  Electronic states in disordered conductors on the verge of localization are
predicted to exhibit critical spatial characteristics indicative of the
proximity to a metal- insulator phase transition. We have used scanning
tunneling microscopy to visualize electronic states in Ga1-xMnxAs samples close
to this transition. Our measurements show that doping-induced disorder produces
strong spatial variations in the local tunneling conductance across a wide
range of energies. Near the Fermi energy, where spectroscopic signatures of
electron-electron interaction are the most prominent, the electronic states
exhibit a diverging spatial correlation length. Power-law decay of the spatial
correlations is accompanied by log-normal distributions of the local density of
states and multifractal spatial characteristics. Our method can be used to
explore critical correlations in other materials close to a quantum critical
point.
