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      Spectrum of a particle on a polyhedron enclosing a synthetic magnetic monopole

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      Author(s)
      Oktel, M. Ö.
      Date
      2012
      Source Title
      European Physical Journal D
      Print ISSN
      1434-6060
      Electronic ISSN
      1434-6079
      Publisher
      Springer
      Volume
      66
      Issue
      4
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      We consider a single particle hopping on a tight binding lattice formed by the vertices of a regular polyhedron and discuss the effect of a magnetic monopole enclosed in the polyhedron. The presence of the monopole induces phases on the hopping terms, given by Peierls substitution. By requiring the flux through each face of a regular polyhedron to be the same, Dirac's quantization condition is obtained in this discrete setting. For each regular polyhedron, we calculate the energy spectrum for an arbitrary value of the flux through a Dirac string coming in from one of the faces. We find that the energy levels are degenerate only when the flux through the Dirac string corresponds to a quantized monopole. We show that the degeneracies in the presence of the monopole can be classified using the double group of the symmetry of the polyhedron and label all energy levels with corresponding irreducible representations.
      Permalink
      http://hdl.handle.net/11693/21535
      Published Version (Please cite this version)
      http://dx.doi.org/10.1140/epjd/e2012-20484-y
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