  The dynamics of a doped hole in the orthogonal-dimer spin system is
investigated systematically in one, two and three dimensions. By combining the
bond-operator method with the self-consistent
  Born approximation, we argue that a dispersive quasi-particle state in the
dimer phase is well defined even for quasi-two-dimensional systems. On the
other hand, a doped hole in the plaquette-singlet phase hardly itinerates,
forming an almost localized mode. We further clarify that although the
quasi-particle weight in the dimer phase is decreased in the presence of the
interchain coupling, it is not suppressed but even enhanced upon the
introduction of the interlayer coupling.
