Quantum Hall droplet laterally coupled to a quantum ring

We study a two-dimensional cylindrically-symmetric electron droplet separated from a surrounding electron ring by a tunable barrier using the exact diagonalization method. The magnetic field is assumed strong so that the electrons become spin-polarized and reside on the lowest Fock-Darwin band. We calculate the ground state phase diagram for 6 electrons. At weak coupling, the phase diagram exhibits a clear diamond structure due to the blockade caused by the angular momentum difference between the two systems. We find separate excitations of the droplet and the ring as well as the transfer of charge between the two parts of the system. At strong coupling, interactions destroy the coherent structure of the phase diagram, while individual phases are still heavily affected by the potential barrier.