engleski

Nonlinear response of strongly correlated materials to large electric fields

The electron-electron interaction in strongly correlated electron materials is so strong, that it is of primary importance in determining how the materials behave. These materials can be tuned to pass through a metal-insulator transition as a function of doping, pressure, or temperature, which makes them strong candidates for use in so-called ?smart materials? that can change their properties to respond to the particular needs of a device. We consider a model system described by the Falicov- Kimball Hamiltonian[1] in the presence of an external field that is spatially uniform but can be time dependent, and can have an arbitrary large amplitude. A number of different approaches is employed to numerically solve this problem, all based on a non- equilibrium generalization of dynamical mean field theory, which has been used for equilibrium many-body problems for the last 20 years. The generalization is based on a time-dependent approach and requires the discretization of the time axis[2]. Our solution is obtained by inverting over 20, 000 dense general complex matrices of size up to 2200×2200 for each iteration of the algorithm. We usually need between 15 and 30 iterations before the results have converged. The central issue is the accuracy of the data obtained for a given time-step and scaling to the zero-step-size limit. Employing a massively parallel algorithm we exactly solve for the response of these strongly correlated materials to the presence of a large electric field, including all nonlinear and non- equilibrium effects. Our algorithm breaks into two portions, one serial and one parallel. By carefully controlling the communications part of the code, we were able to achieve essentially linear scale up of the parallel part of the code, which produced good scaling behavior for up to 3000 processors, although most production runs employed about 1500 processors. We will briefly explain the formalism and the numerical algorithm, discuss the scalability of the data, and present the results for the current as a function of time for a variety of different systems, which represent the range of different behaviors near a Mott metal-insulator transition.

Imaging in Space and Time

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