Finite-frequency noise in a non-interacting quantum dot

TL;DR

This paper derives a comprehensive formula for non-symmetrized finite-frequency noise in a non-interacting quantum dot, analyzing its behavior across various parameters using Green's function formalism.

Contribution

It provides the first general analytical expression for NS-FF noise in a quantum dot, applicable at any temperature, frequency, and bias voltage, and confirms its consistency with scattering theory results.

Findings

Derived a general formula for NS-FF noise in quantum dots.

Validated the formula against scattering theory in the symmetrized case.

Numerically analyzed noise spectrum variations with temperature, energy level, and coupling.

Abstract

We calculate the non-symmetrized finite-frequency NS-FF noise for a single-level quantum dot connected to reservoirs in the spinless non-interacting case. The calculations are performed within the framework of the Keldysh Green's function formalism in the wide band approximation limit. We establish the general formula for NS-FF noise for any values of temperature, frequency and bias voltage. The electron transfer processes from one to the other reservoir act via the transmission amplitude and transmission coefficient depending on the energy. By taking the symmetrized version of this expression, we show that our result coincides with the expression of the finite frequency noise obtained by B\"uttiker using the scattering theory. We also give the explicit analytical expression for the NS-FF noise in the zero temperature limit. By performing numerical calculations, we finally discuss the evolution of the NS-FF noise spectrum when varying temperature, dot energy level, and coupling strength to the reservoirs, revealing a large variety of behaviors with different symmetry properties.