核四极矩可看成是Jahn-Teller(JTE)效应的结果，也可看成是“薛定锷蛋”和薛定锷波的对偶性产生的。A-15型超导化合物中有能带JTE，有人说高温超导体(HTSC)中也有JTE，这说明似乎可以用统一的眼光看待这些不同的现象。From the modern point of view, after the discovery of HTSC the BCS theory may be considered as approximately correct in narrow limits of its application, but not sufficiently accurate beyond these limits. The inaccuracy is due to the neglect of the JTE, meaning ignoring the details of the electron-phonon interaction, in particular, the nonadiabatic influence of the electronic states on the lattice structure and low-symmetry phonons and the back influence of the modified lattice and phonons on the electronic states. The band JTE, as in all the other cases of the JTE, is essentially dependent on the magnitude of the JT electron-phonon coupling constant. For metals with broad bands and almost completely delocalized electronic states the JT electron-phonon coupling constant is small and the JTE implications can be ignored. This explains the success of the BCS for broad-band metals and low temperatures. Moving to crystals with narrower bands and more localized electronic states, we come to stronger JT electron-phonon coupling with implication of the JTE, which involves essentially low-symmetry phonons.
The narrower the conduction band (up to a certain limit), the stronger the electron-phonon coupling, leading to a stronger JTE. For narrower bands the JT coupling constants and the JTE again become small; narrow bands limits also the mobility of the carriers. This window in conduction bandwidth that facilitates the band JTE may be expected to be most important in HTSC. A direct exploration of this issue, has not been performed.