Collapse of fractional quantum Hall states in double-quantum-well systems

We study the collective excitations of fractional quantum Hall states in double-quantum-well systems using a single mode approximation. Due to the symmetry in the system, the collective excitations of the intralevel and the interlevel modes are not coupled. When the separation between the double wells d becomes large, the excitation energy of the intralevel mode is decreased slightly due to the spreading of the single-electron wave function. On the other hand, the interlevel mode goes soft at a critical well separation ${\mathit{d}}_{\mathit{c}}$. This indicates that the fractional quantum Hall state becomes unstable, and the system should undergo a quantum phase transition to an additional ground state. Furthermore, our calculations show that the fractional quantum Hall states with ν=1/3, 1) / 5 and the integral quantum Hall state with ν=1 should be destroyed at about the same critical well separation.