  We study resonant tunneling through a periodic square array of quantum dots
sandwiched between modulation-doped quantum wells. If a magnetic field is
applied parallel to the quantum dot plane, the tunneling current exhibits a
highly complex Aharonov-Bohm oscillation pattern due to the interference of
multiple pathways traversed by a tunneling electron. Individual pathways
associated with conductance beats can be enumerated by sweeping the magnetic
field at various tilt angles. Remarkably, Aharonov-Bohm oscillations are
aperiodic unless the magnetic field slope relative to the quantum dot lattice
axes is a rational number.
