Quantum interference in two independently tunable parallel point contacts

We have fabricated two independently tunable quantum point contacts in a parallel configuration, by wet etching a 2000-Å-diameter hole in the center of the constriction of a split-gate device in an ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs heterojunction. The number of occupied subbands in the point contact on either side of the etched hole can be tuned independently by biasing the gate, with each channel exhibiting conductance steps in units of 2${\mathit{e}}^2$/h, independent of the other. In the quantum Hall regime, nearly periodic resistance fluctuations are observed when both gate biases are fixed and the magnetic field B is swept. Further, periodic resistance fluctuations are observed when B and the bias on one gate is fixed, while the bias on the second gate is swept. In both cases, fluctuations are due to tunneling between the opposite edge channels via magnetically bound states encircling the etched hole, whose energies are quantized such that each encloses an integral number of flux quanta. Tunneling occurs when an allowed bound-state energy coincides with the chemical potential, and when the edge channel occupations of the two quantum point contacts are nearly equal, as discussed in a simple model.