Tunneling between Two Quantum Hall Droplets

We report on tunneling experiment between two quantum Hall droplets separated by a nearly ideal tunnel barrier. The device is produced by cleaved edge overgrowth that laterally juxtaposes two two-dimensional electron systems across a high quality semiconductor barrier. The dramatic evolution of the tunneling characteristics is consistent with the magnetic field-dependent tunneling between the coupled edge states of the quantum Hall droplets. We identify a series of quantum critical points between successive strong and weak tunneling regimes that are reminiscent of the plateau-transitions in quantum Hall effect. Scaling analysis shows that the conductance near the critical magnetic fields $B_{c}$ is a function of a single scaling argument $|B-B_{c}|T^{-\kappa}$, where the exponent $\kappa = 0.42$. This puzzling resemblance to a quantum Hall-insulator transition points to the significance of interedge correlation in the lateral tunneling of quantum Hall droplets.