The self-consistent quantum-electrostatic problem in strongly non-linear regime
Abstract
The self-consistent quantum-electrostatic (also known as Poisson-Schr\"odinger) problem is notoriously difficult in situations where the density of states varies rapidly with energy. At low temperatures, these fluctuations make the problem highly non-linear which renders iterative schemes deeply unstable. We present a stable algorithm that provides a solution to this problem with controlled accuracy. The technique is intrinsically convergent including in highly non-linear regimes. We illustrate our approach with (i) a calculation of the compressible and incompressible stripes in the integer quantum Hall regime and (ii) a calculation of the differential conductance of a quantum point contact geometry. Our technique provides a viable route for the predictive modeling of the transport properties of quantum nanoelectronics devices.
Cite
@article{arxiv.1905.01271,
title = {The self-consistent quantum-electrostatic problem in strongly non-linear regime},
author = {P. Armagnat and A. Lacerda-Santos and B. Rossignol and C. Groth and X. Waintal},
journal= {arXiv preprint arXiv:1905.01271},
year = {2019}
}
Comments
28 pages. 14 figures. Added solution to a potential failure mode of the algorithm