Phase relaxation in the vicinity of the dynamic instability: anomalous temperature dependence of zero-phonon line

We study optical spectra of impurity centers in crystals in the case when in one or in both electronic states of the optical center the local elastic springs are strongly reduced, causing appearance of the pseudolocal mode of a very low or even imaginary frequency. In these cases, the optical transition takes place to the vicinity of a flat minimum or a flat potential barrier in the configurational coordinate space, where the density of states of low-frequency phonons is strongly enhanced. One example of systems of this type is the trigonal center with strong Jahn–Teller effect in the two-fold degenerate E-state, when the adiabatic surface has a shape of the so-called squeezed Mexican hat. We have found that in this case the usual T7-dependence of the homogeneous width of the zero-phonon line (ZPL) at low temperatures is replaced by a dependence close to the T3-one. Besides, the usual T4-dependent red shift of the line is replaced by the T2-dependent shift. Depending on the flatness of the adiabatic surface, the shift may be to the red or to the blue. The theory is applied to the ZPL 637 nm of the nitrogen-containing N−V center in diamond.