| Summary: | Experimental evidence for a transient enhancement of the superconducting critical temperature of YBa_{2}Cu_{3}O_{6+x} in the presence of an intense THz or infrared pump pulse was ascribed to nonlinear phononics effects. Here, I introduce a simple phenomenological Ginzburg-Landau model of this phenomenon, to explore further consequences and possible experimental tests of this interpretation. This treatment predicts that, upon cooling below T_{c} in the absence of pumping, (a) an abrupt softening of a Raman-active mode frequency and (b) a spontaneous lattice distortion, growing linearly with (T_{c}−T) should occur. Numerical estimates for YBa_{2}Cu_{3}O_{6+x} indicate that the frequency softening could likely be observable, whereas the lattice distortion may be too small. A comparison with Raman experiments for the relevant phonon modes in YBa_{2}Cu_{3}O_{6+x} does not lend support to the nonlinear phononics interpretation. On the other hand, however, a very large (up to 18%) phonon frequency softening just below T_{c}, qualitatively similar to the predictions of the present model for its size and abrupt temperature dependence, was observed over 20 years ago in HgBa_{2}Ca_{3}Cu_{4}O_{10+x}; its explanation in terms of Josephson plasmons has been controversial. Light-induced superconductivity still needs to be investigated in this material and it may be of interest to explore if it is present and possibly connected, via the mechanism discussed here, to the observed anomalous phonon behavior.
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