  We numerically study the interaction of a terahertz pulse with monolayer
graphene. We observe that the electron momentum density is affected by the
carrier-envelope phase (CEP) of the single- to few-cycle terahertz laser pulse
that induces the electron dynamics. In particular, we see strong asymmetric
electron momentum distributions for non-zero values of the CEP. We explain the
origin of the asymmetry within the adiabatic-impulse model by finding
conditions to reach minimal adiabatic gap between the valence band and the
conduction band. We discuss how these conditions and the interference pattern,
emanating from successive non-adiabatic transitions at this minimal gap, affect
the electron momentum density and how they are modified by the CEP. This opens
the door to control fundamental time-dependent electron dynamics in the
tunneling regime in Dirac materials. Also, this control suggests a way to
measure the CEP of a terahertz laser pulse when it interacts with condensed
matter systems.
