Magnetization and magnetic susceptibility in nanoscale vertically coupled semiconductor quantum rings

Yi-Ming Li*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


In this paper we computationally examine the magnetization and the magnetic susceptibility for vertically coupled quantum rings (VCQRs) under applied magnetic fields. The theoretical model of VCQRs considers a three-dimensional (3D) effective one-electronic-band Hamiltonian with the position- and energy-dependent effective mass, the finite hard-wall confinement potential, and the Ben Daniel-Duke boundary condition. The nonlinear iterative method is applied to solve the problem in the structure of VCQRs. For the structure formed with nanoscale disk-shaped InAs/GaAs quantum rings, the the tunable states of structure as well as the electron transition energy is dominated by the radius of ring (R) and the inter-distance (d) between quantum rings. The electron energy oscillates non-periodically among the lowest electron states as a function of external magnetic fields due to the penetration of magnetic fields into the inter-regions of VCQRs. The magnetization of VCQRs at zero temperature is non-periodical oscillation and the period of jump is governed by R. Therefore, the differential susceptibility of VCQRs has delta-like paramagnetic peaks. When d is increased, the peak is decreased which is contrary to conventional mesoscopic arguments. Our investigation is constructive for studying the magneto-optical phenomena of the nanoscale semiconductor artificial molecules.

Original languageEnglish
Pages (from-to)135-138
Number of pages4
JournalJournal of Computational Electronics
Issue number1-2
StatePublished - Apr 2005


  • Electron transition energy
  • Magnetic field effects
  • Magnetic susceptibility
  • Magnetization
  • Modeling and simulation
  • Semiconductor artificial molecules
  • Vertically coupled quantum rings

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