Magnetic flux commensurability in coupled quantum dots

We have studied the transition from isolated to coupled quantum dots in a lateral surface-superlattice structure in the presence of a perpendicular magnetic field. The coupling between the dots can be tuned by changing the bias of the grid gate. Our magnetocapacitance measurements reveal three distinct regimes: isolated quantum dots where collective effects are not observed, a tight-binding regime where the measurement results are sensitive to the rationality of flux quanta per unit cell, and a superlattice regime where commensurability effects between the magnetic orbits and the superlattice periodicity are observed.