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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

Submission summary

As Contributors: Xavier Waintal
Arxiv Link: https://arxiv.org/abs/1905.01271v2
Date accepted: 2019-07-05
Date submitted: 2019-07-02
Submitted by: Waintal, Xavier
Submitted to: SciPost Physics
Domain(s): Computational
Subject area: Condensed Matter Physics - Computational

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.

Current status:
Publication decision taken: accept

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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