SUPPRESSION OF THE JOSEPHSON EFFECT BY QUANTUM FLUCTUATIONS IN THE FRACTIONAL QUANTUM HALL STATE

We use the Chern-Simons gauge theory for the fractional quantum Hall e ffect (FQHE) to calculate the Josephson current for two weakly coupled two-dimensional electron gas (2DEG) subsystems separated by a thin tu nnel barrier, for the primary fractional. quantum Hall states v = 1/(2 k + 1) (k = 0,1,2,...), at zero temperature. We find that the Josephso n current amplitude is mainly suppressed by the long-range quantum flu ctuations of the Chern-Simons gauge field, by a factor proportional to exp(- 2k + 1/4 pi L/l(o)), where L is the system size, and l(o) is of the order of the magnetic length. Thus it is unlikely that the Joseph son effect can be observed for weakly coupled 2DEG subsystems, despite the strong analogy between the FQHE in the Chern-Simons formulation a nd two-dimensional superconductivity.