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

Date
2012
Authors
Oktel, M. Ö.
Advisor
Instructor
Source Title
European Physical Journal D
Print ISSN
1434-6060
Electronic ISSN
1434-6079
Publisher
Springer
Volume
66
Issue
4
Pages
Language
English
Type
Article
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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.

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Published Version (Please cite this version)