  The opening of the pseudogap in underdoped cuprates breaks up the Fermi
surface, which may lead to a breakup of the d-wave order parameter into two
subband amplitudes and a low energy Leggett mode due to phase fluctuations
between them. This causes a large increase in the temperature range of
superconducting fluctuations with an overdamped Leggett mode. Almost resonant
scattering of inter-subband phonons to a state with a pair of Leggett modes
causes anomalously strong damping. In the ordered state, the Leggett mode
develops a finite energy, suppressing the anomalous phonon damping but leading
to an anomaly in the phonon dispersion.
