Electrons on the brink: Fractal patterns may be key to semiconductor magnetism (DMR 0819860)

IRG-D: A. Richardella, P. Roushan, S. Mack, B. Zhou, D. Huse, D. Awschalom, and A. Yazdani

Princeton-led team of scientists has observed electrons in a semiconductor on the brink of the metal-insulator transition for the first time. Caught in the act, the electrons formed complex patterns resembling those seen in turbulent fluids, confirming some long-held predictions and providing new insights into how semiconductors can be turned into magnets.The experiments were carried out on magnetically doped GaAs samples that are tuned to be metallic and magnetic by addition (doping) of Mn. Using specialized scanning tunneling microscope (STM), the team was able to map the electronic wavefunction in these samples as function of concentration of Mn. In samples, with the least amount of Mn, in close proximity to the metal-insulator transition, the STM maps of electronic states show clear non-homogenous patterns. While random looking, the patterns have features such as log-normal distribution of their intensity and contain features that resemble fractal objects. Both fractal wavefunction and log-normal distributions has been predicted in the vicinity of a metal-insulator transition. These results suggest that development of magnetism in semiconductor would have to be non-uniform give such spatial structure of electronic states induced by doping.

On the brink of the metal-insulator transition, the electrons in a manganese-doped gallium arsenide semiconductor are distributed across the surface of the material in complex, fractal-like patterns. These shapes are visible in this electron map, where the colors red, orange and yellow indicate areas on the surface of the semiconductor where electrons are most likely to be found at a given point in time. In this image, the fractal-like probability map of electrons is superimposed on the atomic crystal structure of the material, imaged at the same time.

Reference: A. Richardella, P. Roushan, S. Mack, B. Zhou, D. Huse, D. Awschalom, A. Yazdani” Visualizing spatial correlations for electronic states near the metal-insulator transition GaMnAs,” Science 327 665 (2010).