully resolved. A central question is whether disorder sets the length scale of the CDW order, for instance by pinning charge density fluctuations or disrupting an otherwise long range order. Using resonant soft x-ray scattering, we investigate the sensitivity of CDW order in YBa$_2$Cu$_3$O$_{6+x}$ (YBCO) to varying levels of oxygen disorder. We find that quench cooling YBCO$_{6.67}$ (YBCO$_{6.75}$) crystals to destroy their o-V and o-VIII (o-III) chains decreases the intensity of the CDW superlattice peak by a factor of 1.9 (1.3), but has little effect on the CDW correlation length, incommensurability, and temperature dependence. This reveals that while quenched oxygen disorder influences the CDW order parameter, the spatial extent of the CDW order is insensitive to the level of quenched oxygen disorder and may instead be a consequence of competition with superconductivity.
We report the results a comprehensive study of charge density wave (CDW) correlations in untwinned YBCO6+x single crystals with 0.4<x<0.99 using Cu-L3 edge resonant x-ray scattering (RXS). Evidence of CDW formation is found for 0.45<x<0.93, but not for samples with x<0.44 that exhibit incommensurate spin-density-wave order, and in slightly overdoped samples with x=0.99. This suggests the presence of two proximate zero-temperature CDW critical points at doping pc1~0.08 and pc2~0.18. The CDW reflections are observed at incommensurate in-plane wave vectors (d_a, 0) and (0, d_b). Both decrease linearly with increasing doping, in agreement with recent reports on Bi-based high-Tc superconductors, but in sharp contrast to the behavior of the 214 family. The CDW intensity and correlation length exhibit maxima at p~0.12, coincident with a plateau in the superconducting transition temperature Tc. The onset temperature of the CDW reflections depends non-monotonically on p, with a maximum of~160 K for p~0.12. The RXS reflections exhibit a uniaxial intensity anisotropy. We further observe a depression of CDW correlations upon cooling below Tc, and (for samples with p> 0.09) an enhancement of the signal when an external magnetic field up to 6 T is applied in the superconducting state. For samples with p~0.08, where prior work has revealed a field-enhancement of incommensurate magnetic order, the RXS signal is field-independent. This supports a previously suggested scenario in which incommensurate charge and spin orders compete against each other, in addition to individually competing against. We discuss the relationship of these results to stripe order 214, the pseudogap phenomenon, superconducting fluctuations, and quantum oscillations.
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