Mesoscopically confined 2D holes with strong correlation*

We present a transport study on the mesoscopic confinement effects on a strongly interacting two-dimensional holes (2DH) in a GaAs quantum well with low density (~2×10¹⁰/cm²) and high mobility. By applying a voltage to a split-gate, the 2DH underneath the gate is depleted, leaving a narrow (~2 μm wide) channel conducting. The channel formation is reflected in the evolution of the temperature (T)-dependent resistance at various gate voltages V_g as well as the V_g dependent resistance. Interestingly, when the mesoscopic channel starts to form, a strong magneto-resistance peak with an insulating-like T dependence was observed before the ν =1 quantum Hall (QH) state. When the channel is further depleted, the magnetic field induces a rapidly increasing magneto-resistance and a 'metal-to-insulator' transition appears at a moderate magnetic field (~ 0.2 T) where the sample resistivity ρ_xx << h/e² along with the destruction of the ν =1 QH state. Our results suggest that mesoscopically constricted dilute 2D systems can be a rich playground for exploring interaction effects and phase transitions in 2D.