Chapter

Visualizing Critical Correlations Near the Metal–Insulator Transition in Ga<sub>1−<i>x</i></sub>Mn<sub><i>x</i></sub>As

Ali Yazdani

in Conductor-Insulator Quantum Phase Transitions

Published in print June 2012 | ISBN: 9780199592593
Published online September 2012 | e-ISBN: 9780191741050 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199592593.003.0007
Visualizing Critical Correlations Near the Metal–Insulator Transition in Ga1−xMnxAs

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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.

Keywords: metal-insulator transition; localized state; multifractals; critical wavefunctions; magnetic semiconductors

Chapter.  3937 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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