  We explore pump-probe high harmonic generation (HHG) from monolayer
hexagonal-Boron-Nitride, where a terahertz pump excites coherent optical
phonons that are subsequently probed by an intense infrared pulse that drives
HHG. We find, through state-of-the-art ab-initio calculations, that the
structure of the emission spectrum is attenuated by the presence of coherent
phonons, and is no longer comprised of discrete harmonic orders, but rather of
a continuous emission in the plateau region. The HHG yield strongly oscillates
as a function of the pump-probe delay, corresponding to ultrafast changes in
the lattice such as bond compression or stretching. We further show that in the
regime where the excited phonon period and the pulse duration are of the same
order of magnitude, the HHG process becomes sensitive to the
carrier-envelope-phase (CEP) of the driving field, even though the pulse
duration is so long that no such sensitivity is observed in the absence of
coherent phonons. The degree of CEP sensitivity vs. pump-probe delay is shown
to be a highly selective measure for instantaneous structural changes in the
lattice, providing a new approach for ultrafast multi-dimensional
HHG-spectroscopy. Remarkably, the obtained temporal resolution for phonon
dynamics is ~1 femtosecond, which is much shorter than the probe pulse duration
because of the inherent sub-cycle contrast mechanism. Our work paves the way
towards novel routes of probing phonons and ultrafast material structural
changes and provides a mechanism for controlling the high harmonic response.
