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Conductor-Insulator Quantum Phase Transitions$
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Vladimir Dobrosavljevic, Nandini Trivedi, and James M. Valles, Jr.

Print publication date: 2012

Print ISBN-13: 9780199592593

Published to Oxford Scholarship Online: September 2012

DOI: 10.1093/acprof:oso/9780199592593.001.0001

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Visualizing Critical Correlations Near the Metal–Insulator Transition in Ga1−x Mn x As

Visualizing Critical Correlations Near the Metal–Insulator Transition in Ga1−x Mn x As

(p.244) 7 Visualizing Critical Correlations Near the Metal–Insulator Transition in Ga1−xMnxAs
Conductor-Insulator Quantum Phase Transitions

Ali Yazdani

Oxford University Press

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

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