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Article Dans Une Revue SciPost Physics Année : 2019

The self-consistent quantum-electrostatic problem in strongly non-linear regime

Résumé

The self-consistent quantum-electrostatic (also known as Poisson-Schrödinger) 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 even in highly non-linear regimes. We illustrate our approach with both a calculation of the compressible and incompressible stripes in the integer quantum Hall regime as well as 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.

Dates et versions

hal-03942026 , version 1 (16-01-2023)

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Citer

Pacome Armagnat, A. Lacerda-Santos, Benoit Rossignol, Christoph Groth, Xavier Waintal. The self-consistent quantum-electrostatic problem in strongly non-linear regime. SciPost Physics, 2019, 7 (3), pp.031. ⟨10.21468/SciPostPhys.7.3.031⟩. ⟨hal-03942026⟩
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