Four-legged starfish-shaped Cooper pairs with ultrashort antinodal length scales in cuprate superconductors

Cooper pairs of mutually attracting electrons form the building blocks of superconductivity. Thirty years after the discovery of high-temperature superconductivity in cuprates, many details of the pairs remain unknown, including their size and shape. Here we apply brand new ARPES-based methods that allow us to reconstruct the shape and size of the pairs in Bi$_2$Sr$_2$CaCu$_2$O$_{8+{\delta}}$. The pairs are seen to form a characteristic starfish shape that is very long (>50{\AA}) in the near-nodal direction but extremely short (~4.5{\AA}) in the antinodal (Cu-O) direction. We find that this ultrashort antinodal length scale, which is of order a lattice constant, is approximately constant over a wide range of doping levels even as many other parameters including the pairing strength change. This suggests that this new length scale, along with the pair shape, is one of the most fundamental characteristics of the pairs. Further, the shape and ultrashort length scale should make the pairs create or intertwine with variations in charge and pair density, center on various types of lattice positions, and potentially explain aspects of the nematic order in these materials.