Existence of a Sharp Anderson Transition in Disordered Two-Dimensional Systems
We derive the quantum-mechanical energy-dependent diffusivity directly from the Kubo-Greenwood formula for electrical conductivity. The resulting expression suggests a numerical method for the solution of the Schrodinger equation without the introduction of sample boundaries. Instead, we simply analyze the diffusion of a particle outwards from an initial bulk site. This method is applied to calculate the conductivity of a two-dimensional system in the presence of various degrees of time-independent disorder. In the case of the Anderson model for non-interacting electrons, we find a sharp transition from localized to diffusive behavior, contrary to the predictions of scaling theory.
Photographs of the energy-resolved electronic probability waveform during its evolution in time indicate a phenomenon similar to classical percolation, but with the distinct quantum feature of a minimum metallic conductivity, as predicted by Mott. An explanation of the numerical results is based on first principles and utilizes only the essential physical ingredients of the problem: disorder diffusion, and quantum-mechanical probability amplitude.
KeywordsDiffusive Behavior Anderson Model Schrodinger Equation Band Center Anderson Localization
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