Low-field quantum Hall transport in an electron Fabry-Perot interferometer: Dependence of constriction filling on front-gate voltage

We report systematic quantum Hall transport experiments on Fabry-Perot electron interferometers at ultralow temperatures. The GaAs/AlGaAs heterostructure devices consist of two constrictions defined by etch trenches in the two-dimensional electron layer, enclosing an approximately circular island. Front gates deposited in etch trenches allow one to change the constriction filling, relative to the bulk. A systematic variation of the front-gate voltage affects the constriction and the island electron density, while the bulk density remains unaffected. This results in quantized plateaus in longitudinal resistance, while the Hall resistance is dominated by the low-density, low-filling constriction. At lower fields, when the quantum Hall plateaus fail to develop, we observe bulk Shubnikov-de Haas oscillations in series corresponding to an integer filling of the magnetoelectric subbands in the constrictions. This shows that the whole interferometer region is still quantum coherent at these lower fields at 10 mK. Analyzing the data within a Fock-Darwin model, we obtain the constriction electron density as a function of the front-gate bias and, extrapolating to the zero field, the number of electric subbands (conductance channels) resulting from the electron confinement in the constrictions.