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

Metal-Insulator Transition At near-zero temperatures, some materials undergo a metal-insulator transition and their electronic properties change from conducting to insulating. In the dilute magnetic semiconductor Ga1−xMnxAs, a promising spintronics material, the metal-insulator transition is driven by the substitution of Ga atoms with Mn. While disorder clearly plays a key role in this transition, the influence of electron-electron correlations has been far from clear. Richardella et al. (p. 665; see the Perspective by Fiete and de Lozanne) used scanning tunneling microscopy to study the electronic states of this system. The autocorrelation function of the local density of states exhibited a power law (rather than an exponential) decay at Fermi energy. Thus, electron-electron interactions are indeed crucial for understanding dilute magnetic semiconductors. Scanning tunneling microscopy reveals the import role of electron-electron interactions in a dilute magnetic semiconductor. 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 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.