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Thursday, February 19th 2015

1:25 pm:

Hamiltonians describing particles moving in a random potential often have eigenstates which have finite spatial extend, a well-known phenomenon called Anderson localization. Above two dimensional space, localized wave functions all correspond to energies below a critical energy usually called the mobility edge. The size of the localized wave functions diverges as mobility edge is approached, a phenomenon called Anderson transition. It is generally believed that the details of Anderson transition depend on the dimensionality of space only, which is usually referred to as universality of the Anderson transition. We argue that in sufficiently high dimensions a second type of Anderson transition develops if the disorder strength is close to some critical value, distinct from the conventional transition, with a number of unusual features. For a conventional Schrodinger equation with a random potential one has to be above four dimensional space to see this new transition, thus it is not straightforward, although not impossible, to observe it. In electronic systems with a Dirac-like spectrum, one only has to be above two dimensions to observe this transition. We discuss the consequences of the existence of this transition for disordered materials with Dirac-like electronic spectra.

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