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Coarse-grained tight-binding models
Journal article   Open access   Peer reviewed

Coarse-grained tight-binding models

Tian-Xiang Liu, Li Mao, Mats-Erik Pistol and Craig Pryor
Journal of physics. Condensed matter, Vol.34(12), p.125901
03/23/2022
DOI: 10.1088/1361-648X/ac443f
PMID: 34920442
url
https://doi.org/10.1088/1361-648X/ac443fView
Published (Version of record) Open Access

Abstract

Calculating the electronic structure of systems involving very different length scales presents a challenge. Empirical atomistic descriptions such as pseudopotentials or tight-binding models allow one to calculate the effects of atomic placements, but the computational burden increases rapidly with the size of the system, limiting the ability to treat weakly bound extended electronic states. Here we propose a new method to connect atomistic and quasi-continuous models, thus speeding up tight-binding calculations for large systems. We divide a structure into blocks consisting of several unit cells which we diagonalize individually. We then construct a tight-binding Hamiltonian for the full structure using a truncated basis for the blocks, ignoring states having large energy eigenvalues and retaining states with energies close to the band edge energies. A numerical test using a GaAs/AlAs quantum well shows the computation time can be decreased to less than 5% of the full calculation with errors of less than 1%. We give data for the trade-offs between computing time and loss of accuracy. We also tested calculations of the density of states for a GaAs/AlAs quantum well and find a ten times speedup without much loss in accuracy.
 tight-binding models coarse-grained semiconductors

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