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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

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

Ali Yazdani

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199592593.003.0007

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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