Landau levels, edge states, and gauge choice in 2D quantum dots
| Autor: | Asadullah Bhuiyan, Frank Marsiglio |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | American Journal of Physics. 88:986-1005 |
| ISSN: | 1943-2909 0002-9505 |
| DOI: | 10.1119/10.0001703 |
| Popis: | We examine the behavior of a charged particle in a two dimensional quantum dot in the presence of a magnetic field. Emphasis is placed on the high magnetic field regime. Compared to free space geometry, confinement in a dot geometry provides a more realistic system where edge effects arise naturally. It also serves to remove the otherwise infinite degeneracy due to the magnetic field; nonetheless, as described in this paper, additional ingredients are required to produce sensible results. We treat both circular and square geometries, and in the latter, we explicitly demonstrate the gauge invariance of the energy levels and wave function amplitudes. The characteristics of bulk states closely resemble those of free space states. For edge states, with sufficiently high quantum numbers, we achieve significant differences in the square and circular geometries. Both circular and square geometries are shown to exhibit level crossing phenomena, similar to parabolic dots, where the confining potential is a parabolic trap. Confinement effects on the probability current are also analyzed; it is the edge states that contribute non-zero current to the system. The results are achieved using straightforward matrix mechanics, in a manner that is accessible to novices in the field. On a more pedagogical note, we also provide a thorough review of the theory of single electron Landau levels in free space and illustrate how the introduction of surfaces naturally leads to a more physically transparent description of a charged particle in a magnetic field. |
| Databáze: | OpenAIRE |
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