Sideways Tunnelling and Fractional Josephson Frequency in Double Layered Quantum Hall Systems*

The filling fraction 1/k double layered quantum Hall state has been shown to exhibit many superfluid properties including the appearance of an alternating tunnelling current in response to an external voltage V. Here we propose the notion of “sideways tunnelling”, in which a current tunnels between two such 1/k states through an incompressible fractional quantum Hall state of filling fraction 2/m. We predict an alternating tunnelling current or a narrow band noise at a frequency ω = eV h̄m , as a consequence of the tunnelling of e/m fractional charges. We also discuss singularities in the tunnelling current noise spectrum and the non-linear I-V curve. * Published in Europhys. Lett. 35, 227 (1996) In Ref. 1 we predicted within the semiclassical approximation and in the weak tunnelling limit, that a DC voltage V applied across a double-layered quantum Hall system2 in certain special states (to be characterized below) would produce a tunnelling current alternating with frequency ω = eV/h̄. While our effect is reminiscent of the Josephson effect3 there are some important differences. Here the frequency is half of the Josephson frequency: the charge carrier is not a pair of electrons as in a superconductor.4 We claimed that there is a superfluid lurking in certain states of double-layered quantum Hall systems. In this paper, we propose and discuss a novel notion of “sideways tunnelling” involving the juxtaposition of three double layered quantum Hall systems. We will neglect interlayer tunnelling5 in the main part of this paper. In the effective Chern-Simons gauge field theory6 description of quantum Hall fluids, a double layered system is described by