Drag conductance induced by neutral-mode localization in fractional quantum Hall junctions

A junction of two 2/3 fractional quantum Hall (FQH) edges, with no charge tunneling between them, may exhibit Anderson localization of neutral modes. Manifestations of such localization in transport properties of the junction are explored. There are two competing localization channels, ``neutral-mode superconductivity'' and ``neutral-mode backscattering.'' Localization in any of these channels leads to an effective theory of the junction that is characteristic for FQH effect of bosons, with a minimal integer excitation charge equal to 2, and with elementary quasiparticle charge equal to 2/3. These values can be measured by studying shot noise in tunneling experiments. Under the assumption of ballistic transport in the arms connecting the junction to contacts, the two-terminal conductance of the junction is found to be 4/3 for the former localization channel and 1/3 for the latter. The four-terminal conductance matrix reveals in this regime a strong quantized drag between the edges induced by neutral-mode localization. The two localization channels lead to opposite signs of the drag conductance, equal to $\ifmmode\pm\else\textpm\fi{}1/4$, which can also be interpreted as a special type of Andreev scattering. Coherent random tunneling in arms of the device (which are segments of 2/3 edges) leads to strong mesoscopic fluctuations of the conductance matrix. In the case of fully equilibrated arms, transport via the junction is insensitive to neutral-mode localization: The two-terminal conductance is quantized to 2/3 and the drag is absent.