Fig. 1.

Operation of the dual-gate device. a The dual-gate device is formed by applying a Au electrode on top of the eight unit-cell epitaxial LaAlO₃ layer and a Ag electrode from the back of the SrTiO₃ substrate with 0.5 mm thickness. The channel width is 400 μm with Hall bars patterned by predeposited AlO_x hard mask. b, c Schematic diagram of the dual-gate operation for top- and back-gates, respectively. The thin lines represent the electron envelope wavefunction perpendicular to the interface at different gate voltages colour-matched to the thick solid lines, which represent the corresponding confinement potential. d, e Top- and back-gate modulation of carrier density (circles) and Hall mobility (squares) at T = 600 mK. The straight solid black lines are linear fits to the circles. The red and blue curves are estimates of mobility based on the measured sheet resistivity and fitted extrapolation of Hall density. The ranges of the solid lines correspond to the experimentally accessible tuning ranges