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We study resonant tunneling through a periodic square array of quantum dotssandwiched between modulation-doped quantum wells. If a magnetic field isapplied parallel to the quantum dot plane, the tunneling current exhibits ahighly complex Aharonov-Bohm oscillation pattern due to the interference ofmultiple pathways traversed by a tunneling electron. Individual pathwaysassociated with conductance beats can be enumerated by sweeping the magneticfield at various tilt angles. Remarkably, Aharonov-Bohm oscillations areaperiodic unless the magnetic field slope relative to the quantum dot latticeaxes is a rational number.

Tracking electron pathways with magnetic field: Aperiodic Aharonov-Bohm oscillations in coherent transport through a periodic array of quantum dots