We investigate the
effect of thermal fluctuations on the atomic
and electronic structure of a twisted MoSe2/WSe2heterobilayer using a combination of classical molecular dynamics
andab initiodensity functional theory calculations.
Our calculations reveal that thermally excited phason modes give rise
to an almost rigid motion of the moiré lattice. Electrons and
holes in low-energy states are localized in specific stacking regions
of the moiré unit cell and follow the thermal motion of these
regions. In other words, charge carriers surf phason waves that are
excited at finite temperatures. We also show that such surfing survives
in the presence of a substrate and frozen potential. This effect has
potential implications for the design of charge and exciton transport
devices based on moiré materials.