  Experimental evidence for a transient enhancement of the superconducting
critical temperature in presence of an intense THz or IR 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. Upon
cooling below Tc in the absence ofTHz pumping, both an abrupt softening of a
Raman-active mode frequency and a spontaneous lattice distortion, growing
linearly with (Tc - T), are predicted to occur. Numerical estimates for
YBa2Cu3O6+x indicate that the frequency softening should be easily observable,
whereas the lattice distortion may be too small. Comparison with Raman
experiments for YBa2Cu3O6+x is far from conclusive; however very large (up to
18 %) phonon frequency softening below Tc, with behaviour strikingly similar to
the predictions of the present model, was observed over 20 years ago in
HgBa2Ca3Cu4O10+x; its explanation has been controversial. Light induced
superconductivity was never investigated in this material and it may be of
interest to explore if it is present and connected, via the mechanism discussed
here, to the observed anomalous phonon behaviour.
