Aharonov-Bohm electron interferometer in the integer quantum Hall regime

Abstract

We report experiments on a quantum electron interferometer fabricated from high mobility, low density $\mathrm{Al}\mathrm{Ga}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ heterostructure material. In this device, a nearly circular electron island is defined by four front gates deposited in etched trenches. The island is separated from the two-dimensional (2D) electron bulk by two nearly open constrictions. In the quantum Hall regime, two counterpropagating edge channels are coupled by tunneling in the constrictions, thus forming a closed electron interference path. For several fixed front gate voltages, we observe periodic Aharonov-Bohm interference oscillations in four-terminal resistance as a function of the enclosed flux. The oscillation period $\ensuremath{\Delta}B$ gives the area of the interference path $S$ via the quantization condition $S=h∕e\ensuremath{\Delta}B$. We experimentally determine the dependence of $S$ on the front gate voltage, and find that the Aharonov-Bohm quantization condition does not require significant corrections due to the confining potential. These results can be interpreted as a constant integrated compressibility of the island with respect to the front gates. We also analyze experimental results using two classical electrostatics models: one modeling the 2D electron density due to depletion from an etch trench, and another modeling the gate voltage dependence of the electron density profile in the island.