Optical and Quantum Electronics

, Volume 44, Issue 3–5, pp 183–188 | Cite as

A flexible, plane-wave based multiband \({\mathbf{k}\cdot\mathbf{p}}\) model

  • Oliver MarquardtEmail author
  • Stefan Schulz
  • Christoph Freysoldt
  • Sixten Boeck
  • Tilmann Hickel
  • Eoin P. O’Reilly
  • Jörg Neugebauer


In this work, we present a highly generalized implementation of multiband \({\mathbf{k}\cdot\mathbf{p}}\) models. We have achieved a high efficiency of our approach by incorporating it in a plane-wave framework within the Density Functional Theory package S/PHI/nX. To demonstrate the flexibility and applicability of our code, we have chosen two example studies that are directly accessible with the standard eight-band \({\mathbf{k}\cdot\mathbf{p}}\) model. By employing a 14-band \({\mathbf{k}\cdot\mathbf{p}}\) model for the description of pyramidal InAs/GaAs quantum dots (QDs), we show that this model is able to accomodate for the correct symmetry of the underlying zincblende lattice, which is not reflected in the standard eight-band model. Our second example provides a description of site-controlled (111)-oriented InGaAs/GaAs QDs. The extremely small aspect ratio of these QDs makes a description using conventional \({\mathbf{k}\cdot\mathbf{p}}\) Hamiltonians computationally highly expensive. We have therefore rotated the standard eight-band Hamiltonian, to suit the description of these systems. The studies of electronic properties of the above mentioned model systems demonstrate the efficiency and flexibility of our approach.


Nanostructures Electronic properties Multiband \({\mathbf{k}\cdot\mathbf{p}}\) formalism 


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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  • Oliver Marquardt
    • 1
    Email author
  • Stefan Schulz
    • 1
  • Christoph Freysoldt
    • 2
  • Sixten Boeck
    • 3
  • Tilmann Hickel
    • 2
  • Eoin P. O’Reilly
    • 1
  • Jörg Neugebauer
    • 2
  1. 1.Tyndall National InstituteLee Maltings, CorkIreland
  2. 2.Max-Planck-Institut für EisenforschungDüsseldorfGermany
  3. 3.Gemmantics IT-Consulting UGErkrathGermany

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