Manifestation of Luttinger liquid effects in a hybrid metal-semiconductor double-quantum dot device

We theoretically study the transport properties of a hybrid nanodevice comprised of two large metallic islands incorporated in a two-dimensional electron gas. The high-tunability of the conducting channels electrically connecting two islands to each other and to the leads allows us to treat the setup as a realization of a multi-channel two-site charge Kondo (2SCK) model. It is shown that the leading temperature dependence of the conductance in the 2SCK circuit satisfies the conductance scaling of a single-impurity problem in a Luttinger liquid, whose interaction parameter is fully determined by the number of conducting channels in the device. We demonstrate that the finite weak backscattering in all conducting channels features the appearance of the sub-leading temperature dependencies in linear conductance. At the special critical point, we predict an equivalency between the 2SCK nanodevice and a single-site two-channel charge Kondo problem, where one Kondo channel is implemented by a non-interacting electron gas and the second Kondo channel is attributed to the Luttinger liquid.