  Brownian dynamics of Dirac fermions in twisted bilayer graphene is
investigated within the framework of semiclassical relativistic Langevin
equations. We find that under the influence of orthogonal, commensurate ac
drives in the periodic ratchet potential of a substrate, the charge carriers in
the system exhibit pronounced random dynamics, tuned by the twist angle, making
twisted bilayer graphene distinguishable from monolayer graphene. It is shown
that as threshold twist angle matches the optimal angle, deterministic running
states appear in the limit of weak thermal noise where the diffusion rate is
enhanced significantly compared to bare thermal diffusion. Analysis of the real
space trajectories and diffusion coefficient illustrates the significant role
of thermal noise in the random motion of Dirac fermions. In addition, we find
that the Brownian particle shows remarkable ratchet effect as a net current.
