Emission Noise in an Interacting Quantum Dot: Role of Inelastic Scattering and Asymmetric Coupling to the Reservoirs

Abstract

A theory is developed for the emission noise at frequency $\nu$ in a quantum dot in the presence of Coulomb interactions and asymmetric couplings to the reservoirs. We give an analytical expression for the noise in terms of the various transmission amplitudes. Including inelastic scattering contribution, it can be seen as the analog of the Meir-Wingreen formula for the current. A physical interpretation is given on the basis of the transmission of one electron-hole pair to the concerned reservoir where it emits an energy after recombination. We then treat the interactions by solving the self-consistent equations of motion for the Green functions. The results for the noise derivative versus $eV$ show a zero value until $eV = h\nu$, followed by a Kondo peak in the Kondo regime, in good agreement with recent measurements in carbon nanotube quantum dots.