Quantum Wire Hybridized With a Single-Level Impurity

We have studied low-temperature properties of interacting electrons in a one-dimensional quantum wire (Luttinger liquid) side-hybridized with a single-level impurity. The hybridization induces a backscattering of electrons in the wire which strongly affects its low-energy properties. Using a one-loop renormalization group approach valid for a weak electron-electron interaction, we have calculated a transmission coefficient through the wire, $\mathcal{T}(\epsilon )$, and a local density of states, $\nu (\epsilon )$ at low energies $\epsilon$. In particular, we have found that the antiresonance in $\mathcal{T}(\epsilon )$ has a generalized Breit-Wigner shape with the effective width $\Gamma (\epsilon )$ which diverges at the Fermi level.

Figure 1

The lowest-order Fock-type corrections: (a) the LDOS of the conduction electrons and (b) the $d$-electron self-energy (the appropriate Hartree corrections are not shown). Diagram (a) with open ends would represent $\delta \widehat{G}(x,x^{\prime };\epsilon )$. Single and double lines correspond to the Green functions $\widehat{g}$ and ${\widehat{G}}_0$, crosses correspond to the tunneling amplitudes $t_0$, wavy lines correspond to the interaction.