k·p theory for phosphorene: Effective g-factors, Landau levels, and excitons

Paulo E. Faria Junior, Marcin Kurpas, Martin Gmitra, and Jaroslav Fabian
Phys. Rev. B 100, 115203 – Published 18 September 2019
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Abstract

Phosphorene, a single layer of black phosphorus, is a direct band gap two-dimensional semiconductor with promising charge and spin transport properties. The electronic band structure of phosphorene is strongly affected by the structural anisotropy of the underlying crystal lattice. We describe the relevant conduction and valence bands close to the Γ-point by four- and six-band (with spin) k·p models, including the previously overlooked interband spin-orbit coupling which is essential for studying anisotropic crystals. All the k·p parameters are obtained by a robust fit to ab initio data, by taking into account the nominal band structure and the k-dependence of the effective mass close to the Γ-point. The inclusion of interband spin-orbit coupling allows us to determine dipole transitions along both armchair and zigzag directions. The interband coupling is also key to determine the effective g-factors and Zeeman splittings of the Landau levels. We predict the electron and hole g-factor correction of 0.03 due to the intrinsic contributions in phosphorene, which lies within the existing range of experimental data. Furthermore, we investigate excitonic effects using the k·p models and find exciton binding energy (0.81 eV) and exciton diameters consistent with experiments and ab initio based calculations. The proposed k·p Hamiltonians should be useful for investigating magnetic, spin, transport, and optical properties and many-body effects in phosphorene.

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  • Received 23 April 2019
  • Revised 26 June 2019

DOI:https://doi.org/10.1103/PhysRevB.100.115203

©2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Paulo E. Faria Junior1,*, Marcin Kurpas2, Martin Gmitra3, and Jaroslav Fabian1

  • 1Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany
  • 2Institute of Physics, University of Silesia, 75 Pułku Piechoty 1, 41-500 Chorzów, Poland
  • 3Institute of Physics, P. J. Šafárik University in Košice, Park Angelinum 9, 04001 Košice, Slovakia

  • *fariajunior.pe@gmail.com

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Issue

Vol. 100, Iss. 11 — 15 September 2019

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