Excitons in quantum wires

M. Combescot () and T. Guillet

The European Physical Journal B: Condensed Matter and Complex Systems, 2003, vol. 34, issue 1, 9-24

Abstract: This paper deals with excitons in quantum wires. We first study these excitons as the limit of excitons in D dimensions when $D \rightarrow 1$ . In order to do it, we have had to find a new resolution of the hydrogen atom Schrödinger equation: besides the fact that the usual resolution found in textbooks is not valid for D exactly equal to 1, it is, surprisingly enough, inconsistent since it relies on two hypergeometric functions which are not independent for the parameters of physical interest! In a second part, we write down the exact potential felt by the exciton relative motion along the wire in terms of the wire confinement. This allows a quite precise determination of the effective Coulomb potential for this 1D motion, which is of crucial importance to obtain a meaningfull finite value for the exciton ground state energy. In a last part, we study the dependence of the exciton energies on the wire area and anisotropy. While the quantitative results are here given for cylindrica l and rectangular wires with infinite barriers, we show how they can easily be extended to any particular wire shape and barrier height. Copyright Springer-Verlag Berlin/Heidelberg 2003

Date: 2003
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DOI: 10.1140/epjb/e2003-00191-6

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