Submergence of the sidebands in the photon-assisted tunneling through a quantum dot weakly coupled to Luttinger liquid leads

We study theoretically the photon-assisted tunneling through a quantum dot weakly coupled to Luttinger liquid (LL) leads. The linear dc conductance is found to be strongly modified by the interactions in the leads. In comparison with the system with Fermi-liquid (FL) leads, the sideband peaks become blurring for $\frac{1}{2}<g<\mathrm{}1,$ and finally merge into the central peak for $g<\mathrm{}\frac{1}{2}$ $(g$ is the interaction parameter in the LL leads). The sidebands are suppressed for LL leads with strong enough Coulomb interactions, and the conductance always appears as a single peak for any strength and frequency of the external time-dependent field. Furthermore, the quenching effect of the central peak for the FL case does not exist for $g<\mathrm{}\frac{1}{2}.$