A superconductor's order parameter is usually uniform — the Cooper-pair condensate has the same amplitude everywhere, like a calm lake. Cooper-pair density modulation states break this uniformity: the superconducting order parameter oscillates in space, stronger in some regions and weaker in others, creating a periodic pattern of pairing amplitude. These states have been theorized since the Fulde-Ferrell-Larkin-Ovchinnikov proposals of the 1960s and searched for in exotic superconductors, but direct real-space imaging of the modulation has been elusive because the relevant length scales are atomic and the modulation coexists with the uniform component.
Wang, Xia, Paolini, and collaborators (arXiv 2602.22637, February 2026) engineer Cooper-pair density modulation states using a moire superlattice and image them directly with scanning tunneling microscopy.
The structure is a heterostructure of Sb2Te3 (a topological insulator with hexagonal crystal symmetry) and FeTe (an antiferromagnet with square crystal symmetry). The two materials have different lattice types, and when stacked, their tellurium atoms create a moire pattern — a long-wavelength beat frequency arising from the mismatch between hexagonal and square lattices. The moire periodicity is much larger than either lattice constant, creating a superlattice with a tunable wavelength.
The FeTe layer, which becomes superconducting at the interface, has its pairing amplitude modulated by the moire pattern. Where the two lattices align well, the interlayer coupling is strong and the local electronic structure differs from regions where they are misaligned. This spatial variation in the electronic environment produces a spatial variation in the superconducting gap — the order parameter follows the moire periodicity.
Josephson scanning tunneling spectroscopy confirms the modulation. A superconducting STM tip brought close to the surface can detect the local pair density through Josephson tunneling — Cooper pairs tunnel between the tip and the sample at a rate proportional to the local order parameter amplitude. Scanning the tip across the surface maps the superconducting order parameter in real space, directly revealing the moire-periodic modulation.
Substituting Bi2Te3 for Sb2Te3 changes the lattice mismatch and therefore the moire periodicity, demonstrating that the modulation wavelength is engineered by the choice of materials. The amplitude of the modulation also changes, showing that the depth of the spatial variation — how strongly the order parameter oscillates — is tunable.
The result is not an exotic superconducting state discovered in nature but a designed one: the moire pattern is chosen to imprint spatial structure onto the Cooper-pair condensate. The superlattice writes a pattern on the superconductor. The pattern is read back by the Josephson tip. Between writing and reading, the superconducting condensate has faithfully reproduced the geometric template imposed by the lattice mismatch — a macroscopic quantum state shaped by a microscopic stacking choice.