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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/30009

Title: Anderson localization triggered by spin disorder
Authors: Egli, Daniel
Keywords: Anderson Localization
spin disorder
random Schrödinger operator
zeeman interaction
Mott interaction
Issue Date: 23-Oct-2011
Series/Report no.: Analysis and Applied Math Seminar
Abstract: The phenomenon of Anderson localization is studied for a class of one-particle Schrödinger operators with random Zeeman interactions. These operators arise as follows: Static spins are placed randomly on the sites of a simple cubic lattice according to a site percolation process with density x and coupled to one another ferromagnetically. Scattering of an electron in a conduction band at these spins is described by a random Zeeman interaction term that originates from indirect exchange. It is shown rigorously that, for positive values of x below the percolation threshold, the spectrum of the one-electron Schrödinger operator near the band edges is dense pure-point, and the corresponding eigenfunctions are exponentially localized. Localization near the band edges persists in a weak external magnetic field, H, but disappears gradually, as H is increased. Our results lead us to predict the phenomenon of colossal (negative) magnetoresistance and the existence of a Mott transition, as H and/or x are increased. Our analysis is motivated directly by experimental results concerning the magnetic alloy 𝖤𝗎x𝖢𝖺1−x𝖡6.
Description: These are the lecture slides used by Daniel Egli, a postdoc in the Department of Mathematics at the University of Toronto, for a talk he delivered on 2011-10-21.
URI: http://hdl.handle.net/1807/30009
Appears in Collections:Department of Mathematics

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