Emergence of charge order from the vortex state of a high temperature superconductor

Abstract: Evidence is mounting that charge order competes with superconductivity in high Tc cuprates. Whether this has any relationship to the pairing mechanism is unknown since neither the universality of the competition nor its microscopic nature has been established. Here using nuclear magnetic resonance, we show that, similar to La214, charge order in YBCO has maximum strength inside the superconducting dome, at doping levels p = 0.11 - 0.12.We further show that the overlap of halos of incipient charge order around vortex cores, similar to those visualised in Bi2212, can explain the threshold magnetic field at which long-range charge order emerges. These results reveal universal features of a competition in which charge order and superconductivity appear as joint instabilities of the same normal state, whose relative balance can be field-tuned in the vortex state.

Emergence of Charge Order in High-Temperature Superconductors

This paper provides a comprehensive investigation into the coexistence and competition between charge order and superconductivity within high-temperature cuprates, focusing specifically on YBaCu(_2)O(_3). Utilizing nuclear magnetic resonance (NMR) techniques, the authors explore the emergence of long-range charge order in the vortex state of YBaCu(_2)O(_3) as a function of applied magnetic field strength and doping levels.

Overview of Results

The study identifies charge order in YBaCu(_2)O(_3) emerging at magnetic fields perpendicular to copper-oxide planes, notably at doping levels ( p \approx 0.11-0.12 ). This charge order reaches its maximum strength inside the superconducting dome, indicating a critical overlap at the vortex cores akin to observations in Bi-2212 compounds. Key findings reveal that charge order manifests as a static, long-range spatial modulation of charge density above a threshold magnetic field of approximately 10.4 T in the vortex-solid state for certain samples.

Field and Temperature Dependence

A notable result is the square-root increase in quadrupole splitting (\Delta \nu_{quad}) of the NMR lines with increasing magnetic field, signifying a quantum phase transition at (\approx 3) K. This demonstrates the shift from a homogeneous d-wave superconducting state to one disturbed by charge order at fields starting from 10.4 T. This change, controlled by the decrease in superconducting order parameter, aligns with prior evidence of charge order fluctuations observed through techniques such as X-ray scattering.

Relationship with Vortex Physics

Charge order transitions are observed inside the vortex-solid phase, where regions around vortex cores escape the competition with superconductivity. This study suggests that charge order halos facilitate long-range static order when they overlap at higher fields. The onset field ( H_{charge} \approx 9.3 ) T supports the postulated density and overlap model for vortices at which charge halos begin to interact.

Doping Influence

As the doping level increases, the saturation of (\Delta \nu_{quad}) around fields of 30-35 T further emphasizes the relationship between charge order and superconductivity diminishment—with maximum charge order strength near ( p = 0.115-0.12 ) within the superconducting dome. This finding highlights the delicate balance and near-degeneracy between these orders in the cuprate system.

Implications and Future Directions

The illustrated universality of charge order emergence across various cuprates indicates profound implications for understanding high-temperature superconductivity. The study evidences that electronic competition in cuprates might be inherently linked to intertwining instabilities within their normal pseudogap state, suggesting avenues for exploring the role of charge order in superconducting properties theoretically and experimentally. Attaining a clearer picture within the temperature vs. doping phase diagram will be instrumental in advancing cuprate superconductivity models.

Conclusion

Overall, this work underscores the significance of charge order as competing instability within the cuprate phase diagram, revealed through meticulously controlled NMR experiments. The interaction between charge density modulations and superconducting order demonstrates potential guiding principles for future research into unconventional superconductivity and its complex mechanisms.