  Ultrafast electronic dynamics in solids lies at the core of modern condensed
matter and materials physics. To build up a practical ab initio method for
studying solids under photoexcitation, we develop a momentum-resolved real-time
time dependent density functional theory (rt-TDDFT)algorithm using numerical
atomic basis, together with the implementation of both the length and vector
gauge of the electromagnetic field. When applied to simulate elementary
excitations in two-dimensional materials such as graphene, different excitation
modes, only distinguishable in momentum space, are observed. The
momentum-resolved rt-TDDFT is important and computationally efficient for the
study of ultrafast dynamics in extended systems.
