Resonant X-ray Scattering Study of Charge Density Wave Correlations in YBa$_2$Cu$_3$O$_{6+x}$ (1406.1595v2)

Abstract: 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.

• The paper employs resonant x-ray scattering on untwinned single crystals to analyze CDW correlations in YBa2Cu3O6+x.
• It finds that CDW intensity and correlation length peak near a doping level of p ≈ 0.12, defining key critical points for charge order.
• The study highlights a competition between charge density waves and superconductivity, with magnetic fields enhancing CDW correlations below Tc.

Analysis of Charge Density Wave Correlations in YBa$_2$Cu$_3$O$_{6+x}$

The paper "Resonant X-ray Scattering Study of Charge Density Wave Correlations in YBa$_2$Cu$_3$O$_{6+x}$" presents a detailed investigation into the charge density wave (CDW) correlations within the high-temperature superconductor YBa$_2$Cu$_3$O$_{6+x}$ using resonant x-ray scattering techniques. The paper addresses the emergence and characteristics of CDW phenomena across a range of hole-doping levels, focusing on the cuprate family and their implications for understanding the intricacies of high-temperature superconductivity.

Summary of Key Findings

1. Experimental Framework: The researchers utilized Cu-$L_3$ edge resonant x-ray scattering to probe untwinned single crystals of YBa$_2$Cu$_3$O$_{6+x}$ wherein the doping level $x$ ranged from 0.4 to 0.99. Resonant x-ray scattering provided the sensitivity necessary to characterize the subtle charge density modulations.
2. Charge Density Wave and Doping: The paper reports the presence of CDW correlations for doping levels $0.086 \lesssim p \lesssim 0.163$, absent in samples exhibiting either lower or significantly higher doping. This indicates two critical doping points around $p_{c1} \sim 0.08$ and $p_{c2} \sim 0.18$, with the latter close to the optimal doping level for superconductivity.
3. Wave Vector Characteristics: The CDW reflections occur at incommensurate in-plane wave vectors $(\delta_a, 0)$ and $(0, \delta_b)$ with $\delta_a \lesssim \delta_b$. The wave vectors decrease linearly with increasing doping, a trend opposite to that observed in La$_{2-x}$(Ba,Sr)$_x$CuO$_4$.
4. Intensity and Correlation Length: Both the CDW intensity and correlation length peak around $p \sim 0.12$. This doping level also exhibits a plateau in the superconducting transition temperature $T_c$, highlighting possible competition between CDW and superconductivity.
5. Temperature and Magnetic Field Effects: The onset temperature for CDW reflections varies with doping, reaching a maximum at approximately 160 K for $p \approx 0.12$. Below $T_c$, the CDW correlations are weakened, but they are enhanced in the superconducting state under an external magnetic field for samples with $p \geq 0.09$.

Theoretical and Practical Implications

This paper enhances the understanding of CDW behavior in relation to high-temperature superconductivity in cuprates. The findings suggest that charge order competes with superconducting states and may coexist in a delicate balance influenced by doping and external magnetic fields. The critical points $p_{c1}$ and $p_{c2}$ are pivotal in conceptualizing the phase diagram of cuprates, proposing a potential link between charge ordering and quantum fluctuations that impact both pseudogap formation and superconducting transitions.

Future Directions

The identification of the CDW stability range and its correlation to superconducting properties invites further exploration into:

• The interaction between CDWs and fluctuating superconductivity, potentially through detailed measurement of electronic transport properties under varying magnetic fields.
• Theoretical modeling to link observed CDW characteristics with electronic band structures and Fermi surface features.
• Broader application of resonant x-ray techniques to similar superconducting materials to extend the universality of these findings.

In conclusion, this paper advances the knowledge of charge density wave correlations as they relate to high-temperature superconducting mechanisms, thereby paving avenues for theoretical developments and experimental inquiries into next-generation materials.