The Icosahedral Quartet and SO(9) ↓ SO(4) Symmetry Breaking

Arnout Ceulemans
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Arnout Ceulemans: KU Leuven

Chapter Chapter 8 in The Theory of the Jahn-Teller Effect, 2022, pp 199-228 from Springer

Abstract: Abstract The fourfold degenerate orbital representation of the icosahedral group couples to a nine-dimensional boson space, which is invariant under the orthogonal group SO(9). In the equal coupling regime the Jahn-Teller surface develops a four-dimensional trough, exhibiting SO(4) symmetry. Vibronic coupling thus presents an intriguing case of SO(9) ↓ SO(4) symmetry breaking, analogous to the SO(5) ↓ SO(3) symmetry breaking for the triplet case. Based on this analogy an Ansatz is derived which incorporates the symmetry breaking. Quartet instabilities are identified in icosahedral fullerenes, Cn, with n = 20 + 60k.

Date: 2022
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DOI: 10.1007/978-3-031-09528-3_8

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