# Effective theory approach to the Schrödinger-Poisson problem in semiconductor Majorana devices

@article{Woods2018EffectiveTA, title={Effective theory approach to the Schr{\"o}dinger-Poisson problem in semiconductor Majorana devices}, author={Benjamin D. Woods and Tudor D Stanescu and Sankar Das Sarma}, journal={Physical Review B}, year={2018} }

We propose a method for solving to the Schrodinger-Poisson problem that can be efficiently implemented in realistic 3D tight-binding models of semiconductor-based Majorana devices. The method is based on two key ideas: i) For a given geometry, the Poisson problem is only solved once (for each local orbital) and the results are stored as an interaction tensor; using this Green's function scheme, the Poisson component of the iteration procedure is reduced to a few simple summations. ii) The 3D…

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