AC conductance and non-symmetrized noise at finite frequency in quantum wires and carbon nanotubes

TL;DR

This paper investigates the AC conductance and finite-frequency non-symmetrized noise in interacting quantum wires and carbon nanotubes with impurities, revealing asymmetries and oscillations related to electron interactions and impurity position.

Contribution

It provides a detailed analysis of frequency-dependent conductance and noise, including the effects of impurities and interactions, with new insights into asymmetry and oscillatory behavior.

Findings

Asymmetry in non-symmetrized excess noise spectrum proportional to differential AC conductance.

Emission noise equals impurity partition noise at low temperatures.

Noise oscillations depend on impurity position and interaction parameter g.

Abstract

We calculate the AC conductance and the finite-frequency non-symmetrized noise in interacting quantum wires and single-wall carbon nanotubes in the presence of an impurity. We observe a strong asymmetry in the frequency spectrum of the non-symmetrized excess noise, even in the presence of the metallic leads. We find that this asymmetry is proportional to the differential excess AC conductance of the system, defined as the difference between the AC differential conductances at finite and zero voltage, and thus disappears for a linear system. In the quantum regime, for temperatures much smaller than the frequency and the applied voltage, we find that the emission noise is exactly equal to the impurity partition noise. For the case of a weak impurity we expand our results for the AC conductance and the noise perturbatively. In particular, if the impurity is located in the middle of the wire or at one of the contacts, our calculations show that the noise exhibits oscillations with respect to frequency, whose period is directly related to the value of the interaction parameter $g$.