The ground state of two-dimensional electrons in a nonuniform magnetic field |
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Authors: | A M Dyugaev P D Grigoriev |
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Institution: | (1) Landau Institute for Theoretical Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432, Russia;(2) Max-Planck-Institute for the Physics of Complex Systems, Dresden, D-01187, Germany |
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Abstract: | 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=x 2+y 2. 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)/?0 and n(ρ) = H(ρ)/?0, where ?0 = 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. |
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