  Motivated by the emerging experiments [e.g. \textit{Z. Nie et al. Nat.
Photon. \textbf{12}, 489 (2018)}] on producing infrared (IR) single cycle
pulses in the spectral region 5 - 14 $\mu m$, we theoretically investigate
their role for controlling high-order harmonic generation (HHG) process induced
by an intense near-infrared (NIR) multi-cycle pulse ($\lambda$ = 1.27 $\mu m$).
The scenario is demonstrated for a prototype of the hydrogen atom by numerical
simulations of the time-dependent Schr\"odinger equation. In particular, we
show that the combined pulses allow one to generate even-order harmonics and
most importantly to produce high-energy plateaus and that the harmonic cutoff
is extended by a factor of 3 compared to the case with the NIR pulse alone. The
emerged high-energy plateaus is understood as a result of a vast momentum
transfer from the single-cycle field to the ionized electrons while travelling
in the NIR field, and thus leading to high-momentum electron recollisions. We
also identify the role of the IR single-cycle field for controlling the
directionality of the emitted electrons via the IR-field induced electron
displacement effect. We further show that the emerged plateaus can be
controlled by varying the relative carrier-envelope phase between the two
pulses as well as their wavelengths. Thus, our findings open up new
perspectives for time-resolved electron diffraction using an IR single-cycle
field-assisted high-harmonic spectroscopy.
