The symmetry of charge order in cuprates

Abstract: Charge-ordered ground states permeate the phenomenology of 3d-based transition metal oxides, and more generally represent a distinctive hallmark of strongly-correlated states of matter. The recent discovery of charge order in various cuprate families fueled new interest into the role played by this incipient broken symmetry within the complex phase diagram of high-Tc superconductors. Here we use resonant X-ray scattering to resolve the main characteristics of the charge-modulated state in two cuprate families: Bi2201 and YBCO. We detect no signatures of spatial modulations along the nodal direction in Bi2201, thus clarifying the inter-unit-cell momentum-structure of charge order. We also resolve the intra-unit-cell symmetry of the charge ordered state, which is revealed to be best represented by a bond-order with modulated charges on the O-2p orbitals and a prominent d-wave character. These results provide insights on the microscopic description of charge order in cuprates, and on its origin and interplay with superconductivity.

The Symmetry of Charge Order in Cuprates

This study presents a comprehensive analysis of charge-ordered states in cuprates, focusing on their symmetry and implications for high-temperature superconductivity. Utilizing resonant X-ray scattering (RXS), the authors probe the charge-ordering phenomena in two cuprate family compounds: Bi({2})Sr({2-x})La(x)CuO({6+\delta}) (Bi2201) and YBa(2)Cu(_3)O({6+y}) (YBCO). The primary goal is to understand the spatial distribution and symmetry characteristics of charge density waves (CDW) in these materials.

Key Findings

1. Charge Order Directionality: In Bi2201, the study dismisses the possibility of CDW peaks along the diagonal direction ((H, H)), establishing that charge modulations predominantly align along the Cu-O bond directions ((H, 0) and (0, H)).

2. Symmetry Components: For YBCO, the investigation delves into the intra-unit-cell symmetry of the charge order. The analysis identifies a bond-order characterized by modulated charges primarily on the O-(2p) orbitals, with a prominent d-wave character. This is consistent with theoretical frameworks proposing such bond orders in the context of the t-J model and recent scanning tunneling microscopy (STM) results.

3. Comparative Analysis: The analysis employs azimuthal-angle dependent RXS measurements to assess the symmetry of the CDW. The data indicates a predominant d-wave symmetry, suggesting that such a pattern may be universal in certain classes of cuprates, including the Y- and Bi-based families.

Implications and Theoretical Considerations

The presence of d-wave symmetry in the charge order indicates a more intricate relationship with the superconducting state, which also exhibits d-wave symmetry in cuprates. This suggests that electron interactions, which stabilize superconductivity, may also influence the charge order, hinting at a shared mechanism between the particle-particle (superconducting) and particle-hole (CDW) channels.

Such findings emphasize the role of O-(2p) orbitals in the low-energy physics of hole-doped cuprates, reinforcing the complex interaction landscape involving charge, spin, and lattice degrees of freedom. This positions the d-wave bond-order as a potential key player in the high-(T_c) superconductivity phenomenon.

Future Directions

Further exploration into the interplay between charge order symmetry and various physical properties in cuprates is warranted. Given the sensitivity of RXS to the symmetry of charge distributions, more refined measurements across different doping levels and temperatures could illuminate the evolution and stability of charge orders. Additionally, investigating the impact of external perturbations, like magnetic fields or pressure, on these bond-orders could elucidate their role in superconductivity.

The current study lays critical groundwork for future inquiries into unconventional superconductivity, particularly concerning how charge orders might mediate or compete with other electronic orders. These directions could also pave the way for designing new materials with tailored superconducting properties by exploiting the interplay among different charge, spin, and lattice orders.