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

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. In this chapter, we describe how the scanning tunneling microscopy (STM) measurements on doped semiconductors near the metal-insulator transition can be used to access these critical wavefunctions. Specifically, we use the STM to probe to visualize electronic states in Ga1-xMnxAs samples close to the metal-insualtor transition. Our measurements show that doping-induced disorder produces strong spatial variations in the local tunnelling 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.