Suppression of the Josephson effect by quantum fluctuations in the fractional quantum Hall state
Shechao Feng, Alex Levine, Lan Yin
DOI 10.1103/PhysRevB.50.11045 · Physical Review B
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Abstract
We use the Chern-Simons gauge theory for the fractional quantum Hall effect (FQHE) to calculate the Josephson current for two weakly coupled two-dimensional electron gas (2DEG) subsystems separated by a thin tunnel barrier, for the primary fractional quantum Hall states v=1/(2k+1) (k=0,1,2,...), at zero temperature. We find that the Josephson current amplitude is mainly suppressed by the long-range quantum fluctuations of the Chern-Simons gauge field, by a factor ∝exp{[-(2k+1)/4π](L/l0)} where L is the system size, and l0 is of the order of the magnetic length. Thus it is unlikely that the Josephson effect can be observed for weakly coupled 2DEG subsystems, despite the strong analogy between the FQHE in the Chern-Simons formulation and two-dimensional superconductivity.
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