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

Abstract

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 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.

arXiv comment28 pages. 14 figures. Added solution to a potential failure mode of the algorithm

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• Reconstructing the potential configuration in a high-mobility semiconductor heterostructure with scanning gate microscopy
• BinPo: An open-source code to compute the band structure of two-dimensional electron systems
• Semiconductor-based electron flying qubits: Review on recent progress accelerated by numerical modelling
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• Orbital-free approach for large-scale electrostatic simulations of quantum nanoelectronics devices
• Distributed Current Injection into a One-Dimensional Ballistic Edge Channel
• Conductance matrix symmetries of multiterminal semiconductor-superconductor devices
• Electrostatics in semiconducting devices I : The Pure Electrostatics Self Consistent Approximation