Quantum Criticality and the Non-linear I-V Curve of Two-channel Kondo-Luttinger System*

We theoretically study the quantum phase transition and non-linear I-V curve of a Kondo impurity in a Luttinger liquid wire. With decreasing Luttinger parameter K (or increasing electron interactions), it has been known since 1990s that the system undergoes a quantum phase transition from 1-channel (1CK) to 2-channel Kondo (2CK) ground states at K=1/2. However, the quantum critical properties near this transition is not known to date due to the lack of controlled theoretical tools to examine the physics near the strong coupling 2CK fixed point. Via bosonization-refermionization approach, we map the system near 1CK-2CK quantum critical point (QCP) and near the Toulouse limit onto an effective fermionic model in weak coupling regime subject to a bosoinc bath. The 1CK-2CK QCP is identified via renormalization group technique. The analytical form of the non-linear differential conductance and various critical exponents near this novel QCP are obtained. Our results are relevant for the recent experiment in a dissipative quantum dot via a double-barrier potential.