Doping dependence of 2-spinon excitations in the doped 1D cuprate Ba 2 CuO 3+ delta

The gist: The study examines signatures of an attractive potential in doped 1D cuprates by measuring the dispersion of 2-spinon excitations using Cu L3-edge resonant inelastic X-ray scattering (RIXS), which suggests missing ingredients in the simple Hubbard model and supports the presence of an additional attractive potential between holes.

Experimental Setup and Observations

The researchers measured doping dependence of 2-spinon excitations in Ba2CuO3+δ thin films using Cu L3-edge resonant inelastic x-ray scattering (RIXS) Upon doping, they found that the 2-spinon excitations broaden, accompanied by a systematic shift of the gapless momentum qF They also found that the energy scale of the 2-spinons near the zone boundary, ωπ, is substantially lower than predicted by the one-dimensional Hubbard model. This discrepancy implies missing ingredients in the Hubbard model and supports the presence of an additional attractive potential between holes.

Modeling and Theoretical Predictions

The theoretical framework suggests that incorporating such a potential into the Mott-Hubbard model could enhance superconducting pairing. Theory predicts that such an interaction should also leave fingerprints in the bosonic excitation channels, particularly, the dynamic spin structure factor S(q, ω). In the undoped case, S(q, ω) exhibits a typical two-spinon continuum due to electron fractionalization. Upon hole doping, the momentum where the 2-spinon excitations become gapless shifts to qF. In the presence of an attractive potential Vint, ωπ will soften and the spectral weight should spread out in energy and momentum. The softening of ωπ can serve as an estimate for the strength of Vint.

Doping Dependence and Parameter Extraction

The momentum qF where the 2-spinon excitation becomes gapless shifts to smaller values with increasing hole doping. In the most heavily hole-doped sample 5, the 2-spinon continuum becomes gapless at a momentum between q = 0.3 and 0.35, where the peak merges with elastic peak and becomes invisible. The researchers estimated doping concentrations by fitting the dispersion ωs(q) to ωs(q) = ωo · sin(2π q / (1 − x)). The extracted parameters for sample 5 yielded an estimated doping concentration of x = 8.1 %.

Comparison with Models and Conclusions

When comparing the experimental peak positions to calculations, the simple Hubbard model significantly overestimates the energy scale near the zone boundary compared to experimental data. The extendedHubbard model with an effective nearest-neighbor attractive interaction V = −1t showed better agreement with the data than that predicted in the simple Hubbard model. This substantial attractive interaction is consistent with the value previously determined by ARPES. The origin of this unique coupling may stem from charge transfer between the Cu 3d orbitals and O ligand, which appears to be absent in the YbAlO3. In conclusion, the results provide further support for the existence of a long-range attractive potential in quasi1D cuprates that is absent in the simple Hubbard model.

Future Directions

A complimentary study using RIXS at the O K-edge with greater sensitivity to electron-oxygen phonon coupling may shed additional light on this subject. Further investigations into the origin of this potential and how it manifests in higher dimensions could be important for understanding and controlling the properties of high-Tc cuprates.

Acknowledgements

This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Contract No. DE-AC02-76SF00515. J.L. acknowledges the support of the Department of Energy, Laboratory Directed Research and Development program at SLAC National Accelerator Laboratory, under contract DE-AC02-76SF00515. D.J. gratefully acknowledges funding by the Alexander-vonHumboldt foundation. Part of data were taken at the I21 RIXS beamline of Diamond Light Source (UK) using the RIXS spectrometer designed, built, and owned by Diamond Light Source. This research used beamline 2-ID of NSLS-II, a US DOE Office of Science User Facility operated for the DOE Office of Science by Brookhaven National Laboratory under contract no. DE-SC0012704. Y.W. acknowledges support from the Air Force Office of Scientific Research Young Investigator Program under grant FA9550-23-1- 0153. The computational results utilized the resources of the National Energy Research Scientific Computing Center (NERSC), a Department of Energy Office of Science User Facility using NERSC award BES-ERCAP0023181. Some of the computing for this project was performed on the Sherlock cluster. We would like to thank Stanford University and the Stanford Research Computing Center for providing computational resources and support that contributed to these research results.

References

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Supplemental Material Details

See supplemental material for additional details.

1. We can improve materials discovery AI by training models to predict missing ingredients in simplified physical models based on experimental discrepancies; specifically, this system could be used to identify if a simple Hubbard model is insufficient for describing doped cuprates by flagging when observed energy scales like the energy scale of the 2-spinons near the Brillouin zone boundary, ωπ, is substantially lower than predicted by the one-dimensional Hubbard model in one-dimension.

2. The AI system can perform targeted experimental design optimization by suggesting necessary complementary measurements; this involves using a predictive model to determine if additional experiments are necessary for validation and suggesting specific probes, such as a complimentary study using RIXS at the O K-edge with greater sensitivity to electron-oxygen phonon coupling may shed additional light on this subject.

3. We can enhance theoretical modeling of pairing mechanisms by developing an AI capable of evaluating the impact of interaction types; this system could be used to compare results from different models, such as showing that "the calculated 2-spinon excitations capture the essence of the measured dispersion for q < qF, but the Hubbard model significantly overestimates the energy scale near the zone boundary compared to experimental data."

Recent photoemission experiments on the quasi-one-dimensional Ba-based cuprates suggest that doped holes experience an attractive potential not captured using the simple Hubbard model. This observation has garnered significant attention due to its potential relevance to Cooper pair formation in high- T c cuprate superconductors. To scrutinize this assertion, we examined signatures of such an attractive potential in doped 1D cuprates Ba 2 CuO 3+δ by measuring the dispersion of the 2-spinon excitations using Cu L 3-edge resonant inelastic X-ray scattering (RIXS). Upon doping, the 2-spinon excitations appear to weaken, with a shift of the minimal position corresponding to the nesting vector of the Fermi points, q F. Notably, we find that the energy scale of the 2-spinons near the Brillouin zone boundary is substantially softened compared to that predicted by the Hubbard model in one-dimension. Such a discrepancy implies missing ingredients, which lends support for the presence of an additional attractive potential between holes.