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Experimental evidence for a transient enhancement of the superconductingcritical temperature in presence of an intense THz or IR pump pulse wasascribed to nonlinear phononics effects. Here I introduce a simplephenomenological Ginzburg-Landau model of this phenomenon, to explore furtherconsequences and possible experimental tests of this interpretation. Uponcooling below Tc in the absence ofTHz pumping, both an abrupt softening of aRaman-active mode frequency and a spontaneous lattice distortion, growinglinearly with (Tc - T), are predicted to occur. Numerical estimates forYBa2Cu3O6+x indicate that the frequency softening should be easily observable,whereas the lattice distortion may be too small. Comparison with Ramanexperiments for YBa2Cu3O6+x is far from conclusive; however very large (up to18 %) phonon frequency softening below Tc, with behaviour strikingly similar tothe predictions of the present model, was observed over 20 years ago inHgBa2Ca3Cu4O10+x; its explanation has been controversial. Light inducedsuperconductivity was never investigated in this material and it may be ofinterest to explore if it is present and connected, via the mechanism discussedhere, to the observed anomalous phonon behaviour.

A possible experimental test of the nonlinear phononics interpretation of light-induced superconductivity