Density of states of a strongly correlated quantum dot coupled to Luttinger liquid leads

We theoretically investigate the density of states (DOS) of a quantum dot weakly coupled to Luttinger liquid (LL) leads in the Kondo regime by use of the equation-of-motion technique of the nonequilibrium Green functions. At zero temperature, the Kondo peak in DOS is suppressed by the intralead interaction. When the LL interaction parameter K   is about 0.77, a moderately strong interaction, the Kondo peak disappears and then a dip develops, a signature of the intermediate two-channel Kondo (2CK) physics. This shows that the condition for the 2CK to occur ever addressed is not necessary. Applying a finite voltage bias splits the dip in the DOS. Each split dip is located at the chemical potential of a LL lead. This again appears the stabilized 2CK physics for moderately strong interaction K<1$K<1$.