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.
Cited by 1
Pacome Armagnat et al., Reconciling edge states with compressible stripes in a ballistic mesoscopic conductor
J. Phys. Mater. 3, 02LT01 (2020) [Crossref]
Ontology / TopicsSee full Ontology or Topics database.
Authors / Affiliation: mappings to Contributors and OrganizationsSee all Organizations.
- 1 Pacome Armagnat,
- 1 A. Lacerda-Santos,
- 1 Benoit Rossignol,
- 1 Christoph Groth,
- 1 Xavier Waintal