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Jahn’s and Teller’s Last Case: The Spinor Sextet

In: The Theory of the Jahn-Teller Effect

Author

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  • Arnout Ceulemans

    (KU Leuven)

Abstract

The Jahn-Teller activity of the icosahedral sixfold degenerate Γ9 irrep is analyzed from the point of view of Lie group theory. The boson modes are identical to the quintet case and span the group SO(14). This symmetry is broken to the unitary symplectic group USp(6). Due to this symplectic symmetry the secular equation of the Hamiltonian matrix, which is of the sixth order, can be resolved into two equivalent cubic equations. The roots are determined in the equal coupling case. Recent examples of icosahedral clusters with encapsulated heavy metals, showing icosahedral spinor ground states are discussed. The final section reviews all cases considered in Part II, and demonstrates the common characteristics of all the symmetry breakings considered. The group-subgroup relation between the SO(N) group of the boson space and the SO(n) or Sp(2n) subgroup of the fermion space is shown to be of the embedding type.

Suggested Citation

  • Arnout Ceulemans, 2022. "Jahn’s and Teller’s Last Case: The Spinor Sextet," Springer Books, in: The Theory of the Jahn-Teller Effect, chapter 0, pages 253-273, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-09528-3_10
    DOI: 10.1007/978-3-031-09528-3_10
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