Volume 125, Number 2, January 2019
|Number of page(s)||7|
|Section||Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties|
|Published online||25 February 2019|
Why the effective-mass approximation works so well for nano-structures
Física Teórica y Materia Condensada, UAM-Azcapotzalco - Av. S. Pablo 180, C.P. 02200, México D. F., México
Received: 14 September 2018
Accepted: 21 January 2019
The reason why the effective-mass approximation, derived using wave functions of infinite periodic systems, works so well with nanoscopic structures, has been an enigma and a challenge for theorists. To explain this issue, we first show that the essential “only-one-band” and “band-edge” assumptions that are behind the standard derivation of the effective mass approximation are better justified for nano-structures. We show then that the effective-mass approximation can also be derived using, instead of Bloch-type wave functions, the eigenfunctions and eigenvalues obtained in the theory of finite periodic systems, where the finiteness of the number of primitive cells in nanoscopic layers is a prerequisite and a crucial condition. We also show, with specific calculations of the optical response, that the rapidly varying eigenfunctions of the one-band wave functions , can be safely dropped out for the calculation of inter-band transition matrix elements.
PACS: 73.21.-b – Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems / 73.21.Ac – Multilayers / 73.21.Cd – Superlattices
© EPLA, 2019
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