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Abstract
The transfermatrix methodology is used to solve linear systems of differential equations, such as those thatarise when solving Schr ̈odinger’s equation, in situations where the solutions of interest are in the continuouspart of the energy spectrum. The technique is actually a generalization in three dimensions of methods usedto obtain scattering solutions in one dimension. Using the layeraddition algorithm allows one to control thestability of the computation and to describe efficiently periodic repetitions of a basic unit. This paper, whichis an update of an article originally published in Physical and Chemical News 16, 4653 (2004), provides apedagogical presentation of this technique. It describes in details how the band structure associated with aninfinite periodic medium can be extracted from the transfer matrices that characterize a single basic unit.The method is applied to the calculation of the transmission and band structure of electrons subject to cosinepotentials in a cylindrical wire. The simulations show that bound states must be considered because of theirimpact as sharp resonances in the transmission probabilities and to remove unphysical discontinuities in theband structure. Additional states only improve the completeness of the representation
Original language  English 

Article number  1907.06940 
Number of pages  13 
Journal  ArXiv preprint 
Publication status  Published  16 Jul 2019 
Keywords
 electronic transport
 transfert matrix methodology
 S matrices
 band structure calculation
 bound states
 quantum wires
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 1 Active

CÉCI – Consortium of high performance computing centers
CHAMPAGNE, B., Lazzaroni, R., Geuzaine , C., Chatelain, P. & Knaepen, B.
1/01/18 → 31/12/22
Project: Research
Equipment

High Performance Computing Technology Platform
Benoît Champagne (Manager)
Technological Platform High Performance ComputingFacility/equipment: Technological Platform