Non Equilibrium Electronic Transport in Multilayered Nanostructures
Recent advances in strongly correlated materials have produced systems with novel and interesting properties like high Tc superconductors, Mott insulators and others. These novel properties have sparked an interest in industry as well as in academia as new devices are being developed. One such kind of device that can be fabricated is a heterostructure, in which layers of different compounds are stacked in a single direction. Modern deposition techniques like electron beam epitaxy, in which atomic layers of different materials are deposited one at a time creating the device, are capable of fabricating heterostructures with atomic precision. We propose a technique to study heterostructures composed of strongly correlated materials out of equilibrium. By using the Keldysh Green's function formalism in the dynamical mean field theory (DMFT) framework the properties of a multilayered device are analyzed. The system is composed of infinite dimensional 2D lattices, stacked in the z direction. The first and last planes are then connected to a bulk reservoir, and several metallic planes are used to connect the bulk reservoir to the barrier region. The barrier region is the system of interest, also known as the device. The device is composed of a number of planes where the system correlations have been turned on. The correlations are then model by using the Falicov-Kimball Hamiltonian. The device is then connected to the bulk once again from the opposite side using metallic planes creating a symmetric system. In order to study the non equilibrium properties of the device a linear vector potential A(t) = A0 + tE is turned on a long time in the past for a unit of time and then turned off. This in turn will create a current in the bulk, in effect current biasing the device, as opposed to a voltage bias in which opposite sides of the device are held to a different potential. In this document we will explain the importance of the subject, we will derive and develop the algorithm and we will discuss results and challenges obtained from performing the numerical calculations.
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