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Electronic states in disordered conductors on the verge of localization arepredicted to exhibit critical spatial characteristics indicative of theproximity to a metal- insulator phase transition. We have used scanningtunneling microscopy to visualize electronic states in Ga1-xMnxAs samples closeto this transition. Our measurements show that doping-induced disorder producesstrong spatial variations in the local tunneling conductance across a widerange of energies. Near the Fermi energy, where spectroscopic signatures ofelectron-electron interaction are the most prominent, the electronic statesexhibit a diverging spatial correlation length. Power-law decay of the spatialcorrelations is accompanied by log-normal distributions of the local density ofstates and multifractal spatial characteristics. Our method can be used toexplore critical correlations in other materials close to a quantum criticalpoint.

Visualizing Critical Correlations near the Metal-Insulator Transition in Ga1-xMnxAs