Scientists Confirm Elusive Quantum Critical Point in Cuprate Superconductors

Researchers investigating the complex behaviour of high-temperature cuprate superconductors have long sought definitive proof of a quantum critical point (QCP). Now, H. Y. Huang, C. Y. Mou, and A. Singh, working with colleagues from the University of Tokyo, SLAC National Accelerator Laboratory, and National High Magnetic Field Laboratory, present compelling evidence for such a point within these materials. Their study, utilising high-resolution resonant inelastic X-ray scattering on La₂₋ₓSrₓCuO₄, reveals quantum critical scaling, a crucial signature of a QCP, previously obscured by the superconducting state. This finding is significant because it not only confirms the existence of a QCP in cuprates, but also suggests its connection to fundamental symmetries present in the underlying electronic structure, potentially paving the way for a more complete understanding of these fascinating materials and advancing the development of future superconducting technologies.

Scientists have long sought to fully understand the behaviour of cuprate superconductors, materials that conduct electricity with no resistance at relatively high temperatures. Progress in this field has been hampered by the complex interplay of phases within these materials, potentially governed by a quantum critical point (QCP), a precise condition where quantum fluctuations dramatically alter a material’s properties. Recent work utilising high-resolution resonant inelastic X-ray scattering (RIXS) has now revealed evidence of quantum critical scaling in lanthanum-strontium-copper oxide (La₂₋ₓSrₓCuO₄), a key indicator of a QCP. Specifically, researchers observed that the inverse correlation lengths, a measure of how far apart charge fluctuations extend, collapsed onto a single, universal curve across a range of doping levels and temperatures. This collapse yielded a critical exponent of 0.74 ±0.08, a non-negative value that definitively confirms the presence of the QCP. This behaviour reflects the intense quantum fluctuations inherent to the system, a consequence of the QCP being embedded within the superconducting state. The findings offer a more complete picture of the complex phase diagram of cuprate superconductors and provide insights into their unusual non-Fermi liquid behaviour, a deviation from the standard model of metallic conductivity. Understanding the nature of this QCP is crucial for unlocking the full potential of these materials and paving the way for future superconducting technologies. Single crystals with varying doping levels, x = 0.12, 0.15, 0.17, and 0.18, were grown via the travelling-solvent floating zone method and subsequently annealed to eliminate oxygen defects. Precise doping concentrations were then determined using inductively-coupled-plasma atomic-emission spectrometry, yielding values of 0.12 ±0.005, 0.145 ±0.005, 0.166 ±0.004 and 0.182 ±0.008. Measurements were performed at the AGM-AGS spectrometer of beamline 41A at the Taiwan Photon Source, utilising the energy compensation principle of grating dispersion. The beamline’s configuration allowed for an energy resolution of 16 meV at an incident photon energy of 530 eV, essential for resolving subtle spectral features. Samples were aligned using hard X-ray diffraction with a tilting adjustment holder before cleavage in air to ensure a pristine surface for analysis. RIXS spectra were collected with σ-polarized incident X-rays, perpendicular to the scattering plane, and the momentum transfer, q, was carefully controlled. To calibrate the measurements and ensure accurate data analysis, reference spectra from carbon tape were recorded both before and after each sample measurement to establish the zero-energy position and instrument resolution. A non-linear least squares scheme implemented within Igor Pro software, utilising the Levenberg-Marquardt algorithm, was then employed to fit the RIXS data. This involved minimising the chi-square value, calculated from the squared differences between measured and calculated data points, weighted by their uncertainties. The fitting process incorporated Voigt functions to model elastic scattering and damped harmonic oscillator functions to represent phonon excitations, with each component convolved with a Gaussian profile to account for the spectrometer’s energy resolution. In certain analyses, a dynamical structure factor, derived from the charge susceptibility, was substituted for the damped harmonic oscillator to model charge-density wave fluctuations. Measurements reveal a critical exponent of 0.74 ±0.08 for the correlation length of charge-density wave (CDW) dynamics, establishing a key signature of a QCP in La₂₋ₓSrₓCuO₄. This value, determined through high-resolution RIXS, signifies that the inverse correlation lengths for various dopings and temperatures collapse onto a universal scaling curve. The non-negativity of this exponent definitively confirms the presence of the QCP. The research demonstrates that as the QCP is approached, both the relaxation rate and the correlation length of the CDW increase, while the lifetime of CDW quasiparticles decreases. Dynamical structure factor measurements, probing charge-density correlations, revealed a static CDW with a wave vector of Q = (0.235, 0), exhibiting minimal doping dependence. Temperature-dependent measurements of CDW intensity and momentum scan half-width show slight suppression in the superconducting phase, indicating competition between CDW and superconductivity. Scientists studying high-temperature superconductivity have long grappled with the elusive QCP, a theoretical juncture where material properties change dramatically due to quantum fluctuations. Pinpointing this point in cuprate materials has proven extraordinarily difficult because it appears to be hidden within the very state it should be influencing, the superconducting state itself. This new work offers compelling evidence for the existence of this critical point, not through direct observation, but by meticulously charting how charge correlations scale across different doping levels and temperatures. The significance lies in the technique employed; RIXS allows researchers to probe the subtle dynamics of electron interactions, revealing a universal scaling behaviour consistent with a QCP. While the precise nature of the order driving this criticality remains open to debate, the findings suggest a complex interplay of different electronic phases, potentially involving CDWs and other, less understood, arrangements of electrons. Limitations remain, however, as the dissipative nature of the observed critical point implies that quantum fluctuations are strong, making it challenging to isolate and characterise the underlying order. Future research will likely focus on exploring the role of these competing orders and refining our understanding of how they interact to give rise to high-temperature superconductivity, potentially guiding the design of new materials with even more remarkable properties.