Conductance of a Dissipative Quantum Dot: Nonequilibrium Crossover Near a Non-Fermi-Liquid Quantum Critical Point

TL;DR

This paper investigates the nonlinear conductance of a dissipative quantum dot near its quantum critical point, revealing a crossover from non-Fermi-liquid to Fermi-liquid behavior driven by bias or temperature, with results matching experiments.

Contribution

It provides a detailed analysis of the nonequilibrium crossover in a dissipative quantum dot using boundary sine-Gordon and Bethe ansatz methods, including special mappings and analytical results.

Findings

Crossover properties described by boundary sine-Gordon model.

Non-equilibrium crossover sharper than temperature-driven crossover.

Excellent agreement with experimental bias and temperature data.

Abstract

We find the nonlinear conductance of a dissipative resonant level in the nonequilibrium steady state near its quantum critical point. The system consists of a spin-polarized quantum dot connected to two resistive leads that provide ohmic dissipation. We focus on the crossover from the strong-coupling, non-Fermi-liquid regime to the weak-coupling, Fermi-liquid ground state, a crossover driven by the instability of the quantum critical point to hybridization asymmetry or detuning of the level in the dot. We show that the crossover properties are given by tunneling through an effective single barrier described by the boundary sine-Gordon model. The nonlinear conductance is then obtained from thermodynamic Bethe ansatz results in the literature, which were developed to treat tunneling in a Luttinger liquid. The current-voltage characteristics are thus found for any value of the resistance of the leads. For the special case of lead resistance equal to the quantum resistance, we find mappings onto, first, the two-channel Kondo model and, second, an effectively noninteracting model from which the nonlinear conductance is found analytically. A key feature of the general crossover function is that the nonequilibrium crossover driven by applied bias is different from the crossover driven by temperature -- we find that the nonequilibrium crossover is substantially sharper. Finally, we compare to experimental results for both the bias and temperature crossovers: the agreement is excellent.