  The study of the interaction between superconductivity and charge ordering is
helpful to resolve the pairing mechanism in high-temperature superconductors.
Recently, several resistance oscillations studies trigger the speculation that
a long-range charge ordering, with an enormous mesh size of several tens of
nanometer, can possibly emerge in underdoped high Tc superconductor. However,
spectroscopy studies have not traced this kind of long-range charge ordering.
Here, we clarify the disagreement between the transport and spectroscopy
studies on the mysterious long-range charge ordering by investigating the
magneto-oscillations in underdoped Bi2Sr2CaCu2O8+{\delta} flakes. Inspired by
the observation that the oscillations evolve from a periodic to an aperiodic
one with decreasing doping level, we conclude that the magneto-oscillations can
be generated by the interaction between vortices and superconducting loops that
enclose randomly distributed underdoped puddles while an assumption of
long-range charge ordering is not necessary.
