Low-field quantum Hall transport in an electron Fabry-Perot   interferometer: Determination of constriction filling vs front-gate voltage
  We report systematic quantum Hall transport experiments on Fabry-Perot electron interferometers at ultra-low-temperatures. The GaAs/AlGaAs heterostructure devices consist of two constrictions defined by etch trenches in 2D electron layer, enclosing an approximately circular island. Front gates deposited in etch trenches allow to fine-tune the device for symmetry and to change the constriction filling, relative to the bulk. The low-field longitudinal and Hall magnetotransport shows Shubnikov-de Haas oscillations and integer quantum Hall plateaus. A systematic variation of 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 indicates 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. 
Ping V. Lin, F. E. Camino*, and V. J. Goldman