Graphene Phonon Dispersion

Graphene's 2-atom hexagonal unit cell produces 6 phonon branches: 3 acoustic (LA, TA, ZA) and 3 optical (LO, TO, ZO). Linear acoustic branches near K give the high sound velocity ~2×10⁴ m/s.

Force Constants

LA speed (near Γ)
—
Optical gap at Γ
—
Dirac point (K)
LA=TA linear
6 branches from 2 atoms:
LA: longitudinal acoustic
TA: transverse acoustic
ZA: flexural acoustic (quadratic!)
LO/TO/ZO: optical branches

Graphene: only 2D crystal with
quadratic ZA branch (Mermin-Wagner).