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Journal of Physics A Mathematical and General

Berry's geometric quantum phase and the T1⊗ (εg⊕ τ2g) Jahn-Teller effect

C. C. Chancey, Mary Claire O’Brien

Published Aug 21, 1988• 21 citations
Publisher

Abstract

The ground-state wavefunctions of the linear octahedral Jahn-Teller system T 1 ⊗(ε g ⊕ τ 2g ) are shown to exhibit a Berry phase for certain closed circuits in phonon coordinate space. This is shown to result from the coupling between the electronic and phonon parts of the system and from the requirement that the total wavefunction be single-valued. The associated Berry vector potential is also calculated and is interpreted in terms of a flux line.

DOI
10.1088/0305-4470/21/16/011

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The ground-state wavefunctions of the linear octahedral Jahn-Teller system T 1 ⊗(ε g ⊕ τ 2g ) are shown to exhibit a Berry phase for certain closed circuits in phonon coordinate space. This is shown to result from the coupling between the electronic and phonon parts of the system and from the requirement that the total wavefunction be single-valued. The associated Berry vector potential is also calculated and is interpreted in terms of a flux line.
A proof is given for the Jahn-Teller problem of an orbital doublet (E\ensuremath{\bigotimes}\ensuremath{\epsilon}) that the order of the lowest vibronic levels is fixed by the requirement that the vibrational part of the wave function change sign under 2\ensuremath{\pi} rotation in the vibrational coordinates. This sign change in turn is a consequence of the sign change in the electronic part of the wave function, a special case of Berry's geometrical phase. Experimental confirmation of this sign change and thus of Berry's phase is available from studies of Jahn-Teller defects in crystals that reveal the sequence of these lowest levels.
The octahedral Jahn-Teller system T 1 ⊗(ε g ⊕tau 2g ) is studied using generalised Glauber states which are eigenstates of the system in the strong-coupling limit. It is shown that these states become, when limited to a total angular momentum of one, eigenstates in the weak-coupling limit. The lower-branch zero-phonon state is studied using these states and expressions as functions of coupling strength are obtained for the energy and Ham reduction factors. The results compare well with the available numerical calculations.
The octahedral Jahn-Teller system E ⊗ is studied using generalised Glauber states which are strong-coupling eigenstates of the system. It is shown that these Glauber states become, under certain conditions, equivalent to the weak-coupling eigenstates obtainable from standard perturbation theory. Eigenstates are thus obtained for the system which can be applied using perturbative procedures over the complete range of coupling strengths. Expressions which are functions of the coupling strength are obtained for the energies, the ground state Ham factor p and the A to E absorption intensities. The results compare well with the available numerical calculations.