Journal
JOURNAL OF PHYSICS-CONDENSED MATTER
Volume 35, Issue 47, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1361-648X/acef8a
Keywords
effective-mass; self-consistent approach; finite-volume; one-dimensional electron gas; electron-electron interactions
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In this article, a novel self-consistent approach based on finite-volume discretization is developed to simulate the one-dimensional electron gas at ultra-low temperatures. The approach shows excellent self-consistent convergence and allows for considering electron-electron interactions.
Achieving self-consistent convergence with the conventional effective-mass approach at ultra-low temperatures (below 4.2 K) is a challenging task, which mostly lies in the discontinuities in material properties (e.g. effective-mass, electron affinity, dielectric constant). In this article, we develop a novel self-consistent approach based on cell-centered finite-volume discretization of the Sturm-Liouville form of the effective-mass Schrodinger equation and generalized Poisson's equation (FV-SP). We apply this approach to simulate the one-dimensional electron gas formed at the Si-SiO2 interface via a top gate. We find excellent self-consistent convergence from high to extremely low (as low as 50 mK) temperatures. We further examine the solidity of FV-SP method by changing external variables such as the electrochemical potential and the accumulative top gate voltage. Our approach allows for counting electron-electron interactions. Our results demonstrate that FV-SP approach is a powerful tool to solve effective-mass Hamiltonians.
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