Effective Hamiltonian for cooperative Jahn-Teller effect

EFFECTIVE HAMILTONIAN FOR COOPERATIVE JAHN-TELLER EFFECT 

For the sake of clarity we split the derivation in two parts. First the contribution from phonons is considered and then the effect of uniform strains is added. 

The potential energy of the Jahn-Teller crystal is described by the operator 

Thus the problem of finding extrema of the potential energy of Jahn-Teller crystal is reduced to the space of active local distortions only. Having found the equilibrium values of these distortions, q, we obtain the equilibrium values for all phonon modes  

The extrema equations (4) can be viewed as deriving from the following effective Hamiltonian  

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Effective Hamiltonian for cooperative Jahn-Teller effect 650... 

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