The ground state of two-dimensional electrons in a nonuniform magnetic field

  • A. M. Dyugaev
  • P. D. Grigoriev
Atoms, Molecules, Optics


An exact solution to the Schrödinger equation for the ground state of two-dimensional Pauli electrons in a nonuniform transverse magnetic field H is presented for two cases. In the first case, the field H depends on a single variable, H = H(y), while in the second case, the field is axially symmetric, H = H(ρ), ρ2=x2+y2. The electron density distributions n = n(y) and n = n(ρ) that correspond to a completely filled lower level are found. For quasiuniform fields of fixed sign, the functions n(y) and n(ρ) are locally related to the magnetic field: n(y) = H(y)/ϕ0 and n(ρ) = H(ρ)/ϕ0, where ϕ0 = hc/|e| is a magnetic flux quantum. Magnetic fields are considered that are periodic, singular, and bounded in the plane xy. Finite electron objects in a nonuniform magnetic field are analyzed.

PACS numbers

73.20.-r 73.20.At 75.70.-i 


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Copyright information

© Pleiades Publishing, Inc. 2006

Authors and Affiliations

  • A. M. Dyugaev
    • 1
    • 2
  • P. D. Grigoriev
    • 1
  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow oblastRussia
  2. 2.Max-Planck-Institute for the Physics of Complex SystemsDresdenGermany

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