One-channel conductor coupled to a quantum of resistance: exact ac conductance and finite-frequency noise

TL;DR

This paper derives exact formulas for finite-frequency conductance and noise in a strongly correlated one-channel conductor coupled to a quantum resistance, revealing novel relations and behaviors in the quantum regime.

Contribution

It provides the first exact computation of finite-frequency conductance and noise for a strongly interacting system modeled as a Tomonaga-Luttinger liquid with impurity, extending previous scattering approaches.

Findings

Finite-frequency conductance obeys an exact relation with dc current.

Emission excess noise vanishes above eV in the quantum regime.

Results are valid for all temperatures, voltages, and frequencies below the RC frequency.

Abstract

We consider a one-channel coherent conductor with a good transmission embedded into an ohmic environment whose impedance is equal to the quantum of resistance R_q=h/e^2 below the RC frequency. This choice is motivated by the mapping of this problem to a Tomonaga-Luttinger liquid with one impurity whose interaction parameter corresponds to the specific value K=1/2, allowing for a refermionization procedure. The "new" fermions have an energy-dependent transmission amplitude which incorporates the strong correlation effects and yields the exact dc current and zero-frequency noise through expressions similar to those of the scattering approach. We recall and discuss these results for our present purpose. Then we compute, for the first time, the finite-frequency differential conductance and the finite-frequency non-symmetrized noise. Contrary to intuitive expectation, both cannot be expressed within the scattering approach for the new fermions, even though they are still determined by the transmission amplitude. Even more, the finite-frequency conductance obeys an exact relation in terms of the dc current which is similar to that derived perturbatively with respect to weak tunneling within the Tien-Gordon theory, and extended recently to arbitrary strongly interacting systems coupled eventually to an environment or/and with a fractional charge. We also show that the emission excess noise vanishes exactly above eV, even though the underlying Tomonaga-Luttinger liquid model corresponds to a many-body correlated system. Our results apply for all ranges of temperature, voltages and frequencies below the RC frequency, and they allow to explore fully the quantum regime.