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

by P. Armagnat, A. Lacerda-Santos, B. Rossignol, C. Groth, X. Waintal

This Submission thread is now published as SciPost Phys. 7, 031 (2019)

Submission summary

As Contributors: Xavier Waintal
Arxiv Link: (pdf)
Date accepted: 2019-07-05
Date submitted: 2019-07-02 02:00
Submitted by: Waintal, Xavier
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approach: Computational


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.

Ontology / Topics

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Quantum Hall effect

Published as SciPost Phys. 7, 031 (2019)

Author comments upon resubmission

Dear Editor,

Please find the new version of our manuscript for resubmission.
The main modification we did was to add a section and a figure that
summarizes the flowchart of our manuscript.

Yours sincerely,
the authors

List of changes

- we now mention the self-consistent Hartree approximation as an equivalent name in the introduction. (referee 1 suggestion)

- We have replaced the word "including" by "even" in the abstract (referee 1 suggestion)

- We have added a new section 8 "Summary of the Algorithm" in response to our second report. This section contains a chart that explains how the different parts of the algorithm are articulated. (referee 2 suggestion)

- We have added a few more details on the parameters used in the simulations. (referee 2 suggestion)

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