Multifractal Behavior in Ga$_{1-x}$Mn$_{x}$As Close to the Metal-Insulator Transition

ORAL

Abstract

We have used a low temperature scanning tunneling microscope (STM) to study the metal-insulator transition in Ga$_{1-x}$Mn$_{x}$As. STM topographies reveal a variety of electronic modulations indicating the presence of a high level of disorder. Furthermore, spectroscopic mapping reveals that the local density of states (LDOS) near E$_{F}$ is strongly influenced by e-e correlations. Therefore, Ga$_{1-x}$Mn$_{x}$As provides an opportunity to examine critical behavior of electronic states close to the MIT in a correlated system. We have studied the probability distribution and the multifractal character of the spatial distribution of the LDOS. Near the MIT, LDOS shows a transition from a Gaussian to a lognormal distribution. The multifractal character which was studied by calculating the singularity spectrum shows a trend towards strong multifractality with decreasing Mn doping. Our work demonstrates the fractal nature of wavefunctions in a correlated system, and constitutes the first experimental results to map the critical behavior of states near this quantum phase transition

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Authors

  • Pedram Roushan

    Department of Physics, Princeton University, Princeton University

  • Anthony Richardella

    Department of Physics, Princeton University, and Department of Physics, Penn State University

  • S. Mack

    Department of Physics, UCSB, UCSB, Center for Spintronics and Quantum Computation, University of California, Santa Barbara, CA

  • Brian Zhou

    Department of Physics, Princeton University, Princeton University

  • David Huse

    Princeton University, Department of Physics, Princeton University

  • D.D. Awschalom

    Center for Spintronics and Quantum Computation, University of California, Santa Barbara CA 93106, Center for Spintronics and Quantum Computation, University of California, Santa Barbara, CA 93106, Department of Physics, UCSB, UCSB, Center for Spintronics and Quantum Computation, University of California, Santa Barbara, CA

  • Ali Yazdani

    Princeton University, Department of Physics, Princeton University