Spin dependent electron transport through a magnetic resonant tunneling   diode
  Electron transport properties in nanostructures can be modeled, for example, by using the semiclassical Wigner formalism or the quantum mechanical Green's functions formalism. We compare the performance and the results of these methods in the case of magnetic resonant-tunneling diodes. We have implemented the two methods within the self-consistent spin-density-functional theory. Our numerical implementation of the Wigner formalism is based on the finite-difference scheme whereas for the Green's function formalism the finite-element method is used. As a specific application, we consider the device studied by Slobodskyy et all. [Phys. Rev. Lett. 90, 246601 (2003)] and analyze their experimental results. The Wigner and Green's functions formalisms give similar electron densities and potentials but, surprisingly, the former method requires much more computer resources in order to obtain numerically accurate results for currents. Both of the formalisms can successfully be used to model magnetic resonant tunneling diode structures. 
Paula Havu, Noora Tuomisto, Riikka Vaananen, Martti J. Puska and Risto   M. Nieminen