Why a single-sheet graphene has optical phonon mode? 
My understanding for optical phonon mode is that it requires atomic configurations for two atomic basis with opposite charges so that it can respond to electric field. However, I don't think it is the case for a single sheet phonon which only has one type of atoms. 
 A: What matters to have optical phonon is to have at least 2 atoms per unit cell of the lattice. Whether both atoms are identical or not is not relevant.
In graphene, the honeycomb structure is quite misleading and all carbon atoms are not equivalent. The proper description of such a lattice is actually to consider a triangular lattice with a unit cell composed of two atoms (see below). Hence the existence of out of phase movements of the lattice, ie optical phonon.
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A: The literal meaning of "optical phonon" is the phonon mode that can couple to the photon (light). But this concept has evolved through the history. Nowadays, the definition of "optical phonon" in condensed matter physics is the phonon mode that involves relative displacement of the atoms within the unit cell. So as long as the unit cell contains more than one atom, there will be optical phonons.
Theoretically, even if the atoms are charge neutral, and even if the phonon mode does not couple to light, it is still called "optical" phonon as long as the atoms in the unit cell have relative motion. However in reality, even if the atoms are charge neutral since the nucleus and the electrons will not move together exactly, so any relative motion of the atoms in the unit cell will induce some local polarization (not restricted to dipolar polarization, can be quadripolar or higher order) that could still couple to light.
In the monolayer graphene, each unit cell contains two atoms and the optical phonon corresponds to the mode that the two atoms oscillate relative each other.
