  The magnetic field generated Hofstadter butterfly in single-twist trilayer
graphene (TLG) is investigated using circularly polarized light (CPL) and
longitudinal light emanating from a waveguide. We show that single-twist TLG
has two distinct chiral limits in the equilibrium state, and the central branch
of the butterfly splits into two precisely degenerate components. The
Hofstadter butterfly appears to be more discernible. We also discovered that
CPL causes a large gap opening at the central branch of the Hofstadter
butterfly energy spectrum and between the Landau levels, with a clear asymmetry
corresponding to energy $E = 0$. We point out that for right-handed CPL, the
central band shifts downward, in stark contrast to left-handed CPL, where the
central band shifts upward. Finally, we investigated the effect of
longitudinally polarized light, which originates from a waveguide.
Interestingly, we observed that the chiral symmetries of the Hofstadter
butterfly energy spectrum are broken for small driving strengths and get
restored at large ones, contrary to what was observed in twisted bilayer
graphene.
