[Paper Review] Probing electronic order via coupling to low energy phonons in superconducting Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$

Craig Bonnoit, Dillon Gardner+8 more|arXiv (Cornell University)|Feb 22, 2012

Physics of Superconductivity and Magnetism1 references3 citations

TL;DR

This study uses high-resolution inelastic x-ray scattering to probe electronic order in superconducting Bi2Sr2−xLa xCuO6+δ, revealing anomalous broadening of longitudinal acoustic phonons at the (1/4, 1/4, 0) wavevector, indicating coupling to a dynamic electronic density wave. The phonon response and intensity asymmetry between energy gain and loss processes demonstrate simultaneous breaking of time-reversal and inversion symmetries in the pseudogap state, providing direct evidence for hidden order in cuprates.

ABSTRACT

We report high-resolution inelastic x-ray scattering measurements of the acoustic phonons in the single-layer cuprate $Bi_{2}Sr_{2-x)La_{x}CuO_{6+\delta}$. These measurements reveal anomalous broadening of the longitudinal acoustic phonon near the (1/4,1/4,0) wavevector. The observed wavevector and its doping dependence indicate the coupling of the phonons to an underlying electronic density wave state. In addition, a comparison of the scattered intensities for x-ray energy-gain and x-ray energy-loss indicates that both time-reversal and inversion symmetries are broken in the material. Upon cooling, the effects of symmetry breaking are enhanced in the pseudogap state.

Motivation & Objective

• To investigate the coupling between low-energy phonons and electronic order in single-layer cuprates.
• To determine whether electronic density wave order is static or dynamic in Bi2Sr2−xLa xCuO6+δ.
• To probe the nature of broken symmetries—particularly time-reversal and inversion—in the pseudogap phase.
• To reconcile discrepancies between STM and bulk scattering measurements regarding electronic order in cuprates.
• To establish whether lattice dynamics can serve as a sensitive probe of hidden electronic order.

Proposed method

• Performed high-resolution inelastic x-ray scattering (IXS) on single crystals of Bi2Sr2−xLa xCuO6+δ using the HERIX instrument at the Advanced Photon Source.
• Measured both longitudinally and transversely polarized acoustic phonons via polarization-dependent IXS, sensitive to (Q · ε)² dependence.
• Used damped harmonic oscillator fits convoluted with instrumental resolution to extract phonon linewidths and intensities.
• Analyzed energy-gain and energy-loss scattering intensities to compute the asymmetry ratio A(Q), which probes time-reversal and inversion symmetry breaking.
• Applied the fluctuation-dissipation theorem to relate measured dynamic structure factor S(Q, ω) to the imaginary part of the susceptibility χ''(Q).
• Conducted measurements at multiple doping levels (Tc = 25 K, 31 K, 33 K) and temperatures, including above and below T* ≈ 150 K.

Experimental results

Research questions

• RQ1 Does the coupling of acoustic phonons to electronic order manifest as anomalous broadening at specific wavevectors in Bi2201?
• RQ2 Is the electronic order responsible for the phonon anomaly static or dynamic?
• RQ3 Are time-reversal and inversion symmetries broken in the pseudogap state, and how is this reflected in x-ray scattering?
• RQ4 How does the phonon response correlate with the onset of the pseudogap at T*?
• RQ5 Can low-energy phonons serve as a probe of hidden order in high-Tc superconductors?

Key findings

• Anomalous broadening of the longitudinal acoustic phonon mode is observed at q ≈ (0.25, 0.25, 0), indicating coupling to an electronic density wave with wavevector (1/4, 1/4, 0).
• The phonon anomaly is absent in transverse modes, confirming its origin in electronic order rather than lattice anharmonicity.
• The intensity ratio between energy-gain and energy-loss processes, A(Q), is nonzero at T = 300 K and increases upon cooling below T* ≈ 150 K, signaling simultaneous breaking of time-reversal and inversion symmetries.
• The asymmetry is most pronounced at (0.25, 0.25, 0), consistent with broken symmetries at the wavevector of the anomalous phonon.
• The lattice modulation remains dynamic down to low temperatures, suggesting that translational symmetry is not spontaneously broken at T*, unlike in some other cuprates.
• The results reconcile STM and bulk scattering data by showing that electronic order persists as dynamic fluctuations, not static distortions.