  Inside the metals, semiconductors, and magnets of our everyday experience,
electrons are uniformly distributed throughout the material. By contrast,
electrons often form clumpy patterns inside of strongly correlated electronic
systems (SCES) such as colossal magnetoresistance materials and high
temperature superconductors. In copper-oxide based high temperature
superconductors, scanning tunneling microscopy (STM) has detected an electron
nematic on the surface of the material, in which the electrons form nanoscale
structures which break the rotational symmetry of the host crystal. These
structures may hold the key to unlocking the mystery of high temperature
superconductivity in these materials, but only if the nematic also exists
throughout the entire bulk of the material. Using newly developed methods for
decoding these surface structures, we find that the nematic indeed persists
throughout the bulk of the material. We furthermore find that the intricate
pattern formation is set by a delicate balance among disorder, interactions,
and material anisotropy, leading to a fractal nature of the cluster pattern.
The methods we have developed can be extended to many other surface probes and
materials, enabling surface probes to determine whether surface structures are
confined only to the surface, or whether they extend throughout the material.
